From 9be1fde89d373a1317646ecfeefb8aa16e77ade5 Mon Sep 17 00:00:00 2001 From: Alex Sharp Date: Sun, 20 Jun 2021 10:39:05 +0100 Subject: [PATCH] Initial commit --- LICENSE | 50 +- curve.go | 329 + dummy.go | 20 + ext.h | 130 + libsecp256k1/.gitignore | 51 + libsecp256k1/.travis.yml | 108 + libsecp256k1/COPYING | 19 + libsecp256k1/Makefile.am | 154 + libsecp256k1/README.md | 104 + libsecp256k1/SECURITY.md | 15 + libsecp256k1/TODO | 3 + libsecp256k1/autogen.sh | 3 + .../build-aux/m4/ax_prog_cc_for_build.m4 | 125 + libsecp256k1/build-aux/m4/bitcoin_secp.m4 | 71 + libsecp256k1/configure.ac | 566 ++ libsecp256k1/contrib/dummy.go | 7 + libsecp256k1/contrib/lax_der_parsing.c | 150 + libsecp256k1/contrib/lax_der_parsing.h | 91 + .../contrib/lax_der_privatekey_parsing.c | 113 + .../contrib/lax_der_privatekey_parsing.h | 90 + libsecp256k1/contrib/travis.sh | 65 + libsecp256k1/dummy.go | 7 + libsecp256k1/include/dummy.go | 7 + libsecp256k1/include/secp256k1.h | 764 +++ libsecp256k1/include/secp256k1_ecdh.h | 62 + libsecp256k1/include/secp256k1_preallocated.h | 128 + libsecp256k1/include/secp256k1_recovery.h | 110 + libsecp256k1/libsecp256k1.pc.in | 13 + libsecp256k1/obj/.gitignore | 0 libsecp256k1/sage/group_prover.sage | 322 + libsecp256k1/sage/secp256k1.sage | 306 + libsecp256k1/sage/weierstrass_prover.sage | 264 + libsecp256k1/src/asm/field_10x26_arm.s | 913 +++ libsecp256k1/src/basic-config.h | 38 + libsecp256k1/src/bench.h | 133 + libsecp256k1/src/bench_ecdh.c | 59 + libsecp256k1/src/bench_ecmult.c | 214 + libsecp256k1/src/bench_internal.c | 381 ++ libsecp256k1/src/bench_recover.c | 62 + libsecp256k1/src/bench_sign.c | 58 + libsecp256k1/src/bench_verify.c | 115 + libsecp256k1/src/dummy.go | 7 + libsecp256k1/src/ecdsa.h | 21 + libsecp256k1/src/ecdsa_impl.h | 315 + libsecp256k1/src/eckey.h | 25 + libsecp256k1/src/eckey_impl.h | 96 + libsecp256k1/src/ecmult.h | 48 + libsecp256k1/src/ecmult_const.h | 20 + libsecp256k1/src/ecmult_const_impl.h | 264 + libsecp256k1/src/ecmult_gen.h | 50 + libsecp256k1/src/ecmult_gen_impl.h | 208 + libsecp256k1/src/ecmult_impl.h | 1216 ++++ libsecp256k1/src/field.h | 134 + libsecp256k1/src/field_10x26.h | 50 + libsecp256k1/src/field_10x26_impl.h | 1165 ++++ libsecp256k1/src/field_5x52.h | 49 + libsecp256k1/src/field_5x52_asm_impl.h | 502 ++ libsecp256k1/src/field_5x52_impl.h | 499 ++ libsecp256k1/src/field_5x52_int128_impl.h | 279 + libsecp256k1/src/field_impl.h | 320 + libsecp256k1/src/gen_context.c | 87 + libsecp256k1/src/group.h | 141 + libsecp256k1/src/group_impl.h | 708 +++ libsecp256k1/src/hash.h | 41 + libsecp256k1/src/hash_impl.h | 283 + libsecp256k1/src/modules/dummy.go | 7 + .../src/modules/ecdh/Makefile.am.include | 8 + libsecp256k1/src/modules/ecdh/dummy.go | 7 + libsecp256k1/src/modules/ecdh/main_impl.h | 71 + libsecp256k1/src/modules/ecdh/tests_impl.h | 132 + .../src/modules/recovery/Makefile.am.include | 8 + libsecp256k1/src/modules/recovery/dummy.go | 7 + libsecp256k1/src/modules/recovery/main_impl.h | 193 + .../src/modules/recovery/tests_impl.h | 393 ++ libsecp256k1/src/num.h | 74 + libsecp256k1/src/num_gmp.h | 20 + libsecp256k1/src/num_gmp_impl.h | 288 + libsecp256k1/src/num_impl.h | 24 + libsecp256k1/src/scalar.h | 117 + libsecp256k1/src/scalar_4x64.h | 19 + libsecp256k1/src/scalar_4x64_impl.h | 959 +++ libsecp256k1/src/scalar_8x32.h | 19 + libsecp256k1/src/scalar_8x32_impl.h | 735 +++ libsecp256k1/src/scalar_impl.h | 342 ++ libsecp256k1/src/scalar_low.h | 17 + libsecp256k1/src/scalar_low_impl.h | 124 + libsecp256k1/src/scratch.h | 42 + libsecp256k1/src/scratch_impl.h | 88 + libsecp256k1/src/secp256k1.c | 726 +++ libsecp256k1/src/testrand.h | 38 + libsecp256k1/src/testrand_impl.h | 110 + libsecp256k1/src/tests.c | 5453 +++++++++++++++++ libsecp256k1/src/tests_exhaustive.c | 511 ++ libsecp256k1/src/util.h | 178 + libsecp256k1/src/valgrind_ctime_test.c | 100 + panic_cb.go | 21 + secp256.go | 222 + secp256_test.go | 238 + 98 files changed, 24015 insertions(+), 24 deletions(-) create mode 100644 curve.go create mode 100644 dummy.go create mode 100644 ext.h create mode 100644 libsecp256k1/.gitignore create mode 100644 libsecp256k1/.travis.yml create mode 100644 libsecp256k1/COPYING create mode 100644 libsecp256k1/Makefile.am create mode 100644 libsecp256k1/README.md create mode 100644 libsecp256k1/SECURITY.md create mode 100644 libsecp256k1/TODO create mode 100755 libsecp256k1/autogen.sh create mode 100644 libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4 create mode 100644 libsecp256k1/build-aux/m4/bitcoin_secp.m4 create mode 100644 libsecp256k1/configure.ac create mode 100644 libsecp256k1/contrib/dummy.go create mode 100644 libsecp256k1/contrib/lax_der_parsing.c create mode 100644 libsecp256k1/contrib/lax_der_parsing.h create mode 100644 libsecp256k1/contrib/lax_der_privatekey_parsing.c create mode 100644 libsecp256k1/contrib/lax_der_privatekey_parsing.h create mode 100755 libsecp256k1/contrib/travis.sh create mode 100644 libsecp256k1/dummy.go create mode 100644 libsecp256k1/include/dummy.go create mode 100644 libsecp256k1/include/secp256k1.h create mode 100644 libsecp256k1/include/secp256k1_ecdh.h create mode 100644 libsecp256k1/include/secp256k1_preallocated.h create mode 100644 libsecp256k1/include/secp256k1_recovery.h create mode 100644 libsecp256k1/libsecp256k1.pc.in create mode 100644 libsecp256k1/obj/.gitignore create mode 100644 libsecp256k1/sage/group_prover.sage create mode 100644 libsecp256k1/sage/secp256k1.sage create mode 100644 libsecp256k1/sage/weierstrass_prover.sage create mode 100644 libsecp256k1/src/asm/field_10x26_arm.s create mode 100644 libsecp256k1/src/basic-config.h create mode 100644 libsecp256k1/src/bench.h create mode 100644 libsecp256k1/src/bench_ecdh.c create mode 100644 libsecp256k1/src/bench_ecmult.c create mode 100644 libsecp256k1/src/bench_internal.c create mode 100644 libsecp256k1/src/bench_recover.c create mode 100644 libsecp256k1/src/bench_sign.c create mode 100644 libsecp256k1/src/bench_verify.c create mode 100644 libsecp256k1/src/dummy.go create mode 100644 libsecp256k1/src/ecdsa.h create mode 100644 libsecp256k1/src/ecdsa_impl.h create mode 100644 libsecp256k1/src/eckey.h create mode 100644 libsecp256k1/src/eckey_impl.h create mode 100644 libsecp256k1/src/ecmult.h create mode 100644 libsecp256k1/src/ecmult_const.h create mode 100644 libsecp256k1/src/ecmult_const_impl.h create mode 100644 libsecp256k1/src/ecmult_gen.h create mode 100644 libsecp256k1/src/ecmult_gen_impl.h create mode 100644 libsecp256k1/src/ecmult_impl.h create mode 100644 libsecp256k1/src/field.h create mode 100644 libsecp256k1/src/field_10x26.h create mode 100644 libsecp256k1/src/field_10x26_impl.h create mode 100644 libsecp256k1/src/field_5x52.h create mode 100644 libsecp256k1/src/field_5x52_asm_impl.h create mode 100644 libsecp256k1/src/field_5x52_impl.h create mode 100644 libsecp256k1/src/field_5x52_int128_impl.h create mode 100644 libsecp256k1/src/field_impl.h create mode 100644 libsecp256k1/src/gen_context.c create mode 100644 libsecp256k1/src/group.h create mode 100644 libsecp256k1/src/group_impl.h create mode 100644 libsecp256k1/src/hash.h create mode 100644 libsecp256k1/src/hash_impl.h create mode 100644 libsecp256k1/src/modules/dummy.go create mode 100644 libsecp256k1/src/modules/ecdh/Makefile.am.include create mode 100644 libsecp256k1/src/modules/ecdh/dummy.go create mode 100644 libsecp256k1/src/modules/ecdh/main_impl.h create mode 100644 libsecp256k1/src/modules/ecdh/tests_impl.h create mode 100644 libsecp256k1/src/modules/recovery/Makefile.am.include create mode 100644 libsecp256k1/src/modules/recovery/dummy.go create mode 100644 libsecp256k1/src/modules/recovery/main_impl.h create mode 100644 libsecp256k1/src/modules/recovery/tests_impl.h create mode 100644 libsecp256k1/src/num.h create mode 100644 libsecp256k1/src/num_gmp.h create mode 100644 libsecp256k1/src/num_gmp_impl.h create mode 100644 libsecp256k1/src/num_impl.h create mode 100644 libsecp256k1/src/scalar.h create mode 100644 libsecp256k1/src/scalar_4x64.h create mode 100644 libsecp256k1/src/scalar_4x64_impl.h create mode 100644 libsecp256k1/src/scalar_8x32.h create mode 100644 libsecp256k1/src/scalar_8x32_impl.h create mode 100644 libsecp256k1/src/scalar_impl.h create mode 100644 libsecp256k1/src/scalar_low.h create mode 100644 libsecp256k1/src/scalar_low_impl.h create mode 100644 libsecp256k1/src/scratch.h create mode 100644 libsecp256k1/src/scratch_impl.h create mode 100644 libsecp256k1/src/secp256k1.c create mode 100644 libsecp256k1/src/testrand.h create mode 100644 libsecp256k1/src/testrand_impl.h create mode 100644 libsecp256k1/src/tests.c create mode 100644 libsecp256k1/src/tests_exhaustive.c create mode 100644 libsecp256k1/src/util.h create mode 100644 libsecp256k1/src/valgrind_ctime_test.c create mode 100644 panic_cb.go create mode 100644 secp256.go create mode 100644 secp256_test.go diff --git a/LICENSE b/LICENSE index 80d0256..f9090e1 100644 --- a/LICENSE +++ b/LICENSE @@ -1,29 +1,31 @@ -BSD 3-Clause License - -Copyright (c) 2021, ledgerwatch -All rights reserved. +Copyright (c) 2010 The Go Authors. All rights reserved. +Copyright (c) 2011 ThePiachu. All rights reserved. +Copyright (c) 2015 Jeffrey Wilcke. All rights reserved. +Copyright (c) 2015 Felix Lange. All rights reserved. +Copyright (c) 2015 Gustav Simonsson. All rights reserved. Redistribution and use in source and binary forms, with or without -modification, are permitted provided that the following conditions are met: - -1. Redistributions of source code must retain the above copyright notice, this - list of conditions and the following disclaimer. - -2. Redistributions in binary form must reproduce the above copyright notice, - this list of conditions and the following disclaimer in the documentation - and/or other materials provided with the distribution. +modification, are permitted provided that the following conditions are +met: -3. Neither the name of the copyright holder nor the names of its - contributors may be used to endorse or promote products derived from - this software without specific prior written permission. + * Redistributions of source code must retain the above copyright +notice, this list of conditions and the following disclaimer. + * Redistributions in binary form must reproduce the above +copyright notice, this list of conditions and the following disclaimer +in the documentation and/or other materials provided with the +distribution. + * Neither the name of the copyright holder. nor the names of its +contributors may be used to endorse or promote products derived from +this software without specific prior written permission. -THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" -AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE -IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE -DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE -FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL -DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR -SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER -CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, -OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/curve.go b/curve.go new file mode 100644 index 0000000..8f83ccc --- /dev/null +++ b/curve.go @@ -0,0 +1,329 @@ +// Copyright 2010 The Go Authors. All rights reserved. +// Copyright 2011 ThePiachu. All rights reserved. +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// * Redistributions in binary form must reproduce the above +// copyright notice, this list of conditions and the following disclaimer +// in the documentation and/or other materials provided with the +// distribution. +// * Neither the name of Google Inc. nor the names of its +// contributors may be used to endorse or promote products derived from +// this software without specific prior written permission. +// * The name of ThePiachu may not be used to endorse or promote products +// derived from this software without specific prior written permission. +// +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +package secp256k1 + +import ( + "crypto/elliptic" + "math/big" + "unsafe" +) + +/* +#include "libsecp256k1/include/secp256k1.h" +extern int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, const unsigned char *point, const unsigned char *scalar); +*/ +import "C" + +const ( + // number of bits in a big.Word + wordBits = 32 << (uint64(^big.Word(0)) >> 63) + // number of bytes in a big.Word + wordBytes = wordBits / 8 +) + +// readBits encodes the absolute value of bigint as big-endian bytes. Callers +// must ensure that buf has enough space. If buf is too short the result will +// be incomplete. +func readBits(bigint *big.Int, buf []byte) { + i := len(buf) + for _, d := range bigint.Bits() { + for j := 0; j < wordBytes && i > 0; j++ { + i-- + buf[i] = byte(d) + d >>= 8 + } + } +} + +// This code is from https://github.com/ThePiachu/GoBit and implements +// several Koblitz elliptic curves over prime fields. +// +// The curve methods, internally, on Jacobian coordinates. For a given +// (x, y) position on the curve, the Jacobian coordinates are (x1, y1, +// z1) where x = x1/z1² and y = y1/z1³. The greatest speedups come +// when the whole calculation can be performed within the transform +// (as in ScalarMult and ScalarBaseMult). But even for Add and Double, +// it's faster to apply and reverse the transform than to operate in +// affine coordinates. + +// A BitCurve represents a Koblitz Curve with a=0. +// See http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html +type BitCurve struct { + P *big.Int // the order of the underlying field + N *big.Int // the order of the base point + B *big.Int // the constant of the BitCurve equation + Gx, Gy *big.Int // (x,y) of the base point + BitSize int // the size of the underlying field +} + +func (BitCurve *BitCurve) Params() *elliptic.CurveParams { + return &elliptic.CurveParams{ + P: BitCurve.P, + N: BitCurve.N, + B: BitCurve.B, + Gx: BitCurve.Gx, + Gy: BitCurve.Gy, + BitSize: BitCurve.BitSize, + } +} + +// IsOnCurve returns true if the given (x,y) lies on the BitCurve. +func (BitCurve *BitCurve) IsOnCurve(x, y *big.Int) bool { + // y² = x³ + b + y2 := new(big.Int).Mul(y, y) //y² + y2.Mod(y2, BitCurve.P) //y²%P + + x3 := new(big.Int).Mul(x, x) //x² + x3.Mul(x3, x) //x³ + + x3.Add(x3, BitCurve.B) //x³+B + x3.Mod(x3, BitCurve.P) //(x³+B)%P + + return x3.Cmp(y2) == 0 +} + +//TODO: double check if the function is okay +// affineFromJacobian reverses the Jacobian transform. See the comment at the +// top of the file. +func (BitCurve *BitCurve) affineFromJacobian(x, y, z *big.Int) (xOut, yOut *big.Int) { + if z.Sign() == 0 { + return new(big.Int), new(big.Int) + } + + zinv := new(big.Int).ModInverse(z, BitCurve.P) + zinvsq := new(big.Int).Mul(zinv, zinv) + + xOut = new(big.Int).Mul(x, zinvsq) + xOut.Mod(xOut, BitCurve.P) + zinvsq.Mul(zinvsq, zinv) + yOut = new(big.Int).Mul(y, zinvsq) + yOut.Mod(yOut, BitCurve.P) + return +} + +// Add returns the sum of (x1,y1) and (x2,y2) +func (BitCurve *BitCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) { + z := new(big.Int).SetInt64(1) + return BitCurve.affineFromJacobian(BitCurve.addJacobian(x1, y1, z, x2, y2, z)) +} + +// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and +// (x2, y2, z2) and returns their sum, also in Jacobian form. +func (BitCurve *BitCurve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl + z1z1 := new(big.Int).Mul(z1, z1) + z1z1.Mod(z1z1, BitCurve.P) + z2z2 := new(big.Int).Mul(z2, z2) + z2z2.Mod(z2z2, BitCurve.P) + + u1 := new(big.Int).Mul(x1, z2z2) + u1.Mod(u1, BitCurve.P) + u2 := new(big.Int).Mul(x2, z1z1) + u2.Mod(u2, BitCurve.P) + h := new(big.Int).Sub(u2, u1) + if h.Sign() == -1 { + h.Add(h, BitCurve.P) + } + i := new(big.Int).Lsh(h, 1) + i.Mul(i, i) + j := new(big.Int).Mul(h, i) + + s1 := new(big.Int).Mul(y1, z2) + s1.Mul(s1, z2z2) + s1.Mod(s1, BitCurve.P) + s2 := new(big.Int).Mul(y2, z1) + s2.Mul(s2, z1z1) + s2.Mod(s2, BitCurve.P) + r := new(big.Int).Sub(s2, s1) + if r.Sign() == -1 { + r.Add(r, BitCurve.P) + } + r.Lsh(r, 1) + v := new(big.Int).Mul(u1, i) + + x3 := new(big.Int).Set(r) + x3.Mul(x3, x3) + x3.Sub(x3, j) + x3.Sub(x3, v) + x3.Sub(x3, v) + x3.Mod(x3, BitCurve.P) + + y3 := new(big.Int).Set(r) + v.Sub(v, x3) + y3.Mul(y3, v) + s1.Mul(s1, j) + s1.Lsh(s1, 1) + y3.Sub(y3, s1) + y3.Mod(y3, BitCurve.P) + + z3 := new(big.Int).Add(z1, z2) + z3.Mul(z3, z3) + z3.Sub(z3, z1z1) + if z3.Sign() == -1 { + z3.Add(z3, BitCurve.P) + } + z3.Sub(z3, z2z2) + if z3.Sign() == -1 { + z3.Add(z3, BitCurve.P) + } + z3.Mul(z3, h) + z3.Mod(z3, BitCurve.P) + + return x3, y3, z3 +} + +// Double returns 2*(x,y) +func (BitCurve *BitCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) { + z1 := new(big.Int).SetInt64(1) + return BitCurve.affineFromJacobian(BitCurve.doubleJacobian(x1, y1, z1)) +} + +// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and +// returns its double, also in Jacobian form. +func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) { + // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l + + a := new(big.Int).Mul(x, x) //X1² + b := new(big.Int).Mul(y, y) //Y1² + c := new(big.Int).Mul(b, b) //B² + + d := new(big.Int).Add(x, b) //X1+B + d.Mul(d, d) //(X1+B)² + d.Sub(d, a) //(X1+B)²-A + d.Sub(d, c) //(X1+B)²-A-C + d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C) + + e := new(big.Int).Mul(big.NewInt(3), a) //3*A + f := new(big.Int).Mul(e, e) //E² + + x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D + x3.Sub(f, x3) //F-2*D + x3.Mod(x3, BitCurve.P) + + y3 := new(big.Int).Sub(d, x3) //D-X3 + y3.Mul(e, y3) //E*(D-X3) + y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C + y3.Mod(y3, BitCurve.P) + + z3 := new(big.Int).Mul(y, z) //Y1*Z1 + z3.Mul(big.NewInt(2), z3) //3*Y1*Z1 + z3.Mod(z3, BitCurve.P) + + return x3, y3, z3 +} + +func (BitCurve *BitCurve) ScalarMult(Bx, By *big.Int, scalar []byte) (*big.Int, *big.Int) { + // Ensure scalar is exactly 32 bytes. We pad always, even if + // scalar is 32 bytes long, to avoid a timing side channel. + if len(scalar) > 32 { + panic("can't handle scalars > 256 bits") + } + // NOTE: potential timing issue + padded := make([]byte, 32) + copy(padded[32-len(scalar):], scalar) + scalar = padded + + // Do the multiplication in C, updating point. + point := make([]byte, 64) + readBits(Bx, point[:32]) + readBits(By, point[32:]) + + pointPtr := (*C.uchar)(unsafe.Pointer(&point[0])) + scalarPtr := (*C.uchar)(unsafe.Pointer(&scalar[0])) + res := C.secp256k1_ext_scalar_mul(context, pointPtr, scalarPtr) + + // Unpack the result and clear temporaries. + x := new(big.Int).SetBytes(point[:32]) + y := new(big.Int).SetBytes(point[32:]) + for i := range point { + point[i] = 0 + } + for i := range padded { + scalar[i] = 0 + } + if res != 1 { + return nil, nil + } + return x, y +} + +// ScalarBaseMult returns k*G, where G is the base point of the group and k is +// an integer in big-endian form. +func (BitCurve *BitCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) { + return BitCurve.ScalarMult(BitCurve.Gx, BitCurve.Gy, k) +} + +// Marshal converts a point into the form specified in section 4.3.6 of ANSI +// X9.62. +func (BitCurve *BitCurve) Marshal(x, y *big.Int) []byte { + byteLen := (BitCurve.BitSize + 7) >> 3 + ret := make([]byte, 1+2*byteLen) + ret[0] = 4 // uncompressed point flag + readBits(x, ret[1:1+byteLen]) + readBits(y, ret[1+byteLen:]) + return ret +} + +// Unmarshal converts a point, serialised by Marshal, into an x, y pair. On +// error, x = nil. +func (BitCurve *BitCurve) Unmarshal(data []byte) (x, y *big.Int) { + byteLen := (BitCurve.BitSize + 7) >> 3 + if len(data) != 1+2*byteLen { + return + } + if data[0] != 4 { // uncompressed form + return + } + x = new(big.Int).SetBytes(data[1 : 1+byteLen]) + y = new(big.Int).SetBytes(data[1+byteLen:]) + return +} + +var theCurve = new(BitCurve) + +func init() { + // See SEC 2 section 2.7.1 + // curve parameters taken from: + // http://www.secg.org/sec2-v2.pdf + theCurve.P, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 0) + theCurve.N, _ = new(big.Int).SetString("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 0) + theCurve.B, _ = new(big.Int).SetString("0x0000000000000000000000000000000000000000000000000000000000000007", 0) + theCurve.Gx, _ = new(big.Int).SetString("0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 0) + theCurve.Gy, _ = new(big.Int).SetString("0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 0) + theCurve.BitSize = 256 +} + +// S256 returns a BitCurve which implements secp256k1. +func S256() *BitCurve { + return theCurve +} diff --git a/dummy.go b/dummy.go new file mode 100644 index 0000000..1f54039 --- /dev/null +++ b/dummy.go @@ -0,0 +1,20 @@ +// +build dummy + +// This file is part of a workaround for `go mod vendor` which won't vendor +// C files if there's no Go file in the same directory. +// This would prevent the crypto/secp256k1/libsecp256k1/include/secp256k1.h file to be vendored. +// +// This Go file imports the c directory where there is another dummy.go file which +// is the second part of this workaround. +// +// These two files combined make it so `go mod vendor` behaves correctly. +// +// See this issue for reference: https://github.com/golang/go/issues/26366 + +package secp256k1 + +import ( + _ "github.com/ledgerwatch/erigon/crypto/secp256k1/libsecp256k1/include" + _ "github.com/ledgerwatch/erigon/crypto/secp256k1/libsecp256k1/src" + _ "github.com/ledgerwatch/erigon/crypto/secp256k1/libsecp256k1/src/modules/recovery" +) diff --git a/ext.h b/ext.h new file mode 100644 index 0000000..0d219e8 --- /dev/null +++ b/ext.h @@ -0,0 +1,130 @@ +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// Use of this source code is governed by a BSD-style license that can be found in +// the LICENSE file. + +// secp256k1_context_create_sign_verify creates a context for signing and signature verification. +static secp256k1_context* secp256k1_context_create_sign_verify() { + return secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); +} + +// secp256k1_ext_ecdsa_recover recovers the public key of an encoded compact signature. +// +// Returns: 1: recovery was successful +// 0: recovery was not successful +// Args: ctx: pointer to a context object (cannot be NULL) +// Out: pubkey_out: the serialized 65-byte public key of the signer (cannot be NULL) +// In: sigdata: pointer to a 65-byte signature with the recovery id at the end (cannot be NULL) +// msgdata: pointer to a 32-byte message (cannot be NULL) +static int secp256k1_ext_ecdsa_recover( + const secp256k1_context* ctx, + unsigned char *pubkey_out, + const unsigned char *sigdata, + const unsigned char *msgdata +) { + secp256k1_ecdsa_recoverable_signature sig; + secp256k1_pubkey pubkey; + + if (!secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &sig, sigdata, (int)sigdata[64])) { + return 0; + } + if (!secp256k1_ecdsa_recover(ctx, &pubkey, &sig, msgdata)) { + return 0; + } + size_t outputlen = 65; + return secp256k1_ec_pubkey_serialize(ctx, pubkey_out, &outputlen, &pubkey, SECP256K1_EC_UNCOMPRESSED); +} + +// secp256k1_ext_ecdsa_verify verifies an encoded compact signature. +// +// Returns: 1: signature is valid +// 0: signature is invalid +// Args: ctx: pointer to a context object (cannot be NULL) +// In: sigdata: pointer to a 64-byte signature (cannot be NULL) +// msgdata: pointer to a 32-byte message (cannot be NULL) +// pubkeydata: pointer to public key data (cannot be NULL) +// pubkeylen: length of pubkeydata +static int secp256k1_ext_ecdsa_verify( + const secp256k1_context* ctx, + const unsigned char *sigdata, + const unsigned char *msgdata, + const unsigned char *pubkeydata, + size_t pubkeylen +) { + secp256k1_ecdsa_signature sig; + secp256k1_pubkey pubkey; + + if (!secp256k1_ecdsa_signature_parse_compact(ctx, &sig, sigdata)) { + return 0; + } + if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeydata, pubkeylen)) { + return 0; + } + return secp256k1_ecdsa_verify(ctx, &sig, msgdata, &pubkey); +} + +// secp256k1_ext_reencode_pubkey decodes then encodes a public key. It can be used to +// convert between public key formats. The input/output formats are chosen depending on the +// length of the input/output buffers. +// +// Returns: 1: conversion successful +// 0: conversion unsuccessful +// Args: ctx: pointer to a context object (cannot be NULL) +// Out: out: output buffer that will contain the reencoded key (cannot be NULL) +// In: outlen: length of out (33 for compressed keys, 65 for uncompressed keys) +// pubkeydata: the input public key (cannot be NULL) +// pubkeylen: length of pubkeydata +static int secp256k1_ext_reencode_pubkey( + const secp256k1_context* ctx, + unsigned char *out, + size_t outlen, + const unsigned char *pubkeydata, + size_t pubkeylen +) { + secp256k1_pubkey pubkey; + + if (!secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeydata, pubkeylen)) { + return 0; + } + unsigned int flag = (outlen == 33) ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED; + return secp256k1_ec_pubkey_serialize(ctx, out, &outlen, &pubkey, flag); +} + +// secp256k1_ext_scalar_mul multiplies a point by a scalar in constant time. +// +// Returns: 1: multiplication was successful +// 0: scalar was invalid (zero or overflow) +// Args: ctx: pointer to a context object (cannot be NULL) +// Out: point: the multiplied point (usually secret) +// In: point: pointer to a 64-byte public point, +// encoded as two 256bit big-endian numbers. +// scalar: a 32-byte scalar with which to multiply the point +int secp256k1_ext_scalar_mul(const secp256k1_context* ctx, unsigned char *point, const unsigned char *scalar) { + int ret = 0; + int overflow = 0; + secp256k1_fe feX, feY; + secp256k1_gej res; + secp256k1_ge ge; + secp256k1_scalar s; + ARG_CHECK(point != NULL); + ARG_CHECK(scalar != NULL); + (void)ctx; + + secp256k1_fe_set_b32(&feX, point); + secp256k1_fe_set_b32(&feY, point+32); + secp256k1_ge_set_xy(&ge, &feX, &feY); + secp256k1_scalar_set_b32(&s, scalar, &overflow); + if (overflow || secp256k1_scalar_is_zero(&s)) { + ret = 0; + } else { + secp256k1_ecmult_const(&res, &ge, &s, 256); + secp256k1_ge_set_gej(&ge, &res); + /* Note: can't use secp256k1_pubkey_save here because it is not constant time. */ + secp256k1_fe_normalize(&ge.x); + secp256k1_fe_normalize(&ge.y); + secp256k1_fe_get_b32(point, &ge.x); + secp256k1_fe_get_b32(point+32, &ge.y); + ret = 1; + } + secp256k1_scalar_clear(&s); + return ret; +} diff --git a/libsecp256k1/.gitignore b/libsecp256k1/.gitignore new file mode 100644 index 0000000..cb4331a --- /dev/null +++ b/libsecp256k1/.gitignore @@ -0,0 +1,51 @@ +bench_inv +bench_ecdh +bench_ecmult +bench_sign +bench_verify +bench_schnorr_verify +bench_recover +bench_internal +tests +exhaustive_tests +gen_context +valgrind_ctime_test +*.exe +*.so +*.a +!.gitignore + +Makefile +configure +.libs/ +Makefile.in +aclocal.m4 +autom4te.cache/ +config.log +config.status +*.tar.gz +*.la +libtool +.deps/ +.dirstamp +*.lo +*.o +*~ +src/libsecp256k1-config.h +src/libsecp256k1-config.h.in +src/ecmult_static_context.h +build-aux/config.guess +build-aux/config.sub +build-aux/depcomp +build-aux/install-sh +build-aux/ltmain.sh +build-aux/m4/libtool.m4 +build-aux/m4/lt~obsolete.m4 +build-aux/m4/ltoptions.m4 +build-aux/m4/ltsugar.m4 +build-aux/m4/ltversion.m4 +build-aux/missing +build-aux/compile +build-aux/test-driver +src/stamp-h1 +libsecp256k1.pc diff --git a/libsecp256k1/.travis.yml b/libsecp256k1/.travis.yml new file mode 100644 index 0000000..a6ad6fb --- /dev/null +++ b/libsecp256k1/.travis.yml @@ -0,0 +1,108 @@ +language: c +os: + - linux + - osx + +dist: bionic +# Valgrind currently supports upto macOS 10.13, the latest xcode of that version is 10.1 +osx_image: xcode10.1 +addons: + apt: + packages: + - libgmp-dev + - valgrind + - libtool-bin +compiler: + - clang + - gcc +env: + global: + - FIELD=auto BIGNUM=auto SCALAR=auto ENDOMORPHISM=no STATICPRECOMPUTATION=yes ECMULTGENPRECISION=auto ASM=no BUILD=check EXTRAFLAGS= HOST= ECDH=no RECOVERY=no EXPERIMENTAL=no CTIMETEST=yes BENCH=yes ITERS=2 + matrix: + - SCALAR=32bit RECOVERY=yes + - SCALAR=32bit FIELD=32bit ECDH=yes EXPERIMENTAL=yes + - SCALAR=64bit + - FIELD=64bit RECOVERY=yes + - FIELD=64bit ENDOMORPHISM=yes + - FIELD=64bit ENDOMORPHISM=yes ECDH=yes EXPERIMENTAL=yes + - FIELD=64bit ASM=x86_64 + - FIELD=64bit ENDOMORPHISM=yes ASM=x86_64 + - FIELD=32bit ENDOMORPHISM=yes + - BIGNUM=no + - BIGNUM=no ENDOMORPHISM=yes RECOVERY=yes EXPERIMENTAL=yes + - BIGNUM=no STATICPRECOMPUTATION=no + - BUILD=distcheck CTIMETEST= BENCH= + - CPPFLAGS=-DDETERMINISTIC + - CFLAGS=-O0 CTIMETEST= + - ECMULTGENPRECISION=2 + - ECMULTGENPRECISION=8 + - VALGRIND=yes ENDOMORPHISM=yes BIGNUM=no ASM=x86_64 EXPERIMENTAL=yes ECDH=yes RECOVERY=yes EXTRAFLAGS="--disable-openssl-tests" CPPFLAGS=-DVALGRIND BUILD= + - VALGRIND=yes BIGNUM=no ASM=x86_64 EXPERIMENTAL=yes ECDH=yes RECOVERY=yes EXTRAFLAGS="--disable-openssl-tests" CPPFLAGS=-DVALGRIND BUILD= +matrix: + fast_finish: true + include: + - compiler: clang + os: linux + env: HOST=i686-linux-gnu ENDOMORPHISM=yes + addons: + apt: + packages: + - gcc-multilib + - libgmp-dev:i386 + - valgrind + - libtool-bin + - libc6-dbg:i386 + - compiler: clang + env: HOST=i686-linux-gnu + os: linux + addons: + apt: + packages: + - gcc-multilib + - valgrind + - libtool-bin + - libc6-dbg:i386 + - compiler: gcc + env: HOST=i686-linux-gnu ENDOMORPHISM=yes + os: linux + addons: + apt: + packages: + - gcc-multilib + - valgrind + - libtool-bin + - libc6-dbg:i386 + - compiler: gcc + os: linux + env: HOST=i686-linux-gnu + addons: + apt: + packages: + - gcc-multilib + - libgmp-dev:i386 + - valgrind + - libtool-bin + - libc6-dbg:i386 + +# We use this to install macOS dependencies instead of the built in `homebrew` plugin, +# because in xcode earlier than 11 they have a bug requiring updating the system which overall takes ~8 minutes. +# https://travis-ci.community/t/macos-build-fails-because-of-homebrew-bundle-unknown-command/7296 +before_install: + - if [ "${TRAVIS_OS_NAME}" = "osx" ]; then HOMEBREW_NO_AUTO_UPDATE=1 brew install gmp valgrind gcc@9; fi + +before_script: ./autogen.sh + +# travis auto terminates jobs that go for 10 minutes without printing to stdout, but travis_wait doesn't work well with forking programs like valgrind (https://docs.travis-ci.com/user/common-build-problems/#build-times-out-because-no-output-was-received https://github.com/bitcoin-core/secp256k1/pull/750#issuecomment-623476860) +script: + - function keep_alive() { while true; do echo -en "\a"; sleep 60; done } + - keep_alive & + - ./contrib/travis.sh + - kill %keep_alive + +after_script: + - cat ./tests.log + - cat ./exhaustive_tests.log + - cat ./valgrind_ctime_test.log + - cat ./bench.log + - $CC --version + - valgrind --version diff --git a/libsecp256k1/COPYING b/libsecp256k1/COPYING new file mode 100644 index 0000000..4522a59 --- /dev/null +++ b/libsecp256k1/COPYING @@ -0,0 +1,19 @@ +Copyright (c) 2013 Pieter Wuille + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/libsecp256k1/Makefile.am b/libsecp256k1/Makefile.am new file mode 100644 index 0000000..d8c1c79 --- /dev/null +++ b/libsecp256k1/Makefile.am @@ -0,0 +1,154 @@ +ACLOCAL_AMFLAGS = -I build-aux/m4 + +lib_LTLIBRARIES = libsecp256k1.la +include_HEADERS = include/secp256k1.h +include_HEADERS += include/secp256k1_preallocated.h +noinst_HEADERS = +noinst_HEADERS += src/scalar.h +noinst_HEADERS += src/scalar_4x64.h +noinst_HEADERS += src/scalar_8x32.h +noinst_HEADERS += src/scalar_low.h +noinst_HEADERS += src/scalar_impl.h +noinst_HEADERS += src/scalar_4x64_impl.h +noinst_HEADERS += src/scalar_8x32_impl.h +noinst_HEADERS += src/scalar_low_impl.h +noinst_HEADERS += src/group.h +noinst_HEADERS += src/group_impl.h +noinst_HEADERS += src/num_gmp.h +noinst_HEADERS += src/num_gmp_impl.h +noinst_HEADERS += src/ecdsa.h +noinst_HEADERS += src/ecdsa_impl.h +noinst_HEADERS += src/eckey.h +noinst_HEADERS += src/eckey_impl.h +noinst_HEADERS += src/ecmult.h +noinst_HEADERS += src/ecmult_impl.h +noinst_HEADERS += src/ecmult_const.h +noinst_HEADERS += src/ecmult_const_impl.h +noinst_HEADERS += src/ecmult_gen.h +noinst_HEADERS += src/ecmult_gen_impl.h +noinst_HEADERS += src/num.h +noinst_HEADERS += src/num_impl.h +noinst_HEADERS += src/field_10x26.h +noinst_HEADERS += src/field_10x26_impl.h +noinst_HEADERS += src/field_5x52.h +noinst_HEADERS += src/field_5x52_impl.h +noinst_HEADERS += src/field_5x52_int128_impl.h +noinst_HEADERS += src/field_5x52_asm_impl.h +noinst_HEADERS += src/util.h +noinst_HEADERS += src/scratch.h +noinst_HEADERS += src/scratch_impl.h +noinst_HEADERS += src/testrand.h +noinst_HEADERS += src/testrand_impl.h +noinst_HEADERS += src/hash.h +noinst_HEADERS += src/hash_impl.h +noinst_HEADERS += src/field.h +noinst_HEADERS += src/field_impl.h +noinst_HEADERS += src/bench.h +noinst_HEADERS += contrib/lax_der_parsing.h +noinst_HEADERS += contrib/lax_der_parsing.c +noinst_HEADERS += contrib/lax_der_privatekey_parsing.h +noinst_HEADERS += contrib/lax_der_privatekey_parsing.c + +if USE_EXTERNAL_ASM +COMMON_LIB = libsecp256k1_common.la +noinst_LTLIBRARIES = $(COMMON_LIB) +else +COMMON_LIB = +endif + +pkgconfigdir = $(libdir)/pkgconfig +pkgconfig_DATA = libsecp256k1.pc + +if USE_EXTERNAL_ASM +if USE_ASM_ARM +libsecp256k1_common_la_SOURCES = src/asm/field_10x26_arm.s +endif +endif + +libsecp256k1_la_SOURCES = src/secp256k1.c +libsecp256k1_la_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES) +libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB) + +if VALGRIND_ENABLED +libsecp256k1_la_CPPFLAGS += -DVALGRIND +endif + +noinst_PROGRAMS = +if USE_BENCHMARK +noinst_PROGRAMS += bench_verify bench_sign bench_internal bench_ecmult +bench_verify_SOURCES = src/bench_verify.c +bench_verify_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) +# SECP_TEST_INCLUDES are only used here for CRYPTO_CPPFLAGS +bench_verify_CPPFLAGS = -DSECP256K1_BUILD $(SECP_TEST_INCLUDES) +bench_sign_SOURCES = src/bench_sign.c +bench_sign_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) +bench_internal_SOURCES = src/bench_internal.c +bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB) +bench_internal_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES) +bench_ecmult_SOURCES = src/bench_ecmult.c +bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) +bench_ecmult_CPPFLAGS = -DSECP256K1_BUILD $(SECP_INCLUDES) +endif + +TESTS = +if USE_TESTS +noinst_PROGRAMS += tests +tests_SOURCES = src/tests.c +tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src -I$(top_srcdir)/include $(SECP_INCLUDES) $(SECP_TEST_INCLUDES) +if VALGRIND_ENABLED +tests_CPPFLAGS += -DVALGRIND +noinst_PROGRAMS += valgrind_ctime_test +valgrind_ctime_test_SOURCES = src/valgrind_ctime_test.c +valgrind_ctime_test_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) +endif +if !ENABLE_COVERAGE +tests_CPPFLAGS += -DVERIFY +endif +tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) +tests_LDFLAGS = -static +TESTS += tests +endif + +if USE_EXHAUSTIVE_TESTS +noinst_PROGRAMS += exhaustive_tests +exhaustive_tests_SOURCES = src/tests_exhaustive.c +exhaustive_tests_CPPFLAGS = -DSECP256K1_BUILD -I$(top_srcdir)/src $(SECP_INCLUDES) +if !ENABLE_COVERAGE +exhaustive_tests_CPPFLAGS += -DVERIFY +endif +exhaustive_tests_LDADD = $(SECP_LIBS) $(COMMON_LIB) +exhaustive_tests_LDFLAGS = -static +TESTS += exhaustive_tests +endif + +if USE_ECMULT_STATIC_PRECOMPUTATION +CPPFLAGS_FOR_BUILD +=-I$(top_srcdir) -I$(builddir)/src + +gen_context_OBJECTS = gen_context.o +gen_context_BIN = gen_context$(BUILD_EXEEXT) +gen_%.o: src/gen_%.c src/libsecp256k1-config.h + $(CC_FOR_BUILD) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@ + +$(gen_context_BIN): $(gen_context_OBJECTS) + $(CC_FOR_BUILD) $(CFLAGS_FOR_BUILD) $(LDFLAGS_FOR_BUILD) $^ -o $@ + +$(libsecp256k1_la_OBJECTS): src/ecmult_static_context.h +$(tests_OBJECTS): src/ecmult_static_context.h +$(bench_internal_OBJECTS): src/ecmult_static_context.h +$(bench_ecmult_OBJECTS): src/ecmult_static_context.h + +src/ecmult_static_context.h: $(gen_context_BIN) + ./$(gen_context_BIN) + +CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h +endif + +EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h + +if ENABLE_MODULE_ECDH +include src/modules/ecdh/Makefile.am.include +endif + +if ENABLE_MODULE_RECOVERY +include src/modules/recovery/Makefile.am.include +endif diff --git a/libsecp256k1/README.md b/libsecp256k1/README.md new file mode 100644 index 0000000..434178b --- /dev/null +++ b/libsecp256k1/README.md @@ -0,0 +1,104 @@ +libsecp256k1 +============ + +[![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1) + +Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1. + +This library is intended to be the highest quality publicly available library for cryptography on the secp256k1 curve. However, the primary focus of its development has been for usage in the Bitcoin system and usage unlike Bitcoin's may be less well tested, verified, or suffer from a less well thought out interface. Correct usage requires some care and consideration that the library is fit for your application's purpose. + +Features: +* secp256k1 ECDSA signing/verification and key generation. +* Additive and multiplicative tweaking of secret/public keys. +* Serialization/parsing of secret keys, public keys, signatures. +* Constant time, constant memory access signing and public key generation. +* Derandomized ECDSA (via RFC6979 or with a caller provided function.) +* Very efficient implementation. +* Suitable for embedded systems. +* Optional module for public key recovery. +* Optional module for ECDH key exchange (experimental). + +Experimental features have not received enough scrutiny to satisfy the standard of quality of this library but are made available for testing and review by the community. The APIs of these features should not be considered stable. + +Implementation details +---------------------- + +* General + * No runtime heap allocation. + * Extensive testing infrastructure. + * Structured to facilitate review and analysis. + * Intended to be portable to any system with a C89 compiler and uint64_t support. + * No use of floating types. + * Expose only higher level interfaces to minimize the API surface and improve application security. ("Be difficult to use insecurely.") +* Field operations + * Optimized implementation of arithmetic modulo the curve's field size (2^256 - 0x1000003D1). + * Using 5 52-bit limbs (including hand-optimized assembly for x86_64, by Diederik Huys). + * Using 10 26-bit limbs (including hand-optimized assembly for 32-bit ARM, by Wladimir J. van der Laan). + * Field inverses and square roots using a sliding window over blocks of 1s (by Peter Dettman). +* Scalar operations + * Optimized implementation without data-dependent branches of arithmetic modulo the curve's order. + * Using 4 64-bit limbs (relying on __int128 support in the compiler). + * Using 8 32-bit limbs. +* Group operations + * Point addition formula specifically simplified for the curve equation (y^2 = x^3 + 7). + * Use addition between points in Jacobian and affine coordinates where possible. + * Use a unified addition/doubling formula where necessary to avoid data-dependent branches. + * Point/x comparison without a field inversion by comparison in the Jacobian coordinate space. +* Point multiplication for verification (a*P + b*G). + * Use wNAF notation for point multiplicands. + * Use a much larger window for multiples of G, using precomputed multiples. + * Use Shamir's trick to do the multiplication with the public key and the generator simultaneously. + * Optionally (off by default) use secp256k1's efficiently-computable endomorphism to split the P multiplicand into 2 half-sized ones. +* Point multiplication for signing + * Use a precomputed table of multiples of powers of 16 multiplied with the generator, so general multiplication becomes a series of additions. + * Intended to be completely free of timing sidechannels for secret-key operations (on reasonable hardware/toolchains) + * Access the table with branch-free conditional moves so memory access is uniform. + * No data-dependent branches + * Optional runtime blinding which attempts to frustrate differential power analysis. + * The precomputed tables add and eventually subtract points for which no known scalar (secret key) is known, preventing even an attacker with control over the secret key used to control the data internally. + +Build steps +----------- + +libsecp256k1 is built using autotools: + + $ ./autogen.sh + $ ./configure + $ make + $ make check + $ sudo make install # optional + +Exhaustive tests +----------- + + $ ./exhaustive_tests + +With valgrind, you might need to increase the max stack size: + + $ valgrind --max-stackframe=2500000 ./exhaustive_tests + +Test coverage +----------- + +This library aims to have full coverage of the reachable lines and branches. + +To create a test coverage report, configure with `--enable-coverage` (use of GCC is necessary): + + $ ./configure --enable-coverage + +Run the tests: + + $ make check + +To create a report, `gcovr` is recommended, as it includes branch coverage reporting: + + $ gcovr --exclude 'src/bench*' --print-summary + +To create a HTML report with coloured and annotated source code: + + $ gcovr --exclude 'src/bench*' --html --html-details -o coverage.html + +Reporting a vulnerability +------------ + +See [SECURITY.md](SECURITY.md) diff --git a/libsecp256k1/SECURITY.md b/libsecp256k1/SECURITY.md new file mode 100644 index 0000000..0e4d588 --- /dev/null +++ b/libsecp256k1/SECURITY.md @@ -0,0 +1,15 @@ +# Security Policy + +## Reporting a Vulnerability + +To report security issues send an email to secp256k1-security@bitcoincore.org (not for support). + +The following keys may be used to communicate sensitive information to developers: + +| Name | Fingerprint | +|------|-------------| +| Pieter Wuille | 133E AC17 9436 F14A 5CF1 B794 860F EB80 4E66 9320 | +| Andrew Poelstra | 699A 63EF C17A D3A9 A34C FFC0 7AD0 A91C 40BD 0091 | +| Tim Ruffing | 09E0 3F87 1092 E40E 106E 902B 33BC 86AB 80FF 5516 | + +You can import a key by running the following command with that individual’s fingerprint: `gpg --recv-keys ""` Ensure that you put quotes around fingerprints containing spaces. diff --git a/libsecp256k1/TODO b/libsecp256k1/TODO new file mode 100644 index 0000000..a300e1c --- /dev/null +++ b/libsecp256k1/TODO @@ -0,0 +1,3 @@ +* Unit tests for fieldelem/groupelem, including ones intended to + trigger fieldelem's boundary cases. +* Complete constant-time operations for signing/keygen diff --git a/libsecp256k1/autogen.sh b/libsecp256k1/autogen.sh new file mode 100755 index 0000000..65286b9 --- /dev/null +++ b/libsecp256k1/autogen.sh @@ -0,0 +1,3 @@ +#!/bin/sh +set -e +autoreconf -if --warnings=all diff --git a/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4 b/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4 new file mode 100644 index 0000000..77fd346 --- /dev/null +++ b/libsecp256k1/build-aux/m4/ax_prog_cc_for_build.m4 @@ -0,0 +1,125 @@ +# =========================================================================== +# http://www.gnu.org/software/autoconf-archive/ax_prog_cc_for_build.html +# =========================================================================== +# +# SYNOPSIS +# +# AX_PROG_CC_FOR_BUILD +# +# DESCRIPTION +# +# This macro searches for a C compiler that generates native executables, +# that is a C compiler that surely is not a cross-compiler. This can be +# useful if you have to generate source code at compile-time like for +# example GCC does. +# +# The macro sets the CC_FOR_BUILD and CPP_FOR_BUILD macros to anything +# needed to compile or link (CC_FOR_BUILD) and preprocess (CPP_FOR_BUILD). +# The value of these variables can be overridden by the user by specifying +# a compiler with an environment variable (like you do for standard CC). +# +# It also sets BUILD_EXEEXT and BUILD_OBJEXT to the executable and object +# file extensions for the build platform, and GCC_FOR_BUILD to `yes' if +# the compiler we found is GCC. All these variables but GCC_FOR_BUILD are +# substituted in the Makefile. +# +# LICENSE +# +# Copyright (c) 2008 Paolo Bonzini +# +# Copying and distribution of this file, with or without modification, are +# permitted in any medium without royalty provided the copyright notice +# and this notice are preserved. This file is offered as-is, without any +# warranty. + +#serial 8 + +AU_ALIAS([AC_PROG_CC_FOR_BUILD], [AX_PROG_CC_FOR_BUILD]) +AC_DEFUN([AX_PROG_CC_FOR_BUILD], [dnl +AC_REQUIRE([AC_PROG_CC])dnl +AC_REQUIRE([AC_PROG_CPP])dnl +AC_REQUIRE([AC_EXEEXT])dnl +AC_REQUIRE([AC_CANONICAL_HOST])dnl + +dnl Use the standard macros, but make them use other variable names +dnl +pushdef([ac_cv_prog_CPP], ac_cv_build_prog_CPP)dnl +pushdef([ac_cv_prog_gcc], ac_cv_build_prog_gcc)dnl +pushdef([ac_cv_prog_cc_works], ac_cv_build_prog_cc_works)dnl +pushdef([ac_cv_prog_cc_cross], ac_cv_build_prog_cc_cross)dnl +pushdef([ac_cv_prog_cc_g], ac_cv_build_prog_cc_g)dnl +pushdef([ac_cv_exeext], ac_cv_build_exeext)dnl +pushdef([ac_cv_objext], ac_cv_build_objext)dnl +pushdef([ac_exeext], ac_build_exeext)dnl +pushdef([ac_objext], ac_build_objext)dnl +pushdef([CC], CC_FOR_BUILD)dnl +pushdef([CPP], CPP_FOR_BUILD)dnl +pushdef([CFLAGS], CFLAGS_FOR_BUILD)dnl +pushdef([CPPFLAGS], CPPFLAGS_FOR_BUILD)dnl +pushdef([LDFLAGS], LDFLAGS_FOR_BUILD)dnl +pushdef([host], build)dnl +pushdef([host_alias], build_alias)dnl +pushdef([host_cpu], build_cpu)dnl +pushdef([host_vendor], build_vendor)dnl +pushdef([host_os], build_os)dnl +pushdef([ac_cv_host], ac_cv_build)dnl +pushdef([ac_cv_host_alias], ac_cv_build_alias)dnl +pushdef([ac_cv_host_cpu], ac_cv_build_cpu)dnl +pushdef([ac_cv_host_vendor], ac_cv_build_vendor)dnl +pushdef([ac_cv_host_os], ac_cv_build_os)dnl +pushdef([ac_cpp], ac_build_cpp)dnl +pushdef([ac_compile], ac_build_compile)dnl +pushdef([ac_link], ac_build_link)dnl + +save_cross_compiling=$cross_compiling +save_ac_tool_prefix=$ac_tool_prefix +cross_compiling=no +ac_tool_prefix= + +AC_PROG_CC +AC_PROG_CPP +AC_EXEEXT + +ac_tool_prefix=$save_ac_tool_prefix +cross_compiling=$save_cross_compiling + +dnl Restore the old definitions +dnl +popdef([ac_link])dnl +popdef([ac_compile])dnl +popdef([ac_cpp])dnl +popdef([ac_cv_host_os])dnl +popdef([ac_cv_host_vendor])dnl +popdef([ac_cv_host_cpu])dnl +popdef([ac_cv_host_alias])dnl +popdef([ac_cv_host])dnl +popdef([host_os])dnl +popdef([host_vendor])dnl +popdef([host_cpu])dnl +popdef([host_alias])dnl +popdef([host])dnl +popdef([LDFLAGS])dnl +popdef([CPPFLAGS])dnl +popdef([CFLAGS])dnl +popdef([CPP])dnl +popdef([CC])dnl +popdef([ac_objext])dnl +popdef([ac_exeext])dnl +popdef([ac_cv_objext])dnl +popdef([ac_cv_exeext])dnl +popdef([ac_cv_prog_cc_g])dnl +popdef([ac_cv_prog_cc_cross])dnl +popdef([ac_cv_prog_cc_works])dnl +popdef([ac_cv_prog_gcc])dnl +popdef([ac_cv_prog_CPP])dnl + +dnl Finally, set Makefile variables +dnl +BUILD_EXEEXT=$ac_build_exeext +BUILD_OBJEXT=$ac_build_objext +AC_SUBST(BUILD_EXEEXT)dnl +AC_SUBST(BUILD_OBJEXT)dnl +AC_SUBST([CFLAGS_FOR_BUILD])dnl +AC_SUBST([CPPFLAGS_FOR_BUILD])dnl +AC_SUBST([LDFLAGS_FOR_BUILD])dnl +]) diff --git a/libsecp256k1/build-aux/m4/bitcoin_secp.m4 b/libsecp256k1/build-aux/m4/bitcoin_secp.m4 new file mode 100644 index 0000000..1b2b71e --- /dev/null +++ b/libsecp256k1/build-aux/m4/bitcoin_secp.m4 @@ -0,0 +1,71 @@ +dnl libsecp25k1 helper checks +AC_DEFUN([SECP_INT128_CHECK],[ +has_int128=$ac_cv_type___int128 +]) + +dnl escape "$0x" below using the m4 quadrigaph @S|@, and escape it again with a \ for the shell. +AC_DEFUN([SECP_64BIT_ASM_CHECK],[ +AC_MSG_CHECKING(for x86_64 assembly availability) +AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[ + #include ]],[[ + uint64_t a = 11, tmp; + __asm__ __volatile__("movq \@S|@0x100000000,%1; mulq %%rsi" : "+a"(a) : "S"(tmp) : "cc", "%rdx"); + ]])],[has_64bit_asm=yes],[has_64bit_asm=no]) +AC_MSG_RESULT([$has_64bit_asm]) +]) + +dnl +AC_DEFUN([SECP_OPENSSL_CHECK],[ + has_libcrypto=no + m4_ifdef([PKG_CHECK_MODULES],[ + PKG_CHECK_MODULES([CRYPTO], [libcrypto], [has_libcrypto=yes],[has_libcrypto=no]) + if test x"$has_libcrypto" = x"yes"; then + TEMP_LIBS="$LIBS" + LIBS="$LIBS $CRYPTO_LIBS" + AC_CHECK_LIB(crypto, main,[AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed])],[has_libcrypto=no]) + LIBS="$TEMP_LIBS" + fi + ]) + if test x$has_libcrypto = xno; then + AC_CHECK_HEADER(openssl/crypto.h,[ + AC_CHECK_LIB(crypto, main,[ + has_libcrypto=yes + CRYPTO_LIBS=-lcrypto + AC_DEFINE(HAVE_LIBCRYPTO,1,[Define this symbol if libcrypto is installed]) + ]) + ]) + LIBS= + fi +if test x"$has_libcrypto" = x"yes" && test x"$has_openssl_ec" = x; then + AC_MSG_CHECKING(for EC functions in libcrypto) + CPPFLAGS_TEMP="$CPPFLAGS" + CPPFLAGS="$CRYPTO_CPPFLAGS $CPPFLAGS" + AC_COMPILE_IFELSE([AC_LANG_PROGRAM([[ + #include + #include + #include ]],[[ + EC_KEY *eckey = EC_KEY_new_by_curve_name(NID_secp256k1); + ECDSA_sign(0, NULL, 0, NULL, NULL, eckey); + ECDSA_verify(0, NULL, 0, NULL, 0, eckey); + EC_KEY_free(eckey); + ECDSA_SIG *sig_openssl; + sig_openssl = ECDSA_SIG_new(); + ECDSA_SIG_free(sig_openssl); + ]])],[has_openssl_ec=yes],[has_openssl_ec=no]) + AC_MSG_RESULT([$has_openssl_ec]) + CPPFLAGS="$CPPFLAGS_TEMP" +fi +]) + +dnl +AC_DEFUN([SECP_GMP_CHECK],[ +if test x"$has_gmp" != x"yes"; then + CPPFLAGS_TEMP="$CPPFLAGS" + CPPFLAGS="$GMP_CPPFLAGS $CPPFLAGS" + LIBS_TEMP="$LIBS" + LIBS="$GMP_LIBS $LIBS" + AC_CHECK_HEADER(gmp.h,[AC_CHECK_LIB(gmp, __gmpz_init,[has_gmp=yes; GMP_LIBS="$GMP_LIBS -lgmp"; AC_DEFINE(HAVE_LIBGMP,1,[Define this symbol if libgmp is installed])])]) + CPPFLAGS="$CPPFLAGS_TEMP" + LIBS="$LIBS_TEMP" +fi +]) diff --git a/libsecp256k1/configure.ac b/libsecp256k1/configure.ac new file mode 100644 index 0000000..6021b76 --- /dev/null +++ b/libsecp256k1/configure.ac @@ -0,0 +1,566 @@ +AC_PREREQ([2.60]) +AC_INIT([libsecp256k1],[0.1]) +AC_CONFIG_AUX_DIR([build-aux]) +AC_CONFIG_MACRO_DIR([build-aux/m4]) +AC_CANONICAL_HOST +AH_TOP([#ifndef LIBSECP256K1_CONFIG_H]) +AH_TOP([#define LIBSECP256K1_CONFIG_H]) +AH_BOTTOM([#endif /*LIBSECP256K1_CONFIG_H*/]) +AM_INIT_AUTOMAKE([foreign subdir-objects]) + +# Set -g if CFLAGS are not already set, which matches the default autoconf +# behavior (see PROG_CC in the Autoconf manual) with the exception that we don't +# set -O2 here because we set it in any case (see further down). +: ${CFLAGS="-g"} +LT_INIT + +dnl make the compilation flags quiet unless V=1 is used +m4_ifdef([AM_SILENT_RULES], [AM_SILENT_RULES([yes])]) + +PKG_PROG_PKG_CONFIG + +AC_PATH_TOOL(AR, ar) +AC_PATH_TOOL(RANLIB, ranlib) +AC_PATH_TOOL(STRIP, strip) +AX_PROG_CC_FOR_BUILD + +AM_PROG_CC_C_O + +AC_PROG_CC_C89 +if test x"$ac_cv_prog_cc_c89" = x"no"; then + AC_MSG_ERROR([c89 compiler support required]) +fi +AM_PROG_AS + +case $host_os in + *darwin*) + if test x$cross_compiling != xyes; then + AC_PATH_PROG([BREW],brew,) + if test x$BREW != x; then + dnl These Homebrew packages may be keg-only, meaning that they won't be found + dnl in expected paths because they may conflict with system files. Ask + dnl Homebrew where each one is located, then adjust paths accordingly. + + openssl_prefix=`$BREW --prefix openssl 2>/dev/null` + gmp_prefix=`$BREW --prefix gmp 2>/dev/null` + if test x$openssl_prefix != x; then + PKG_CONFIG_PATH="$openssl_prefix/lib/pkgconfig:$PKG_CONFIG_PATH" + export PKG_CONFIG_PATH + CRYPTO_CPPFLAGS="-I$openssl_prefix/include" + fi + if test x$gmp_prefix != x; then + GMP_CPPFLAGS="-I$gmp_prefix/include" + GMP_LIBS="-L$gmp_prefix/lib" + fi + else + AC_PATH_PROG([PORT],port,) + dnl if homebrew isn't installed and macports is, add the macports default paths + dnl as a last resort. + if test x$PORT != x; then + CPPFLAGS="$CPPFLAGS -isystem /opt/local/include" + LDFLAGS="$LDFLAGS -L/opt/local/lib" + fi + fi + fi + ;; +esac + +CFLAGS="-W $CFLAGS" + +warn_CFLAGS="-std=c89 -pedantic -Wall -Wextra -Wcast-align -Wnested-externs -Wshadow -Wstrict-prototypes -Wno-unused-function -Wno-long-long -Wno-overlength-strings" +saved_CFLAGS="$CFLAGS" +CFLAGS="$warn_CFLAGS $CFLAGS" +AC_MSG_CHECKING([if ${CC} supports ${warn_CFLAGS}]) +AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], + [ AC_MSG_RESULT([yes]) ], + [ AC_MSG_RESULT([no]) + CFLAGS="$saved_CFLAGS" + ]) + +saved_CFLAGS="$CFLAGS" +CFLAGS="-fvisibility=hidden $CFLAGS" +AC_MSG_CHECKING([if ${CC} supports -fvisibility=hidden]) +AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], + [ AC_MSG_RESULT([yes]) ], + [ AC_MSG_RESULT([no]) + CFLAGS="$saved_CFLAGS" + ]) + +AC_ARG_ENABLE(benchmark, + AS_HELP_STRING([--enable-benchmark],[compile benchmark [default=yes]]), + [use_benchmark=$enableval], + [use_benchmark=yes]) + +AC_ARG_ENABLE(coverage, + AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis [default=no]]), + [enable_coverage=$enableval], + [enable_coverage=no]) + +AC_ARG_ENABLE(tests, + AS_HELP_STRING([--enable-tests],[compile tests [default=yes]]), + [use_tests=$enableval], + [use_tests=yes]) + +AC_ARG_ENABLE(openssl_tests, + AS_HELP_STRING([--enable-openssl-tests],[enable OpenSSL tests [default=auto]]), + [enable_openssl_tests=$enableval], + [enable_openssl_tests=auto]) + +AC_ARG_ENABLE(experimental, + AS_HELP_STRING([--enable-experimental],[allow experimental configure options [default=no]]), + [use_experimental=$enableval], + [use_experimental=no]) + +AC_ARG_ENABLE(exhaustive_tests, + AS_HELP_STRING([--enable-exhaustive-tests],[compile exhaustive tests [default=yes]]), + [use_exhaustive_tests=$enableval], + [use_exhaustive_tests=yes]) + +AC_ARG_ENABLE(endomorphism, + AS_HELP_STRING([--enable-endomorphism],[enable endomorphism [default=no]]), + [use_endomorphism=$enableval], + [use_endomorphism=no]) + +AC_ARG_ENABLE(ecmult_static_precomputation, + AS_HELP_STRING([--enable-ecmult-static-precomputation],[enable precomputed ecmult table for signing [default=auto]]), + [use_ecmult_static_precomputation=$enableval], + [use_ecmult_static_precomputation=auto]) + +AC_ARG_ENABLE(module_ecdh, + AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation (experimental)]), + [enable_module_ecdh=$enableval], + [enable_module_ecdh=no]) + +AC_ARG_ENABLE(module_recovery, + AS_HELP_STRING([--enable-module-recovery],[enable ECDSA pubkey recovery module [default=no]]), + [enable_module_recovery=$enableval], + [enable_module_recovery=no]) + +AC_ARG_ENABLE(external_default_callbacks, + AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]), + [use_external_default_callbacks=$enableval], + [use_external_default_callbacks=no]) + +AC_ARG_WITH([field], [AS_HELP_STRING([--with-field=64bit|32bit|auto], +[finite field implementation to use [default=auto]])],[req_field=$withval], [req_field=auto]) + +AC_ARG_WITH([bignum], [AS_HELP_STRING([--with-bignum=gmp|no|auto], +[bignum implementation to use [default=auto]])],[req_bignum=$withval], [req_bignum=auto]) + +AC_ARG_WITH([scalar], [AS_HELP_STRING([--with-scalar=64bit|32bit|auto], +[scalar implementation to use [default=auto]])],[req_scalar=$withval], [req_scalar=auto]) + +AC_ARG_WITH([asm], [AS_HELP_STRING([--with-asm=x86_64|arm|no|auto], +[assembly optimizations to use (experimental: arm) [default=auto]])],[req_asm=$withval], [req_asm=auto]) + +AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto], +[window size for ecmult precomputation for verification, specified as integer in range [2..24].] +[Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.] +[The table will store 2^(SIZE-2) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.] +[If the endomorphism optimization is enabled, two tables of this size are used instead of only one.] +["auto" is a reasonable setting for desktop machines (currently 15). [default=auto]] +)], +[req_ecmult_window=$withval], [req_ecmult_window=auto]) + +AC_ARG_WITH([ecmult-gen-precision], [AS_HELP_STRING([--with-ecmult-gen-precision=2|4|8|auto], +[Precision bits to tune the precomputed table size for signing.] +[The size of the table is 32kB for 2 bits, 64kB for 4 bits, 512kB for 8 bits of precision.] +[A larger table size usually results in possible faster signing.] +["auto" is a reasonable setting for desktop machines (currently 4). [default=auto]] +)], +[req_ecmult_gen_precision=$withval], [req_ecmult_gen_precision=auto]) + +AC_CHECK_TYPES([__int128]) + +AC_CHECK_HEADER([valgrind/memcheck.h], [enable_valgrind=yes], [enable_valgrind=no], []) +AM_CONDITIONAL([VALGRIND_ENABLED],[test "$enable_valgrind" = "yes"]) + +if test x"$enable_coverage" = x"yes"; then + AC_DEFINE(COVERAGE, 1, [Define this symbol to compile out all VERIFY code]) + CFLAGS="-O0 --coverage $CFLAGS" + LDFLAGS="--coverage $LDFLAGS" +else + CFLAGS="-O2 $CFLAGS" +fi + +if test x"$use_ecmult_static_precomputation" != x"no"; then + # Temporarily switch to an environment for the native compiler + save_cross_compiling=$cross_compiling + cross_compiling=no + SAVE_CC="$CC" + CC="$CC_FOR_BUILD" + SAVE_CFLAGS="$CFLAGS" + CFLAGS="$CFLAGS_FOR_BUILD" + SAVE_CPPFLAGS="$CPPFLAGS" + CPPFLAGS="$CPPFLAGS_FOR_BUILD" + SAVE_LDFLAGS="$LDFLAGS" + LDFLAGS="$LDFLAGS_FOR_BUILD" + + warn_CFLAGS_FOR_BUILD="-Wall -Wextra -Wno-unused-function" + saved_CFLAGS="$CFLAGS" + CFLAGS="$warn_CFLAGS_FOR_BUILD $CFLAGS" + AC_MSG_CHECKING([if native ${CC_FOR_BUILD} supports ${warn_CFLAGS_FOR_BUILD}]) + AC_COMPILE_IFELSE([AC_LANG_SOURCE([[char foo;]])], + [ AC_MSG_RESULT([yes]) ], + [ AC_MSG_RESULT([no]) + CFLAGS="$saved_CFLAGS" + ]) + + AC_MSG_CHECKING([for working native compiler: ${CC_FOR_BUILD}]) + AC_RUN_IFELSE( + [AC_LANG_PROGRAM([], [])], + [working_native_cc=yes], + [working_native_cc=no],[:]) + + CFLAGS_FOR_BUILD="$CFLAGS" + + # Restore the environment + cross_compiling=$save_cross_compiling + CC="$SAVE_CC" + CFLAGS="$SAVE_CFLAGS" + CPPFLAGS="$SAVE_CPPFLAGS" + LDFLAGS="$SAVE_LDFLAGS" + + if test x"$working_native_cc" = x"no"; then + AC_MSG_RESULT([no]) + set_precomp=no + m4_define([please_set_for_build], [Please set CC_FOR_BUILD, CFLAGS_FOR_BUILD, CPPFLAGS_FOR_BUILD, and/or LDFLAGS_FOR_BUILD.]) + if test x"$use_ecmult_static_precomputation" = x"yes"; then + AC_MSG_ERROR([native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) + else + AC_MSG_WARN([Disabling statically generated ecmult table because the native compiler ${CC_FOR_BUILD} does not produce working binaries. please_set_for_build]) + fi + else + AC_MSG_RESULT([yes]) + set_precomp=yes + fi +else + set_precomp=no +fi + +if test x"$req_asm" = x"auto"; then + SECP_64BIT_ASM_CHECK + if test x"$has_64bit_asm" = x"yes"; then + set_asm=x86_64 + fi + if test x"$set_asm" = x; then + set_asm=no + fi +else + set_asm=$req_asm + case $set_asm in + x86_64) + SECP_64BIT_ASM_CHECK + if test x"$has_64bit_asm" != x"yes"; then + AC_MSG_ERROR([x86_64 assembly optimization requested but not available]) + fi + ;; + arm) + ;; + no) + ;; + *) + AC_MSG_ERROR([invalid assembly optimization selection]) + ;; + esac +fi + +if test x"$req_field" = x"auto"; then + if test x"set_asm" = x"x86_64"; then + set_field=64bit + fi + if test x"$set_field" = x; then + SECP_INT128_CHECK + if test x"$has_int128" = x"yes"; then + set_field=64bit + fi + fi + if test x"$set_field" = x; then + set_field=32bit + fi +else + set_field=$req_field + case $set_field in + 64bit) + if test x"$set_asm" != x"x86_64"; then + SECP_INT128_CHECK + if test x"$has_int128" != x"yes"; then + AC_MSG_ERROR([64bit field explicitly requested but neither __int128 support or x86_64 assembly available]) + fi + fi + ;; + 32bit) + ;; + *) + AC_MSG_ERROR([invalid field implementation selection]) + ;; + esac +fi + +if test x"$req_scalar" = x"auto"; then + SECP_INT128_CHECK + if test x"$has_int128" = x"yes"; then + set_scalar=64bit + fi + if test x"$set_scalar" = x; then + set_scalar=32bit + fi +else + set_scalar=$req_scalar + case $set_scalar in + 64bit) + SECP_INT128_CHECK + if test x"$has_int128" != x"yes"; then + AC_MSG_ERROR([64bit scalar explicitly requested but __int128 support not available]) + fi + ;; + 32bit) + ;; + *) + AC_MSG_ERROR([invalid scalar implementation selected]) + ;; + esac +fi + +if test x"$req_bignum" = x"auto"; then + SECP_GMP_CHECK + if test x"$has_gmp" = x"yes"; then + set_bignum=gmp + fi + + if test x"$set_bignum" = x; then + set_bignum=no + fi +else + set_bignum=$req_bignum + case $set_bignum in + gmp) + SECP_GMP_CHECK + if test x"$has_gmp" != x"yes"; then + AC_MSG_ERROR([gmp bignum explicitly requested but libgmp not available]) + fi + ;; + no) + ;; + *) + AC_MSG_ERROR([invalid bignum implementation selection]) + ;; + esac +fi + +# select assembly optimization +use_external_asm=no + +case $set_asm in +x86_64) + AC_DEFINE(USE_ASM_X86_64, 1, [Define this symbol to enable x86_64 assembly optimizations]) + ;; +arm) + use_external_asm=yes + ;; +no) + ;; +*) + AC_MSG_ERROR([invalid assembly optimizations]) + ;; +esac + +# select field implementation +case $set_field in +64bit) + AC_DEFINE(USE_FIELD_5X52, 1, [Define this symbol to use the FIELD_5X52 implementation]) + ;; +32bit) + AC_DEFINE(USE_FIELD_10X26, 1, [Define this symbol to use the FIELD_10X26 implementation]) + ;; +*) + AC_MSG_ERROR([invalid field implementation]) + ;; +esac + +# select bignum implementation +case $set_bignum in +gmp) + AC_DEFINE(HAVE_LIBGMP, 1, [Define this symbol if libgmp is installed]) + AC_DEFINE(USE_NUM_GMP, 1, [Define this symbol to use the gmp implementation for num]) + AC_DEFINE(USE_FIELD_INV_NUM, 1, [Define this symbol to use the num-based field inverse implementation]) + AC_DEFINE(USE_SCALAR_INV_NUM, 1, [Define this symbol to use the num-based scalar inverse implementation]) + ;; +no) + AC_DEFINE(USE_NUM_NONE, 1, [Define this symbol to use no num implementation]) + AC_DEFINE(USE_FIELD_INV_BUILTIN, 1, [Define this symbol to use the native field inverse implementation]) + AC_DEFINE(USE_SCALAR_INV_BUILTIN, 1, [Define this symbol to use the native scalar inverse implementation]) + ;; +*) + AC_MSG_ERROR([invalid bignum implementation]) + ;; +esac + +#select scalar implementation +case $set_scalar in +64bit) + AC_DEFINE(USE_SCALAR_4X64, 1, [Define this symbol to use the 4x64 scalar implementation]) + ;; +32bit) + AC_DEFINE(USE_SCALAR_8X32, 1, [Define this symbol to use the 8x32 scalar implementation]) + ;; +*) + AC_MSG_ERROR([invalid scalar implementation]) + ;; +esac + +#set ecmult window size +if test x"$req_ecmult_window" = x"auto"; then + set_ecmult_window=15 +else + set_ecmult_window=$req_ecmult_window +fi + +error_window_size=['window size for ecmult precomputation not an integer in range [2..24] or "auto"'] +case $set_ecmult_window in +''|*[[!0-9]]*) + # no valid integer + AC_MSG_ERROR($error_window_size) + ;; +*) + if test "$set_ecmult_window" -lt 2 -o "$set_ecmult_window" -gt 24 ; then + # not in range + AC_MSG_ERROR($error_window_size) + fi + AC_DEFINE_UNQUOTED(ECMULT_WINDOW_SIZE, $set_ecmult_window, [Set window size for ecmult precomputation]) + ;; +esac + +#set ecmult gen precision +if test x"$req_ecmult_gen_precision" = x"auto"; then + set_ecmult_gen_precision=4 +else + set_ecmult_gen_precision=$req_ecmult_gen_precision +fi + +case $set_ecmult_gen_precision in +2|4|8) + AC_DEFINE_UNQUOTED(ECMULT_GEN_PREC_BITS, $set_ecmult_gen_precision, [Set ecmult gen precision bits]) + ;; +*) + AC_MSG_ERROR(['ecmult gen precision not 2, 4, 8 or "auto"']) + ;; +esac + +if test x"$use_tests" = x"yes"; then + SECP_OPENSSL_CHECK + if test x"$has_openssl_ec" = x"yes"; then + if test x"$enable_openssl_tests" != x"no"; then + AC_DEFINE(ENABLE_OPENSSL_TESTS, 1, [Define this symbol if OpenSSL EC functions are available]) + SECP_TEST_INCLUDES="$SSL_CFLAGS $CRYPTO_CFLAGS $CRYPTO_CPPFLAGS" + SECP_TEST_LIBS="$CRYPTO_LIBS" + + case $host in + *mingw*) + SECP_TEST_LIBS="$SECP_TEST_LIBS -lgdi32" + ;; + esac + fi + else + if test x"$enable_openssl_tests" = x"yes"; then + AC_MSG_ERROR([OpenSSL tests requested but OpenSSL with EC support is not available]) + fi + fi +else + if test x"$enable_openssl_tests" = x"yes"; then + AC_MSG_ERROR([OpenSSL tests requested but tests are not enabled]) + fi +fi + +if test x"$set_bignum" = x"gmp"; then + SECP_LIBS="$SECP_LIBS $GMP_LIBS" + SECP_INCLUDES="$SECP_INCLUDES $GMP_CPPFLAGS" +fi + +if test x"$use_endomorphism" = x"yes"; then + AC_DEFINE(USE_ENDOMORPHISM, 1, [Define this symbol to use endomorphism optimization]) +fi + +if test x"$set_precomp" = x"yes"; then + AC_DEFINE(USE_ECMULT_STATIC_PRECOMPUTATION, 1, [Define this symbol to use a statically generated ecmult table]) +fi + +if test x"$enable_module_ecdh" = x"yes"; then + AC_DEFINE(ENABLE_MODULE_ECDH, 1, [Define this symbol to enable the ECDH module]) +fi + +if test x"$enable_module_recovery" = x"yes"; then + AC_DEFINE(ENABLE_MODULE_RECOVERY, 1, [Define this symbol to enable the ECDSA pubkey recovery module]) +fi + +AC_C_BIGENDIAN() + +if test x"$use_external_asm" = x"yes"; then + AC_DEFINE(USE_EXTERNAL_ASM, 1, [Define this symbol if an external (non-inline) assembly implementation is used]) +fi + +if test x"$use_external_default_callbacks" = x"yes"; then + AC_DEFINE(USE_EXTERNAL_DEFAULT_CALLBACKS, 1, [Define this symbol if an external implementation of the default callbacks is used]) +fi + +if test x"$enable_experimental" = x"yes"; then + AC_MSG_NOTICE([******]) + AC_MSG_NOTICE([WARNING: experimental build]) + AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.]) + AC_MSG_NOTICE([Building ECDH module: $enable_module_ecdh]) + AC_MSG_NOTICE([******]) +else + if test x"$enable_module_ecdh" = x"yes"; then + AC_MSG_ERROR([ECDH module is experimental. Use --enable-experimental to allow.]) + fi + if test x"$set_asm" = x"arm"; then + AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.]) + fi +fi + +AC_CONFIG_HEADERS([src/libsecp256k1-config.h]) +AC_CONFIG_FILES([Makefile libsecp256k1.pc]) +AC_SUBST(SECP_INCLUDES) +AC_SUBST(SECP_LIBS) +AC_SUBST(SECP_TEST_LIBS) +AC_SUBST(SECP_TEST_INCLUDES) +AM_CONDITIONAL([ENABLE_COVERAGE], [test x"$enable_coverage" = x"yes"]) +AM_CONDITIONAL([USE_TESTS], [test x"$use_tests" != x"no"]) +AM_CONDITIONAL([USE_EXHAUSTIVE_TESTS], [test x"$use_exhaustive_tests" != x"no"]) +AM_CONDITIONAL([USE_BENCHMARK], [test x"$use_benchmark" = x"yes"]) +AM_CONDITIONAL([USE_ECMULT_STATIC_PRECOMPUTATION], [test x"$set_precomp" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"]) +AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"]) +AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"]) + +dnl make sure nothing new is exported so that we don't break the cache +PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH" +unset PKG_CONFIG_PATH +PKG_CONFIG_PATH="$PKGCONFIG_PATH_TEMP" + +AC_OUTPUT + +echo +echo "Build Options:" +echo " with endomorphism = $use_endomorphism" +echo " with ecmult precomp = $set_precomp" +echo " with external callbacks = $use_external_default_callbacks" +echo " with benchmarks = $use_benchmark" +echo " with coverage = $enable_coverage" +echo " module ecdh = $enable_module_ecdh" +echo " module recovery = $enable_module_recovery" +echo +echo " asm = $set_asm" +echo " bignum = $set_bignum" +echo " field = $set_field" +echo " scalar = $set_scalar" +echo " ecmult window size = $set_ecmult_window" +echo " ecmult gen prec. bits = $set_ecmult_gen_precision" +echo +echo " valgrind = $enable_valgrind" +echo " CC = $CC" +echo " CFLAGS = $CFLAGS" +echo " CPPFLAGS = $CPPFLAGS" +echo " LDFLAGS = $LDFLAGS" +echo diff --git a/libsecp256k1/contrib/dummy.go b/libsecp256k1/contrib/dummy.go new file mode 100644 index 0000000..fda594b --- /dev/null +++ b/libsecp256k1/contrib/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package contrib diff --git a/libsecp256k1/contrib/lax_der_parsing.c b/libsecp256k1/contrib/lax_der_parsing.c new file mode 100644 index 0000000..e177a05 --- /dev/null +++ b/libsecp256k1/contrib/lax_der_parsing.c @@ -0,0 +1,150 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "lax_der_parsing.h" + +int ecdsa_signature_parse_der_lax(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + size_t rpos, rlen, spos, slen; + size_t pos = 0; + size_t lenbyte; + unsigned char tmpsig[64] = {0}; + int overflow = 0; + + /* Hack to initialize sig with a correctly-parsed but invalid signature. */ + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + + /* Sequence tag byte */ + if (pos == inputlen || input[pos] != 0x30) { + return 0; + } + pos++; + + /* Sequence length bytes */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + pos += lenbyte; + } + + /* Integer tag byte for R */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for R */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + rlen = 0; + while (lenbyte > 0) { + rlen = (rlen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + rlen = lenbyte; + } + if (rlen > inputlen - pos) { + return 0; + } + rpos = pos; + pos += rlen; + + /* Integer tag byte for S */ + if (pos == inputlen || input[pos] != 0x02) { + return 0; + } + pos++; + + /* Integer length for S */ + if (pos == inputlen) { + return 0; + } + lenbyte = input[pos++]; + if (lenbyte & 0x80) { + lenbyte -= 0x80; + if (lenbyte > inputlen - pos) { + return 0; + } + while (lenbyte > 0 && input[pos] == 0) { + pos++; + lenbyte--; + } + if (lenbyte >= sizeof(size_t)) { + return 0; + } + slen = 0; + while (lenbyte > 0) { + slen = (slen << 8) + input[pos]; + pos++; + lenbyte--; + } + } else { + slen = lenbyte; + } + if (slen > inputlen - pos) { + return 0; + } + spos = pos; + pos += slen; + + /* Ignore leading zeroes in R */ + while (rlen > 0 && input[rpos] == 0) { + rlen--; + rpos++; + } + /* Copy R value */ + if (rlen > 32) { + overflow = 1; + } else { + memcpy(tmpsig + 32 - rlen, input + rpos, rlen); + } + + /* Ignore leading zeroes in S */ + while (slen > 0 && input[spos] == 0) { + slen--; + spos++; + } + /* Copy S value */ + if (slen > 32) { + overflow = 1; + } else { + memcpy(tmpsig + 64 - slen, input + spos, slen); + } + + if (!overflow) { + overflow = !secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + if (overflow) { + memset(tmpsig, 0, 64); + secp256k1_ecdsa_signature_parse_compact(ctx, sig, tmpsig); + } + return 1; +} + diff --git a/libsecp256k1/contrib/lax_der_parsing.h b/libsecp256k1/contrib/lax_der_parsing.h new file mode 100644 index 0000000..7eaf63b --- /dev/null +++ b/libsecp256k1/contrib/lax_der_parsing.h @@ -0,0 +1,91 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file defines a function that parses DER with various errors and + * violations. This is not a part of the library itself, because the allowed + * violations are chosen arbitrarily and do not follow or establish any + * standard. + * + * In many places it matters that different implementations do not only accept + * the same set of valid signatures, but also reject the same set of signatures. + * The only means to accomplish that is by strictly obeying a standard, and not + * accepting anything else. + * + * Nonetheless, sometimes there is a need for compatibility with systems that + * use signatures which do not strictly obey DER. The snippet below shows how + * certain violations are easily supported. You may need to adapt it. + * + * Do not use this for new systems. Use well-defined DER or compact signatures + * instead if you have the choice (see secp256k1_ecdsa_signature_parse_der and + * secp256k1_ecdsa_signature_parse_compact). + * + * The supported violations are: + * - All numbers are parsed as nonnegative integers, even though X.609-0207 + * section 8.3.3 specifies that integers are always encoded as two's + * complement. + * - Integers can have length 0, even though section 8.3.1 says they can't. + * - Integers with overly long padding are accepted, violation section + * 8.3.2. + * - 127-byte long length descriptors are accepted, even though section + * 8.1.3.5.c says that they are not. + * - Trailing garbage data inside or after the signature is ignored. + * - The length descriptor of the sequence is ignored. + * + * Compared to for example OpenSSL, many violations are NOT supported: + * - Using overly long tag descriptors for the sequence or integers inside, + * violating section 8.1.2.2. + * - Encoding primitive integers as constructed values, violating section + * 8.3.1. + */ + +#ifndef SECP256K1_CONTRIB_LAX_DER_PARSING_H +#define SECP256K1_CONTRIB_LAX_DER_PARSING_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif + +/** Parse a signature in "lax DER" format + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. In addition, it will accept signatures + * which violate the DER spec in various ways. Its purpose is to allow + * validation of the Bitcoin blockchain, which includes non-DER signatures + * from before the network rules were updated to enforce DER. Note that + * the set of supported violations is a strict subset of what OpenSSL will + * accept. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +int ecdsa_signature_parse_der_lax( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_LAX_DER_PARSING_H */ diff --git a/libsecp256k1/contrib/lax_der_privatekey_parsing.c b/libsecp256k1/contrib/lax_der_privatekey_parsing.c new file mode 100644 index 0000000..c2e63b4 --- /dev/null +++ b/libsecp256k1/contrib/lax_der_privatekey_parsing.c @@ -0,0 +1,113 @@ +/********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "lax_der_privatekey_parsing.h" + +int ec_privkey_import_der(const secp256k1_context* ctx, unsigned char *out32, const unsigned char *privkey, size_t privkeylen) { + const unsigned char *end = privkey + privkeylen; + int lenb = 0; + int len = 0; + memset(out32, 0, 32); + /* sequence header */ + if (end < privkey+1 || *privkey != 0x30) { + return 0; + } + privkey++; + /* sequence length constructor */ + if (end < privkey+1 || !(*privkey & 0x80)) { + return 0; + } + lenb = *privkey & ~0x80; privkey++; + if (lenb < 1 || lenb > 2) { + return 0; + } + if (end < privkey+lenb) { + return 0; + } + /* sequence length */ + len = privkey[lenb-1] | (lenb > 1 ? privkey[lenb-2] << 8 : 0); + privkey += lenb; + if (end < privkey+len) { + return 0; + } + /* sequence element 0: version number (=1) */ + if (end < privkey+3 || privkey[0] != 0x02 || privkey[1] != 0x01 || privkey[2] != 0x01) { + return 0; + } + privkey += 3; + /* sequence element 1: octet string, up to 32 bytes */ + if (end < privkey+2 || privkey[0] != 0x04 || privkey[1] > 0x20 || end < privkey+2+privkey[1]) { + return 0; + } + memcpy(out32 + 32 - privkey[1], privkey + 2, privkey[1]); + if (!secp256k1_ec_seckey_verify(ctx, out32)) { + memset(out32, 0, 32); + return 0; + } + return 1; +} + +int ec_privkey_export_der(const secp256k1_context *ctx, unsigned char *privkey, size_t *privkeylen, const unsigned char *key32, int compressed) { + secp256k1_pubkey pubkey; + size_t pubkeylen = 0; + if (!secp256k1_ec_pubkey_create(ctx, &pubkey, key32)) { + *privkeylen = 0; + return 0; + } + if (compressed) { + static const unsigned char begin[] = { + 0x30,0x81,0xD3,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0x85,0x30,0x81,0x82,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x21,0x02,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x24,0x03,0x22,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 33; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } else { + static const unsigned char begin[] = { + 0x30,0x82,0x01,0x13,0x02,0x01,0x01,0x04,0x20 + }; + static const unsigned char middle[] = { + 0xA0,0x81,0xA5,0x30,0x81,0xA2,0x02,0x01,0x01,0x30,0x2C,0x06,0x07,0x2A,0x86,0x48, + 0xCE,0x3D,0x01,0x01,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F,0x30,0x06,0x04,0x01,0x00,0x04,0x01,0x07,0x04, + 0x41,0x04,0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0,0x62,0x95,0xCE,0x87, + 0x0B,0x07,0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98,0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,0x5D,0xA4,0xFB,0xFC,0x0E,0x11, + 0x08,0xA8,0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,0x9C,0x47,0xD0,0x8F,0xFB,0x10, + 0xD4,0xB8,0x02,0x21,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E, + 0x8C,0xD0,0x36,0x41,0x41,0x02,0x01,0x01,0xA1,0x44,0x03,0x42,0x00 + }; + unsigned char *ptr = privkey; + memcpy(ptr, begin, sizeof(begin)); ptr += sizeof(begin); + memcpy(ptr, key32, 32); ptr += 32; + memcpy(ptr, middle, sizeof(middle)); ptr += sizeof(middle); + pubkeylen = 65; + secp256k1_ec_pubkey_serialize(ctx, ptr, &pubkeylen, &pubkey, SECP256K1_EC_UNCOMPRESSED); + ptr += pubkeylen; + *privkeylen = ptr - privkey; + } + return 1; +} diff --git a/libsecp256k1/contrib/lax_der_privatekey_parsing.h b/libsecp256k1/contrib/lax_der_privatekey_parsing.h new file mode 100644 index 0000000..fece261 --- /dev/null +++ b/libsecp256k1/contrib/lax_der_privatekey_parsing.h @@ -0,0 +1,90 @@ +/********************************************************************** + * Copyright (c) 2014, 2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +/**** + * Please do not link this file directly. It is not part of the libsecp256k1 + * project and does not promise any stability in its API, functionality or + * presence. Projects which use this code should instead copy this header + * and its accompanying .c file directly into their codebase. + ****/ + +/* This file contains code snippets that parse DER private keys with + * various errors and violations. This is not a part of the library + * itself, because the allowed violations are chosen arbitrarily and + * do not follow or establish any standard. + * + * It also contains code to serialize private keys in a compatible + * manner. + * + * These functions are meant for compatibility with applications + * that require BER encoded keys. When working with secp256k1-specific + * code, the simple 32-byte private keys normally used by the + * library are sufficient. + */ + +#ifndef SECP256K1_CONTRIB_BER_PRIVATEKEY_H +#define SECP256K1_CONTRIB_BER_PRIVATEKEY_H + +#include + +#ifdef __cplusplus +extern "C" { +#endif + +/** Export a private key in DER format. + * + * Returns: 1 if the private key was valid. + * Args: ctx: pointer to a context object, initialized for signing (cannot + * be NULL) + * Out: privkey: pointer to an array for storing the private key in BER. + * Should have space for 279 bytes, and cannot be NULL. + * privkeylen: Pointer to an int where the length of the private key in + * privkey will be stored. + * In: seckey: pointer to a 32-byte secret key to export. + * compressed: 1 if the key should be exported in + * compressed format, 0 otherwise + * + * This function is purely meant for compatibility with applications that + * require BER encoded keys. When working with secp256k1-specific code, the + * simple 32-byte private keys are sufficient. + * + * Note that this function does not guarantee correct DER output. It is + * guaranteed to be parsable by secp256k1_ec_privkey_import_der + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_export_der( + const secp256k1_context* ctx, + unsigned char *privkey, + size_t *privkeylen, + const unsigned char *seckey, + int compressed +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Import a private key in DER format. + * Returns: 1 if a private key was extracted. + * Args: ctx: pointer to a context object (cannot be NULL). + * Out: seckey: pointer to a 32-byte array for storing the private key. + * (cannot be NULL). + * In: privkey: pointer to a private key in DER format (cannot be NULL). + * privkeylen: length of the DER private key pointed to be privkey. + * + * This function will accept more than just strict DER, and even allow some BER + * violations. The public key stored inside the DER-encoded private key is not + * verified for correctness, nor are the curve parameters. Use this function + * only if you know in advance it is supposed to contain a secp256k1 private + * key. + */ +SECP256K1_WARN_UNUSED_RESULT int ec_privkey_import_der( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *privkey, + size_t privkeylen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_CONTRIB_BER_PRIVATEKEY_H */ diff --git a/libsecp256k1/contrib/travis.sh b/libsecp256k1/contrib/travis.sh new file mode 100755 index 0000000..3909d16 --- /dev/null +++ b/libsecp256k1/contrib/travis.sh @@ -0,0 +1,65 @@ +#!/bin/sh + +set -e +set -x + +if [ -n "$HOST" ] +then + export USE_HOST="--host=$HOST" +fi +if [ "$HOST" = "i686-linux-gnu" ] +then + export CC="$CC -m32" +fi +if [ "$TRAVIS_OS_NAME" = "osx" ] && [ "$TRAVIS_COMPILER" = "gcc" ] +then + export CC="gcc-9" +fi + +./configure \ + --enable-experimental="$EXPERIMENTAL" --enable-endomorphism="$ENDOMORPHISM" \ + --with-field="$FIELD" --with-bignum="$BIGNUM" --with-asm="$ASM" --with-scalar="$SCALAR" \ + --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \ + --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" "$EXTRAFLAGS" "$USE_HOST" + +if [ -n "$BUILD" ] +then + make -j2 "$BUILD" +fi +if [ -n "$VALGRIND" ] +then + make -j2 + # the `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (http://valgrind.org/docs/manual/manual-core.html) + valgrind --error-exitcode=42 ./tests 16 + valgrind --error-exitcode=42 ./exhaustive_tests +fi +if [ -n "$BENCH" ] +then + if [ -n "$VALGRIND" ] + then + # Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool + EXEC='./libtool --mode=execute valgrind --error-exitcode=42' + else + EXEC= + fi + # This limits the iterations in the benchmarks below to ITER(set in .travis.yml) iterations. + export SECP256K1_BENCH_ITERS="$ITERS" + { + $EXEC ./bench_ecmult + $EXEC ./bench_internal + $EXEC ./bench_sign + $EXEC ./bench_verify + } >> bench.log 2>&1 + if [ "$RECOVERY" = "yes" ] + then + $EXEC ./bench_recover >> bench.log 2>&1 + fi + if [ "$ECDH" = "yes" ] + then + $EXEC ./bench_ecdh >> bench.log 2>&1 + fi +fi +if [ -n "$CTIMETEST" ] +then + ./libtool --mode=execute valgrind --error-exitcode=42 ./valgrind_ctime_test > valgrind_ctime_test.log 2>&1 +fi diff --git a/libsecp256k1/dummy.go b/libsecp256k1/dummy.go new file mode 100644 index 0000000..379b169 --- /dev/null +++ b/libsecp256k1/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package libsecp256k1 diff --git a/libsecp256k1/include/dummy.go b/libsecp256k1/include/dummy.go new file mode 100644 index 0000000..5af540c --- /dev/null +++ b/libsecp256k1/include/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package include diff --git a/libsecp256k1/include/secp256k1.h b/libsecp256k1/include/secp256k1.h new file mode 100644 index 0000000..2ba2dca --- /dev/null +++ b/libsecp256k1/include/secp256k1.h @@ -0,0 +1,764 @@ +#ifndef SECP256K1_H +#define SECP256K1_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include + +/* These rules specify the order of arguments in API calls: + * + * 1. Context pointers go first, followed by output arguments, combined + * output/input arguments, and finally input-only arguments. + * 2. Array lengths always immediately the follow the argument whose length + * they describe, even if this violates rule 1. + * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated + * later go first. This means: signatures, public nonces, secret nonces, + * messages, public keys, secret keys, tweaks. + * 4. Arguments that are not data pointers go last, from more complex to less + * complex: function pointers, algorithm names, messages, void pointers, + * counts, flags, booleans. + * 5. Opaque data pointers follow the function pointer they are to be passed to. + */ + +/** Opaque data structure that holds context information (precomputed tables etc.). + * + * The purpose of context structures is to cache large precomputed data tables + * that are expensive to construct, and also to maintain the randomization data + * for blinding. + * + * Do not create a new context object for each operation, as construction is + * far slower than all other API calls (~100 times slower than an ECDSA + * verification). + * + * A constructed context can safely be used from multiple threads + * simultaneously, but API calls that take a non-const pointer to a context + * need exclusive access to it. In particular this is the case for + * secp256k1_context_destroy, secp256k1_context_preallocated_destroy, + * and secp256k1_context_randomize. + * + * Regarding randomization, either do it once at creation time (in which case + * you do not need any locking for the other calls), or use a read-write lock. + */ +typedef struct secp256k1_context_struct secp256k1_context; + +/** Opaque data structure that holds rewriteable "scratch space" + * + * The purpose of this structure is to replace dynamic memory allocations, + * because we target architectures where this may not be available. It is + * essentially a resizable (within specified parameters) block of bytes, + * which is initially created either by memory allocation or TODO as a pointer + * into some fixed rewritable space. + * + * Unlike the context object, this cannot safely be shared between threads + * without additional synchronization logic. + */ +typedef struct secp256k1_scratch_space_struct secp256k1_scratch_space; + +/** Opaque data structure that holds a parsed and valid public key. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, or + * comparison, use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_pubkey; + +/** Opaque data structured that holds a parsed ECDSA signature. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 64 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage, transmission, or + * comparison, use the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + */ +typedef struct { + unsigned char data[64]; +} secp256k1_ecdsa_signature; + +/** A pointer to a function to deterministically generate a nonce. + * + * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail. + * Out: nonce32: pointer to a 32-byte array to be filled by the function. + * In: msg32: the 32-byte message hash being verified (will not be NULL) + * key32: pointer to a 32-byte secret key (will not be NULL) + * algo16: pointer to a 16-byte array describing the signature + * algorithm (will be NULL for ECDSA for compatibility). + * data: Arbitrary data pointer that is passed through. + * attempt: how many iterations we have tried to find a nonce. + * This will almost always be 0, but different attempt values + * are required to result in a different nonce. + * + * Except for test cases, this function should compute some cryptographic hash of + * the message, the algorithm, the key and the attempt. + */ +typedef int (*secp256k1_nonce_function)( + unsigned char *nonce32, + const unsigned char *msg32, + const unsigned char *key32, + const unsigned char *algo16, + void *data, + unsigned int attempt +); + +# if !defined(SECP256K1_GNUC_PREREQ) +# if defined(__GNUC__)&&defined(__GNUC_MINOR__) +# define SECP256K1_GNUC_PREREQ(_maj,_min) \ + ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min)) +# else +# define SECP256K1_GNUC_PREREQ(_maj,_min) 0 +# endif +# endif + +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(2,7) +# define SECP256K1_INLINE __inline__ +# elif (defined(_MSC_VER)) +# define SECP256K1_INLINE __inline +# else +# define SECP256K1_INLINE +# endif +# else +# define SECP256K1_INLINE inline +# endif + +#ifndef SECP256K1_API +# if defined(_WIN32) +# ifdef SECP256K1_BUILD +# define SECP256K1_API __declspec(dllexport) +# else +# define SECP256K1_API +# endif +# elif defined(__GNUC__) && defined(SECP256K1_BUILD) +# define SECP256K1_API __attribute__ ((visibility ("default"))) +# else +# define SECP256K1_API +# endif +#endif + +/**Warning attributes + * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out + * some paranoid null checks. */ +# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__)) +# else +# define SECP256K1_WARN_UNUSED_RESULT +# endif +# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4) +# define SECP256K1_ARG_NONNULL(_x) __attribute__ ((__nonnull__(_x))) +# else +# define SECP256K1_ARG_NONNULL(_x) +# endif + +/** All flags' lower 8 bits indicate what they're for. Do not use directly. */ +#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1) +#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0) +#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1) +/** The higher bits contain the actual data. Do not use directly. */ +#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8) +#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9) +#define SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY (1 << 10) +#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8) + +/** Flags to pass to secp256k1_context_create, secp256k1_context_preallocated_size, and + * secp256k1_context_preallocated_create. */ +#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) +#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN) +#define SECP256K1_CONTEXT_DECLASSIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY) +#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT) + +/** Flag to pass to secp256k1_ec_pubkey_serialize. */ +#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION) +#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION) + +/** Prefix byte used to tag various encoded curvepoints for specific purposes */ +#define SECP256K1_TAG_PUBKEY_EVEN 0x02 +#define SECP256K1_TAG_PUBKEY_ODD 0x03 +#define SECP256K1_TAG_PUBKEY_UNCOMPRESSED 0x04 +#define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06 +#define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07 + +/** A simple secp256k1 context object with no precomputed tables. These are useful for + * type serialization/parsing functions which require a context object to maintain + * API consistency, but currently do not require expensive precomputations or dynamic + * allocations. + */ +SECP256K1_API extern const secp256k1_context *secp256k1_context_no_precomp; + +/** Create a secp256k1 context object (in dynamically allocated memory). + * + * This function uses malloc to allocate memory. It is guaranteed that malloc is + * called at most once for every call of this function. If you need to avoid dynamic + * memory allocation entirely, see the functions in secp256k1_preallocated.h. + * + * Returns: a newly created context object. + * In: flags: which parts of the context to initialize. + * + * See also secp256k1_context_randomize. + */ +SECP256K1_API secp256k1_context* secp256k1_context_create( + unsigned int flags +) SECP256K1_WARN_UNUSED_RESULT; + +/** Copy a secp256k1 context object (into dynamically allocated memory). + * + * This function uses malloc to allocate memory. It is guaranteed that malloc is + * called at most once for every call of this function. If you need to avoid dynamic + * memory allocation entirely, see the functions in secp256k1_preallocated.h. + * + * Returns: a newly created context object. + * Args: ctx: an existing context to copy (cannot be NULL) + */ +SECP256K1_API secp256k1_context* secp256k1_context_clone( + const secp256k1_context* ctx +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Destroy a secp256k1 context object (created in dynamically allocated memory). + * + * The context pointer may not be used afterwards. + * + * The context to destroy must have been created using secp256k1_context_create + * or secp256k1_context_clone. If the context has instead been created using + * secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone, the + * behaviour is undefined. In that case, secp256k1_context_preallocated_destroy must + * be used instead. + * + * Args: ctx: an existing context to destroy, constructed using + * secp256k1_context_create or secp256k1_context_clone + */ +SECP256K1_API void secp256k1_context_destroy( + secp256k1_context* ctx +); + +/** Set a callback function to be called when an illegal argument is passed to + * an API call. It will only trigger for violations that are mentioned + * explicitly in the header. + * + * The philosophy is that these shouldn't be dealt with through a + * specific return value, as calling code should not have branches to deal with + * the case that this code itself is broken. + * + * On the other hand, during debug stage, one would want to be informed about + * such mistakes, and the default (crashing) may be inadvisable. + * When this callback is triggered, the API function called is guaranteed not + * to cause a crash, though its return value and output arguments are + * undefined. + * + * When this function has not been called (or called with fn==NULL), then the + * default handler will be used. The library provides a default handler which + * writes the message to stderr and calls abort. This default handler can be + * replaced at link time if the preprocessor macro + * USE_EXTERNAL_DEFAULT_CALLBACKS is defined, which is the case if the build + * has been configured with --enable-external-default-callbacks. Then the + * following two symbols must be provided to link against: + * - void secp256k1_default_illegal_callback_fn(const char* message, void* data); + * - void secp256k1_default_error_callback_fn(const char* message, void* data); + * The library can call these default handlers even before a proper callback data + * pointer could have been set using secp256k1_context_set_illegal_callback or + * secp256k1_context_set_error_callback, e.g., when the creation of a context + * fails. In this case, the corresponding default handler will be called with + * the data pointer argument set to NULL. + * + * Args: ctx: an existing context object (cannot be NULL) + * In: fun: a pointer to a function to call when an illegal argument is + * passed to the API, taking a message and an opaque pointer. + * (NULL restores the default handler.) + * data: the opaque pointer to pass to fun above. + * + * See also secp256k1_context_set_error_callback. + */ +SECP256K1_API void secp256k1_context_set_illegal_callback( + secp256k1_context* ctx, + void (*fun)(const char* message, void* data), + const void* data +) SECP256K1_ARG_NONNULL(1); + +/** Set a callback function to be called when an internal consistency check + * fails. The default is crashing. + * + * This can only trigger in case of a hardware failure, miscompilation, + * memory corruption, serious bug in the library, or other error would can + * otherwise result in undefined behaviour. It will not trigger due to mere + * incorrect usage of the API (see secp256k1_context_set_illegal_callback + * for that). After this callback returns, anything may happen, including + * crashing. + * + * Args: ctx: an existing context object (cannot be NULL) + * In: fun: a pointer to a function to call when an internal error occurs, + * taking a message and an opaque pointer (NULL restores the + * default handler, see secp256k1_context_set_illegal_callback + * for details). + * data: the opaque pointer to pass to fun above. + * + * See also secp256k1_context_set_illegal_callback. + */ +SECP256K1_API void secp256k1_context_set_error_callback( + secp256k1_context* ctx, + void (*fun)(const char* message, void* data), + const void* data +) SECP256K1_ARG_NONNULL(1); + +/** Create a secp256k1 scratch space object. + * + * Returns: a newly created scratch space. + * Args: ctx: an existing context object (cannot be NULL) + * In: size: amount of memory to be available as scratch space. Some extra + * (<100 bytes) will be allocated for extra accounting. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT secp256k1_scratch_space* secp256k1_scratch_space_create( + const secp256k1_context* ctx, + size_t size +) SECP256K1_ARG_NONNULL(1); + +/** Destroy a secp256k1 scratch space. + * + * The pointer may not be used afterwards. + * Args: ctx: a secp256k1 context object. + * scratch: space to destroy + */ +SECP256K1_API void secp256k1_scratch_space_destroy( + const secp256k1_context* ctx, + secp256k1_scratch_space* scratch +) SECP256K1_ARG_NONNULL(1); + +/** Parse a variable-length public key into the pubkey object. + * + * Returns: 1 if the public key was fully valid. + * 0 if the public key could not be parsed or is invalid. + * Args: ctx: a secp256k1 context object. + * Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a + * parsed version of input. If not, its value is undefined. + * In: input: pointer to a serialized public key + * inputlen: length of the array pointed to by input + * + * This function supports parsing compressed (33 bytes, header byte 0x02 or + * 0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header + * byte 0x06 or 0x07) format public keys. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse( + const secp256k1_context* ctx, + secp256k1_pubkey* pubkey, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize a pubkey object into a serialized byte sequence. + * + * Returns: 1 always. + * Args: ctx: a secp256k1 context object. + * Out: output: a pointer to a 65-byte (if compressed==0) or 33-byte (if + * compressed==1) byte array to place the serialized key + * in. + * In/Out: outputlen: a pointer to an integer which is initially set to the + * size of output, and is overwritten with the written + * size. + * In: pubkey: a pointer to a secp256k1_pubkey containing an + * initialized public key. + * flags: SECP256K1_EC_COMPRESSED if serialization should be in + * compressed format, otherwise SECP256K1_EC_UNCOMPRESSED. + */ +SECP256K1_API int secp256k1_ec_pubkey_serialize( + const secp256k1_context* ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_pubkey* pubkey, + unsigned int flags +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Parse an ECDSA signature in compact (64 bytes) format. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to the 64-byte array to parse + * + * The signature must consist of a 32-byte big endian R value, followed by a + * 32-byte big endian S value. If R or S fall outside of [0..order-1], the + * encoding is invalid. R and S with value 0 are allowed in the encoding. + * + * After the call, sig will always be initialized. If parsing failed or R or + * S are zero, the resulting sig value is guaranteed to fail validation for any + * message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_compact( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input64 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Parse a DER ECDSA signature. + * + * Returns: 1 when the signature could be parsed, 0 otherwise. + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input: a pointer to the signature to be parsed + * inputlen: the length of the array pointed to be input + * + * This function will accept any valid DER encoded signature, even if the + * encoded numbers are out of range. + * + * After the call, sig will always be initialized. If parsing failed or the + * encoded numbers are out of range, signature validation with it is + * guaranteed to fail for every message and public key. + */ +SECP256K1_API int secp256k1_ecdsa_signature_parse_der( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const unsigned char *input, + size_t inputlen +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in DER format. + * + * Returns: 1 if enough space was available to serialize, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: output: a pointer to an array to store the DER serialization + * In/Out: outputlen: a pointer to a length integer. Initially, this integer + * should be set to the length of output. After the call + * it will be set to the length of the serialization (even + * if 0 was returned). + * In: sig: a pointer to an initialized signature object + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_der( + const secp256k1_context* ctx, + unsigned char *output, + size_t *outputlen, + const secp256k1_ecdsa_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Serialize an ECDSA signature in compact (64 byte) format. + * + * Returns: 1 + * Args: ctx: a secp256k1 context object + * Out: output64: a pointer to a 64-byte array to store the compact serialization + * In: sig: a pointer to an initialized signature object + * + * See secp256k1_ecdsa_signature_parse_compact for details about the encoding. + */ +SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact( + const secp256k1_context* ctx, + unsigned char *output64, + const secp256k1_ecdsa_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Verify an ECDSA signature. + * + * Returns: 1: correct signature + * 0: incorrect or unparseable signature + * Args: ctx: a secp256k1 context object, initialized for verification. + * In: sig: the signature being verified (cannot be NULL) + * msg32: the 32-byte message hash being verified (cannot be NULL) + * pubkey: pointer to an initialized public key to verify with (cannot be NULL) + * + * To avoid accepting malleable signatures, only ECDSA signatures in lower-S + * form are accepted. + * + * If you need to accept ECDSA signatures from sources that do not obey this + * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to + * validation, but be aware that doing so results in malleable signatures. + * + * For details, see the comments for that function. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify( + const secp256k1_context* ctx, + const secp256k1_ecdsa_signature *sig, + const unsigned char *msg32, + const secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Convert a signature to a normalized lower-S form. + * + * Returns: 1 if sigin was not normalized, 0 if it already was. + * Args: ctx: a secp256k1 context object + * Out: sigout: a pointer to a signature to fill with the normalized form, + * or copy if the input was already normalized. (can be NULL if + * you're only interested in whether the input was already + * normalized). + * In: sigin: a pointer to a signature to check/normalize (cannot be NULL, + * can be identical to sigout) + * + * With ECDSA a third-party can forge a second distinct signature of the same + * message, given a single initial signature, but without knowing the key. This + * is done by negating the S value modulo the order of the curve, 'flipping' + * the sign of the random point R which is not included in the signature. + * + * Forgery of the same message isn't universally problematic, but in systems + * where message malleability or uniqueness of signatures is important this can + * cause issues. This forgery can be blocked by all verifiers forcing signers + * to use a normalized form. + * + * The lower-S form reduces the size of signatures slightly on average when + * variable length encodings (such as DER) are used and is cheap to verify, + * making it a good choice. Security of always using lower-S is assured because + * anyone can trivially modify a signature after the fact to enforce this + * property anyway. + * + * The lower S value is always between 0x1 and + * 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0, + * inclusive. + * + * No other forms of ECDSA malleability are known and none seem likely, but + * there is no formal proof that ECDSA, even with this additional restriction, + * is free of other malleability. Commonly used serialization schemes will also + * accept various non-unique encodings, so care should be taken when this + * property is required for an application. + * + * The secp256k1_ecdsa_sign function will by default create signatures in the + * lower-S form, and secp256k1_ecdsa_verify will not accept others. In case + * signatures come from a system that cannot enforce this property, + * secp256k1_ecdsa_signature_normalize must be called before verification. + */ +SECP256K1_API int secp256k1_ecdsa_signature_normalize( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature *sigout, + const secp256k1_ecdsa_signature *sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3); + +/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function. + * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of + * extra entropy. + */ +SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_rfc6979; + +/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */ +SECP256K1_API extern const secp256k1_nonce_function secp256k1_nonce_function_default; + +/** Create an ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the secret key was invalid. + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msg32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used + * ndata: pointer to arbitrary data used by the nonce generation function (can be NULL) + * + * The created signature is always in lower-S form. See + * secp256k1_ecdsa_signature_normalize for more details. + */ +SECP256K1_API int secp256k1_ecdsa_sign( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature *sig, + const unsigned char *msg32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Verify an ECDSA secret key. + * + * A secret key is valid if it is not 0 and less than the secp256k1 curve order + * when interpreted as an integer (most significant byte first). The + * probability of choosing a 32-byte string uniformly at random which is an + * invalid secret key is negligible. + * + * Returns: 1: secret key is valid + * 0: secret key is invalid + * Args: ctx: pointer to a context object (cannot be NULL) + * In: seckey: pointer to a 32-byte secret key (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify( + const secp256k1_context* ctx, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Compute the public key for a secret key. + * + * Returns: 1: secret was valid, public key stores + * 0: secret was invalid, try again + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: pubkey: pointer to the created public key (cannot be NULL) + * In: seckey: pointer to a 32-byte secret key (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Negates a secret key in place. + * + * Returns: 0 if the given secret key is invalid according to + * secp256k1_ec_seckey_verify. 1 otherwise + * Args: ctx: pointer to a context object + * In/Out: seckey: pointer to the 32-byte secret key to be negated. If the + * secret key is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0 and + * seckey will be set to some unspecified value. (cannot be + * NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_negate( + const secp256k1_context* ctx, + unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Same as secp256k1_ec_seckey_negate, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate( + const secp256k1_context* ctx, + unsigned char *seckey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Negates a public key in place. + * + * Returns: 1 always + * Args: ctx: pointer to a context object + * In/Out: pubkey: pointer to the public key to be negated (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2); + +/** Tweak a secret key by adding tweak to it. + * + * Returns: 0 if the arguments are invalid or the resulting secret key would be + * invalid (only when the tweak is the negation of the secret key). 1 + * otherwise. + * Args: ctx: pointer to a context object (cannot be NULL). + * In/Out: seckey: pointer to a 32-byte secret key. If the secret key is + * invalid according to secp256k1_ec_seckey_verify, this + * function returns 0. seckey will be set to some unspecified + * value if this function returns 0. (cannot be NULL) + * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128) (cannot be NULL). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Same as secp256k1_ec_seckey_tweak_add, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a public key by adding tweak times the generator to it. + * + * Returns: 0 if the arguments are invalid or the resulting public key would be + * invalid (only when the tweak is the negation of the corresponding + * secret key). 1 otherwise. + * Args: ctx: pointer to a context object initialized for validation + * (cannot be NULL). + * In/Out: pubkey: pointer to a public key object. pubkey will be set to an + * invalid value if this function returns 0 (cannot be NULL). + * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128) (cannot be NULL). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a secret key by multiplying it by a tweak. + * + * Returns: 0 if the arguments are invalid. 1 otherwise. + * Args: ctx: pointer to a context object (cannot be NULL). + * In/Out: seckey: pointer to a 32-byte secret key. If the secret key is + * invalid according to secp256k1_ec_seckey_verify, this + * function returns 0. seckey will be set to some unspecified + * value if this function returns 0. (cannot be NULL) + * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128) (cannot be NULL). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Same as secp256k1_ec_seckey_tweak_mul, but DEPRECATED. Will be removed in + * future versions. */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul( + const secp256k1_context* ctx, + unsigned char *seckey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Tweak a public key by multiplying it by a tweak value. + * + * Returns: 0 if the arguments are invalid. 1 otherwise. + * Args: ctx: pointer to a context object initialized for validation + * (cannot be NULL). + * In/Out: pubkey: pointer to a public key object. pubkey will be set to an + * invalid value if this function returns 0 (cannot be NULL). + * In: tweak: pointer to a 32-byte tweak. If the tweak is invalid according to + * secp256k1_ec_seckey_verify, this function returns 0. For + * uniformly random 32-byte arrays the chance of being invalid + * is negligible (around 1 in 2^128) (cannot be NULL). + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *tweak +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Updates the context randomization to protect against side-channel leakage. + * Returns: 1: randomization successfully updated or nothing to randomize + * 0: error + * Args: ctx: pointer to a context object (cannot be NULL) + * In: seed32: pointer to a 32-byte random seed (NULL resets to initial state) + * + * While secp256k1 code is written to be constant-time no matter what secret + * values are, it's possible that a future compiler may output code which isn't, + * and also that the CPU may not emit the same radio frequencies or draw the same + * amount power for all values. + * + * This function provides a seed which is combined into the blinding value: that + * blinding value is added before each multiplication (and removed afterwards) so + * that it does not affect function results, but shields against attacks which + * rely on any input-dependent behaviour. + * + * This function has currently an effect only on contexts initialized for signing + * because randomization is currently used only for signing. However, this is not + * guaranteed and may change in the future. It is safe to call this function on + * contexts not initialized for signing; then it will have no effect and return 1. + * + * You should call this after secp256k1_context_create or + * secp256k1_context_clone (and secp256k1_context_preallocated_create or + * secp256k1_context_clone, resp.), and you may call this repeatedly afterwards. + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize( + secp256k1_context* ctx, + const unsigned char *seed32 +) SECP256K1_ARG_NONNULL(1); + +/** Add a number of public keys together. + * + * Returns: 1: the sum of the public keys is valid. + * 0: the sum of the public keys is not valid. + * Args: ctx: pointer to a context object + * Out: out: pointer to a public key object for placing the resulting public key + * (cannot be NULL) + * In: ins: pointer to array of pointers to public keys (cannot be NULL) + * n: the number of public keys to add together (must be at least 1) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine( + const secp256k1_context* ctx, + secp256k1_pubkey *out, + const secp256k1_pubkey * const * ins, + size_t n +) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_H */ diff --git a/libsecp256k1/include/secp256k1_ecdh.h b/libsecp256k1/include/secp256k1_ecdh.h new file mode 100644 index 0000000..4058e9c --- /dev/null +++ b/libsecp256k1/include/secp256k1_ecdh.h @@ -0,0 +1,62 @@ +#ifndef SECP256K1_ECDH_H +#define SECP256K1_ECDH_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** A pointer to a function that hashes an EC point to obtain an ECDH secret + * + * Returns: 1 if the point was successfully hashed. + * 0 will cause secp256k1_ecdh to fail and return 0. + * Other return values are not allowed, and the behaviour of + * secp256k1_ecdh is undefined for other return values. + * Out: output: pointer to an array to be filled by the function + * In: x32: pointer to a 32-byte x coordinate + * y32: pointer to a 32-byte y coordinate + * data: arbitrary data pointer that is passed through + */ +typedef int (*secp256k1_ecdh_hash_function)( + unsigned char *output, + const unsigned char *x32, + const unsigned char *y32, + void *data +); + +/** An implementation of SHA256 hash function that applies to compressed public key. + * Populates the output parameter with 32 bytes. */ +SECP256K1_API extern const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256; + +/** A default ECDH hash function (currently equal to secp256k1_ecdh_hash_function_sha256). + * Populates the output parameter with 32 bytes. */ +SECP256K1_API extern const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default; + +/** Compute an EC Diffie-Hellman secret in constant time + * + * Returns: 1: exponentiation was successful + * 0: scalar was invalid (zero or overflow) or hashfp returned 0 + * Args: ctx: pointer to a context object (cannot be NULL) + * Out: output: pointer to an array to be filled by hashfp + * In: pubkey: a pointer to a secp256k1_pubkey containing an + * initialized public key + * seckey: a 32-byte scalar with which to multiply the point + * hashfp: pointer to a hash function. If NULL, secp256k1_ecdh_hash_function_sha256 is used + * (in which case, 32 bytes will be written to output) + * data: arbitrary data pointer that is passed through to hashfp + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh( + const secp256k1_context* ctx, + unsigned char *output, + const secp256k1_pubkey *pubkey, + const unsigned char *seckey, + secp256k1_ecdh_hash_function hashfp, + void *data +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_ECDH_H */ diff --git a/libsecp256k1/include/secp256k1_preallocated.h b/libsecp256k1/include/secp256k1_preallocated.h new file mode 100644 index 0000000..a9ae15d --- /dev/null +++ b/libsecp256k1/include/secp256k1_preallocated.h @@ -0,0 +1,128 @@ +#ifndef SECP256K1_PREALLOCATED_H +#define SECP256K1_PREALLOCATED_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/* The module provided by this header file is intended for settings in which it + * is not possible or desirable to rely on dynamic memory allocation. It provides + * functions for creating, cloning, and destroying secp256k1 context objects in a + * contiguous fixed-size block of memory provided by the caller. + * + * Context objects created by functions in this module can be used like contexts + * objects created by functions in secp256k1.h, i.e., they can be passed to any + * API function that expects a context object (see secp256k1.h for details). The + * only exception is that context objects created by functions in this module + * must be destroyed using secp256k1_context_preallocated_destroy (in this + * module) instead of secp256k1_context_destroy (in secp256k1.h). + * + * It is guaranteed that functions in this module will not call malloc or its + * friends realloc, calloc, and free. + */ + +/** Determine the memory size of a secp256k1 context object to be created in + * caller-provided memory. + * + * The purpose of this function is to determine how much memory must be provided + * to secp256k1_context_preallocated_create. + * + * Returns: the required size of the caller-provided memory block + * In: flags: which parts of the context to initialize. + */ +SECP256K1_API size_t secp256k1_context_preallocated_size( + unsigned int flags +) SECP256K1_WARN_UNUSED_RESULT; + +/** Create a secp256k1 context object in caller-provided memory. + * + * The caller must provide a pointer to a rewritable contiguous block of memory + * of size at least secp256k1_context_preallocated_size(flags) bytes, suitably + * aligned to hold an object of any type. + * + * The block of memory is exclusively owned by the created context object during + * the lifetime of this context object, which begins with the call to this + * function and ends when a call to secp256k1_context_preallocated_destroy + * (which destroys the context object again) returns. During the lifetime of the + * context object, the caller is obligated not to access this block of memory, + * i.e., the caller may not read or write the memory, e.g., by copying the memory + * contents to a different location or trying to create a second context object + * in the memory. In simpler words, the prealloc pointer (or any pointer derived + * from it) should not be used during the lifetime of the context object. + * + * Returns: a newly created context object. + * In: prealloc: a pointer to a rewritable contiguous block of memory of + * size at least secp256k1_context_preallocated_size(flags) + * bytes, as detailed above (cannot be NULL) + * flags: which parts of the context to initialize. + * + * See also secp256k1_context_randomize (in secp256k1.h) + * and secp256k1_context_preallocated_destroy. + */ +SECP256K1_API secp256k1_context* secp256k1_context_preallocated_create( + void* prealloc, + unsigned int flags +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Determine the memory size of a secp256k1 context object to be copied into + * caller-provided memory. + * + * Returns: the required size of the caller-provided memory block. + * In: ctx: an existing context to copy (cannot be NULL) + */ +SECP256K1_API size_t secp256k1_context_preallocated_clone_size( + const secp256k1_context* ctx +) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT; + +/** Copy a secp256k1 context object into caller-provided memory. + * + * The caller must provide a pointer to a rewritable contiguous block of memory + * of size at least secp256k1_context_preallocated_size(flags) bytes, suitably + * aligned to hold an object of any type. + * + * The block of memory is exclusively owned by the created context object during + * the lifetime of this context object, see the description of + * secp256k1_context_preallocated_create for details. + * + * Returns: a newly created context object. + * Args: ctx: an existing context to copy (cannot be NULL) + * In: prealloc: a pointer to a rewritable contiguous block of memory of + * size at least secp256k1_context_preallocated_size(flags) + * bytes, as detailed above (cannot be NULL) + */ +SECP256K1_API secp256k1_context* secp256k1_context_preallocated_clone( + const secp256k1_context* ctx, + void* prealloc +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_WARN_UNUSED_RESULT; + +/** Destroy a secp256k1 context object that has been created in + * caller-provided memory. + * + * The context pointer may not be used afterwards. + * + * The context to destroy must have been created using + * secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone. + * If the context has instead been created using secp256k1_context_create or + * secp256k1_context_clone, the behaviour is undefined. In that case, + * secp256k1_context_destroy must be used instead. + * + * If required, it is the responsibility of the caller to deallocate the block + * of memory properly after this function returns, e.g., by calling free on the + * preallocated pointer given to secp256k1_context_preallocated_create or + * secp256k1_context_preallocated_clone. + * + * Args: ctx: an existing context to destroy, constructed using + * secp256k1_context_preallocated_create or + * secp256k1_context_preallocated_clone (cannot be NULL) + */ +SECP256K1_API void secp256k1_context_preallocated_destroy( + secp256k1_context* ctx +); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PREALLOCATED_H */ diff --git a/libsecp256k1/include/secp256k1_recovery.h b/libsecp256k1/include/secp256k1_recovery.h new file mode 100644 index 0000000..f8ccaec --- /dev/null +++ b/libsecp256k1/include/secp256k1_recovery.h @@ -0,0 +1,110 @@ +#ifndef SECP256K1_RECOVERY_H +#define SECP256K1_RECOVERY_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/** Opaque data structured that holds a parsed ECDSA signature, + * supporting pubkey recovery. + * + * The exact representation of data inside is implementation defined and not + * guaranteed to be portable between different platforms or versions. It is + * however guaranteed to be 65 bytes in size, and can be safely copied/moved. + * If you need to convert to a format suitable for storage or transmission, use + * the secp256k1_ecdsa_signature_serialize_* and + * secp256k1_ecdsa_signature_parse_* functions. + * + * Furthermore, it is guaranteed that identical signatures (including their + * recoverability) will have identical representation, so they can be + * memcmp'ed. + */ +typedef struct { + unsigned char data[65]; +} secp256k1_ecdsa_recoverable_signature; + +/** Parse a compact ECDSA signature (64 bytes + recovery id). + * + * Returns: 1 when the signature could be parsed, 0 otherwise + * Args: ctx: a secp256k1 context object + * Out: sig: a pointer to a signature object + * In: input64: a pointer to a 64-byte compact signature + * recid: the recovery id (0, 1, 2 or 3) + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact( + const secp256k1_context* ctx, + secp256k1_ecdsa_recoverable_signature* sig, + const unsigned char *input64, + int recid +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Convert a recoverable signature into a normal signature. + * + * Returns: 1 + * Out: sig: a pointer to a normal signature (cannot be NULL). + * In: sigin: a pointer to a recoverable signature (cannot be NULL). + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert( + const secp256k1_context* ctx, + secp256k1_ecdsa_signature* sig, + const secp256k1_ecdsa_recoverable_signature* sigin +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +/** Serialize an ECDSA signature in compact format (64 bytes + recovery id). + * + * Returns: 1 + * Args: ctx: a secp256k1 context object + * Out: output64: a pointer to a 64-byte array of the compact signature (cannot be NULL) + * recid: a pointer to an integer to hold the recovery id (can be NULL). + * In: sig: a pointer to an initialized signature object (cannot be NULL) + */ +SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact( + const secp256k1_context* ctx, + unsigned char *output64, + int *recid, + const secp256k1_ecdsa_recoverable_signature* sig +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Create a recoverable ECDSA signature. + * + * Returns: 1: signature created + * 0: the nonce generation function failed, or the secret key was invalid. + * Args: ctx: pointer to a context object, initialized for signing (cannot be NULL) + * Out: sig: pointer to an array where the signature will be placed (cannot be NULL) + * In: msg32: the 32-byte message hash being signed (cannot be NULL) + * seckey: pointer to a 32-byte secret key (cannot be NULL) + * noncefp:pointer to a nonce generation function. If NULL, secp256k1_nonce_function_default is used + * ndata: pointer to arbitrary data used by the nonce generation function (can be NULL) + */ +SECP256K1_API int secp256k1_ecdsa_sign_recoverable( + const secp256k1_context* ctx, + secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msg32, + const unsigned char *seckey, + secp256k1_nonce_function noncefp, + const void *ndata +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Recover an ECDSA public key from a signature. + * + * Returns: 1: public key successfully recovered (which guarantees a correct signature). + * 0: otherwise. + * Args: ctx: pointer to a context object, initialized for verification (cannot be NULL) + * Out: pubkey: pointer to the recovered public key (cannot be NULL) + * In: sig: pointer to initialized signature that supports pubkey recovery (cannot be NULL) + * msg32: the 32-byte message hash assumed to be signed (cannot be NULL) + */ +SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const secp256k1_ecdsa_recoverable_signature *sig, + const unsigned char *msg32 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_RECOVERY_H */ diff --git a/libsecp256k1/libsecp256k1.pc.in b/libsecp256k1/libsecp256k1.pc.in new file mode 100644 index 0000000..694e98e --- /dev/null +++ b/libsecp256k1/libsecp256k1.pc.in @@ -0,0 +1,13 @@ +prefix=@prefix@ +exec_prefix=@exec_prefix@ +libdir=@libdir@ +includedir=@includedir@ + +Name: libsecp256k1 +Description: Optimized C library for EC operations on curve secp256k1 +URL: https://github.com/bitcoin-core/secp256k1 +Version: @PACKAGE_VERSION@ +Cflags: -I${includedir} +Libs: -L${libdir} -lsecp256k1 +Libs.private: @SECP_LIBS@ + diff --git a/libsecp256k1/obj/.gitignore b/libsecp256k1/obj/.gitignore new file mode 100644 index 0000000..e69de29 diff --git a/libsecp256k1/sage/group_prover.sage b/libsecp256k1/sage/group_prover.sage new file mode 100644 index 0000000..8521f07 --- /dev/null +++ b/libsecp256k1/sage/group_prover.sage @@ -0,0 +1,322 @@ +# This code supports verifying group implementations which have branches +# or conditional statements (like cmovs), by allowing each execution path +# to independently set assumptions on input or intermediary variables. +# +# The general approach is: +# * A constraint is a tuple of two sets of symbolic expressions: +# the first of which are required to evaluate to zero, the second of which +# are required to evaluate to nonzero. +# - A constraint is said to be conflicting if any of its nonzero expressions +# is in the ideal with basis the zero expressions (in other words: when the +# zero expressions imply that one of the nonzero expressions are zero). +# * There is a list of laws that describe the intended behaviour, including +# laws for addition and doubling. Each law is called with the symbolic point +# coordinates as arguments, and returns: +# - A constraint describing the assumptions under which it is applicable, +# called "assumeLaw" +# - A constraint describing the requirements of the law, called "require" +# * Implementations are transliterated into functions that operate as well on +# algebraic input points, and are called once per combination of branches +# executed. Each execution returns: +# - A constraint describing the assumptions this implementation requires +# (such as Z1=1), called "assumeFormula" +# - A constraint describing the assumptions this specific branch requires, +# but which is by construction guaranteed to cover the entire space by +# merging the results from all branches, called "assumeBranch" +# - The result of the computation +# * All combinations of laws with implementation branches are tried, and: +# - If the combination of assumeLaw, assumeFormula, and assumeBranch results +# in a conflict, it means this law does not apply to this branch, and it is +# skipped. +# - For others, we try to prove the require constraints hold, assuming the +# information in assumeLaw + assumeFormula + assumeBranch, and if this does +# not succeed, we fail. +# + To prove an expression is zero, we check whether it belongs to the +# ideal with the assumed zero expressions as basis. This test is exact. +# + To prove an expression is nonzero, we check whether each of its +# factors is contained in the set of nonzero assumptions' factors. +# This test is not exact, so various combinations of original and +# reduced expressions' factors are tried. +# - If we succeed, we print out the assumptions from assumeFormula that +# weren't implied by assumeLaw already. Those from assumeBranch are skipped, +# as we assume that all constraints in it are complementary with each other. +# +# Based on the sage verification scripts used in the Explicit-Formulas Database +# by Tanja Lange and others, see http://hyperelliptic.org/EFD + +class fastfrac: + """Fractions over rings.""" + + def __init__(self,R,top,bot=1): + """Construct a fractional, given a ring, a numerator, and denominator.""" + self.R = R + if parent(top) == ZZ or parent(top) == R: + self.top = R(top) + self.bot = R(bot) + elif top.__class__ == fastfrac: + self.top = top.top + self.bot = top.bot * bot + else: + self.top = R(numerator(top)) + self.bot = R(denominator(top)) * bot + + def iszero(self,I): + """Return whether this fraction is zero given an ideal.""" + return self.top in I and self.bot not in I + + def reduce(self,assumeZero): + zero = self.R.ideal(map(numerator, assumeZero)) + return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot)) + + def __add__(self,other): + """Add two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top + self.bot * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot + self.bot * other.top,self.bot * other.bot) + return NotImplemented + + def __sub__(self,other): + """Subtract two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top - self.bot * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot - self.bot * other.top,self.bot * other.bot) + return NotImplemented + + def __neg__(self): + """Return the negation of a fraction.""" + return fastfrac(self.R,-self.top,self.bot) + + def __mul__(self,other): + """Multiply two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top * other,self.bot) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.top,self.bot * other.bot) + return NotImplemented + + def __rmul__(self,other): + """Multiply something else with a fraction.""" + return self.__mul__(other) + + def __div__(self,other): + """Divide two fractions.""" + if parent(other) == ZZ: + return fastfrac(self.R,self.top,self.bot * other) + if other.__class__ == fastfrac: + return fastfrac(self.R,self.top * other.bot,self.bot * other.top) + return NotImplemented + + def __pow__(self,other): + """Compute a power of a fraction.""" + if parent(other) == ZZ: + if other < 0: + # Negative powers require flipping top and bottom + return fastfrac(self.R,self.bot ^ (-other),self.top ^ (-other)) + else: + return fastfrac(self.R,self.top ^ other,self.bot ^ other) + return NotImplemented + + def __str__(self): + return "fastfrac((" + str(self.top) + ") / (" + str(self.bot) + "))" + def __repr__(self): + return "%s" % self + + def numerator(self): + return self.top + +class constraints: + """A set of constraints, consisting of zero and nonzero expressions. + + Constraints can either be used to express knowledge or a requirement. + + Both the fields zero and nonzero are maps from expressions to description + strings. The expressions that are the keys in zero are required to be zero, + and the expressions that are the keys in nonzero are required to be nonzero. + + Note that (a != 0) and (b != 0) is the same as (a*b != 0), so all keys in + nonzero could be multiplied into a single key. This is often much less + efficient to work with though, so we keep them separate inside the + constraints. This allows higher-level code to do fast checks on the individual + nonzero elements, or combine them if needed for stronger checks. + + We can't multiply the different zero elements, as it would suffice for one of + the factors to be zero, instead of all of them. Instead, the zero elements are + typically combined into an ideal first. + """ + + def __init__(self, **kwargs): + if 'zero' in kwargs: + self.zero = dict(kwargs['zero']) + else: + self.zero = dict() + if 'nonzero' in kwargs: + self.nonzero = dict(kwargs['nonzero']) + else: + self.nonzero = dict() + + def negate(self): + return constraints(zero=self.nonzero, nonzero=self.zero) + + def __add__(self, other): + zero = self.zero.copy() + zero.update(other.zero) + nonzero = self.nonzero.copy() + nonzero.update(other.nonzero) + return constraints(zero=zero, nonzero=nonzero) + + def __str__(self): + return "constraints(zero=%s,nonzero=%s)" % (self.zero, self.nonzero) + + def __repr__(self): + return "%s" % self + + +def conflicts(R, con): + """Check whether any of the passed non-zero assumptions is implied by the zero assumptions""" + zero = R.ideal(map(numerator, con.zero)) + if 1 in zero: + return True + # First a cheap check whether any of the individual nonzero terms conflict on + # their own. + for nonzero in con.nonzero: + if nonzero.iszero(zero): + return True + # It can be the case that entries in the nonzero set do not individually + # conflict with the zero set, but their combination does. For example, knowing + # that either x or y is zero is equivalent to having x*y in the zero set. + # Having x or y individually in the nonzero set is not a conflict, but both + # simultaneously is, so that is the right thing to check for. + if reduce(lambda a,b: a * b, con.nonzero, fastfrac(R, 1)).iszero(zero): + return True + return False + + +def get_nonzero_set(R, assume): + """Calculate a simple set of nonzero expressions""" + zero = R.ideal(map(numerator, assume.zero)) + nonzero = set() + for nz in map(numerator, assume.nonzero): + for (f,n) in nz.factor(): + nonzero.add(f) + rnz = zero.reduce(nz) + for (f,n) in rnz.factor(): + nonzero.add(f) + return nonzero + + +def prove_nonzero(R, exprs, assume): + """Check whether an expression is provably nonzero, given assumptions""" + zero = R.ideal(map(numerator, assume.zero)) + nonzero = get_nonzero_set(R, assume) + expl = set() + ok = True + for expr in exprs: + if numerator(expr) in zero: + return (False, [exprs[expr]]) + allexprs = reduce(lambda a,b: numerator(a)*numerator(b), exprs, 1) + for (f, n) in allexprs.factor(): + if f not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for (f, n) in zero.reduce(numerator(allexprs)).factor(): + if f not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for expr in exprs: + for (f,n) in numerator(expr).factor(): + if f not in nonzero: + ok = False + if ok: + return (True, None) + ok = True + for expr in exprs: + for (f,n) in zero.reduce(numerator(expr)).factor(): + if f not in nonzero: + expl.add(exprs[expr]) + if expl: + return (False, list(expl)) + else: + return (True, None) + + +def prove_zero(R, exprs, assume): + """Check whether all of the passed expressions are provably zero, given assumptions""" + r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume) + if not r: + return (False, map(lambda x: "Possibly zero denominator: %s" % x, e)) + zero = R.ideal(map(numerator, assume.zero)) + nonzero = prod(x for x in assume.nonzero) + expl = [] + for expr in exprs: + if not expr.iszero(zero): + expl.append(exprs[expr]) + if not expl: + return (True, None) + return (False, expl) + + +def describe_extra(R, assume, assumeExtra): + """Describe what assumptions are added, given existing assumptions""" + zerox = assume.zero.copy() + zerox.update(assumeExtra.zero) + zero = R.ideal(map(numerator, assume.zero)) + zeroextra = R.ideal(map(numerator, zerox)) + nonzero = get_nonzero_set(R, assume) + ret = set() + # Iterate over the extra zero expressions + for base in assumeExtra.zero: + if base not in zero: + add = [] + for (f, n) in numerator(base).factor(): + if f not in nonzero: + add += ["%s" % f] + if add: + ret.add((" * ".join(add)) + " = 0 [%s]" % assumeExtra.zero[base]) + # Iterate over the extra nonzero expressions + for nz in assumeExtra.nonzero: + nzr = zeroextra.reduce(numerator(nz)) + if nzr not in zeroextra: + for (f,n) in nzr.factor(): + if zeroextra.reduce(f) not in nonzero: + ret.add("%s != 0" % zeroextra.reduce(f)) + return ", ".join(x for x in ret) + + +def check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require): + """Check a set of zero and nonzero requirements, given a set of zero and nonzero assumptions""" + assume = assumeLaw + assumeAssert + assumeBranch + + if conflicts(R, assume): + # This formula does not apply + return None + + describe = describe_extra(R, assumeLaw + assumeBranch, assumeAssert) + + ok, msg = prove_zero(R, require.zero, assume) + if not ok: + return "FAIL, %s fails (assuming %s)" % (str(msg), describe) + + res, expl = prove_nonzero(R, require.nonzero, assume) + if not res: + return "FAIL, %s fails (assuming %s)" % (str(expl), describe) + + if describe != "": + return "OK (assuming %s)" % describe + else: + return "OK" + + +def concrete_verify(c): + for k in c.zero: + if k != 0: + return (False, c.zero[k]) + for k in c.nonzero: + if k == 0: + return (False, c.nonzero[k]) + return (True, None) diff --git a/libsecp256k1/sage/secp256k1.sage b/libsecp256k1/sage/secp256k1.sage new file mode 100644 index 0000000..a97e732 --- /dev/null +++ b/libsecp256k1/sage/secp256k1.sage @@ -0,0 +1,306 @@ +# Test libsecp256k1' group operation implementations using prover.sage + +import sys + +load("group_prover.sage") +load("weierstrass_prover.sage") + +def formula_secp256k1_gej_double_var(a): + """libsecp256k1's secp256k1_gej_double_var, used by various addition functions""" + rz = a.Z * a.Y + rz = rz * 2 + t1 = a.X^2 + t1 = t1 * 3 + t2 = t1^2 + t3 = a.Y^2 + t3 = t3 * 2 + t4 = t3^2 + t4 = t4 * 2 + t3 = t3 * a.X + rx = t3 + rx = rx * 4 + rx = -rx + rx = rx + t2 + t2 = -t2 + t3 = t3 * 6 + t3 = t3 + t2 + ry = t1 * t3 + t2 = -t4 + ry = ry + t2 + return jacobianpoint(rx, ry, rz) + +def formula_secp256k1_gej_add_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_var""" + if branch == 0: + return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z22 = b.Z^2 + z12 = a.Z^2 + u1 = a.X * z22 + u2 = b.X * z12 + s1 = a.Y * z22 + s1 = s1 * b.Z + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r) + if branch == 3: + return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h2 * h + h = h * b.Z + rz = a.Z * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1""" + if branch == 0: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z12 = a.Z^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if (branch == 2): + r = formula_secp256k1_gej_double_var(a) + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if (branch == 3): + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h * h2 + rz = a.Z * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_zinv_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_zinv_var""" + bzinv = b.Z^(-1) + if branch == 0: + return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a) + if branch == 1: + bzinv2 = bzinv^2 + bzinv3 = bzinv2 * bzinv + rx = b.X * bzinv2 + ry = b.Y * bzinv3 + rz = 1 + return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz)) + azz = a.Z * bzinv + z12 = azz^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * azz + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if branch == 3: + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h * h2 + rz = a.Z + rz = rz * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge""" + zeroes = {} + nonzeroes = {} + a_infinity = False + if (branch & 4) != 0: + nonzeroes.update({a.Infinity : 'a_infinite'}) + a_infinity = True + else: + zeroes.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + rr = t^2 + m_alt = -u2 + tt = u1 * m_alt + rr = rr + tt + degenerate = (branch & 3) == 3 + if (branch & 1) != 0: + zeroes.update({m : 'm_zero'}) + else: + nonzeroes.update({m : 'm_nonzero'}) + if (branch & 2) != 0: + zeroes.update({rr : 'rr_zero'}) + else: + nonzeroes.update({rr : 'rr_nonzero'}) + rr_alt = s1 + rr_alt = rr_alt * 2 + m_alt = m_alt + u1 + if not degenerate: + rr_alt = rr + m_alt = m + n = m_alt^2 + q = n * t + n = n^2 + if degenerate: + n = m + t = rr_alt^2 + rz = a.Z * m_alt + infinity = False + if (branch & 8) != 0: + if not a_infinity: + infinity = True + zeroes.update({rz : 'r.z=0'}) + else: + nonzeroes.update({rz : 'r.z!=0'}) + rz = rz * 2 + q = -q + t = t + q + rx = t + t = t * 2 + t = t + q + t = t * rr_alt + t = t + n + ry = -t + rx = rx * 4 + ry = ry * 4 + if a_infinity: + rx = b.X + ry = b.Y + rz = 1 + if infinity: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity()) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge_old(branch, a, b): + """libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx""" + a_infinity = (branch & 1) != 0 + zero = {} + nonzero = {} + if a_infinity: + nonzero.update({a.Infinity : 'a_infinite'}) + else: + zero.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + z = a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + n = m^2 + q = n * t + n = n^2 + rr = t^2 + t = u1 * u2 + t = -t + rr = rr + t + t = rr^2 + rz = m * z + infinity = False + if (branch & 2) != 0: + if not a_infinity: + infinity = True + else: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity()) + zero.update({rz : 'r.z=0'}) + else: + nonzero.update({rz : 'r.z!=0'}) + rz = rz * (0 if a_infinity else 2) + rx = t + q = -q + rx = rx + q + q = q * 3 + t = t * 2 + t = t + q + t = t * rr + t = t + n + ry = -t + rx = rx * (0 if a_infinity else 4) + ry = ry * (0 if a_infinity else 4) + t = b.X + t = t * (1 if a_infinity else 0) + rx = rx + t + t = b.Y + t = t * (1 if a_infinity else 0) + ry = ry + t + t = (1 if a_infinity else 0) + rz = rz + t + if infinity: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity()) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz)) + +if __name__ == "__main__": + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old) + + if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive": + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43) diff --git a/libsecp256k1/sage/weierstrass_prover.sage b/libsecp256k1/sage/weierstrass_prover.sage new file mode 100644 index 0000000..03ef2ec --- /dev/null +++ b/libsecp256k1/sage/weierstrass_prover.sage @@ -0,0 +1,264 @@ +# Prover implementation for Weierstrass curves of the form +# y^2 = x^3 + A * x + B, specifically with a = 0 and b = 7, with group laws +# operating on affine and Jacobian coordinates, including the point at infinity +# represented by a 4th variable in coordinates. + +load("group_prover.sage") + + +class affinepoint: + def __init__(self, x, y, infinity=0): + self.x = x + self.y = y + self.infinity = infinity + def __str__(self): + return "affinepoint(x=%s,y=%s,inf=%s)" % (self.x, self.y, self.infinity) + + +class jacobianpoint: + def __init__(self, x, y, z, infinity=0): + self.X = x + self.Y = y + self.Z = z + self.Infinity = infinity + def __str__(self): + return "jacobianpoint(X=%s,Y=%s,Z=%s,inf=%s)" % (self.X, self.Y, self.Z, self.Infinity) + + +def point_at_infinity(): + return jacobianpoint(1, 1, 1, 1) + + +def negate(p): + if p.__class__ == affinepoint: + return affinepoint(p.x, -p.y) + if p.__class__ == jacobianpoint: + return jacobianpoint(p.X, -p.Y, p.Z) + assert(False) + + +def on_weierstrass_curve(A, B, p): + """Return a set of zero-expressions for an affine point to be on the curve""" + return constraints(zero={p.x^3 + A*p.x + B - p.y^2: 'on_curve'}) + + +def tangential_to_weierstrass_curve(A, B, p12, p3): + """Return a set of zero-expressions for ((x12,y12),(x3,y3)) to be a line that is tangential to the curve at (x12,y12)""" + return constraints(zero={ + (p12.y - p3.y) * (p12.y * 2) - (p12.x^2 * 3 + A) * (p12.x - p3.x): 'tangential_to_curve' + }) + + +def colinear(p1, p2, p3): + """Return a set of zero-expressions for ((x1,y1),(x2,y2),(x3,y3)) to be collinear""" + return constraints(zero={ + (p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x): 'colinear_1', + (p2.y - p3.y) * (p2.x - p1.x) - (p2.y - p1.y) * (p2.x - p3.x): 'colinear_2', + (p3.y - p1.y) * (p3.x - p2.x) - (p3.y - p2.y) * (p3.x - p1.x): 'colinear_3' + }) + + +def good_affine_point(p): + return constraints(nonzero={p.x : 'nonzero_x', p.y : 'nonzero_y'}) + + +def good_jacobian_point(p): + return constraints(nonzero={p.X : 'nonzero_X', p.Y : 'nonzero_Y', p.Z^6 : 'nonzero_Z'}) + + +def good_point(p): + return constraints(nonzero={p.Z^6 : 'nonzero_X'}) + + +def finite(p, *affine_fns): + con = good_point(p) + constraints(zero={p.Infinity : 'finite_point'}) + if p.Z != 0: + return con + reduce(lambda a, b: a + b, (f(affinepoint(p.X / p.Z^2, p.Y / p.Z^3)) for f in affine_fns), con) + else: + return con + +def infinite(p): + return constraints(nonzero={p.Infinity : 'infinite_point'}) + + +def law_jacobian_weierstrass_add(A, B, pa, pb, pA, pB, pC): + """Check whether the passed set of coordinates is a valid Jacobian add, given assumptions""" + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(nonzero={pa.x - pb.x : 'different_x'})) + require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) + + colinear(pa, pb, negate(pc)))) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_double(A, B, pa, pb, pA, pB, pC): + """Check whether the passed set of coordinates is a valid Jacobian doubling, given assumptions""" + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(zero={pa.x - pb.x : 'equal_x', pa.y - pb.y : 'equal_y'})) + require = (finite(pC, lambda pc: on_weierstrass_curve(A, B, pc) + + tangential_to_weierstrass_curve(A, B, pa, negate(pc)))) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_opposites(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + on_weierstrass_curve(A, B, pb) + + finite(pA) + + finite(pB) + + constraints(zero={pa.x - pb.x : 'equal_x', pa.y + pb.y : 'opposite_y'})) + require = infinite(pC) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_a(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pb) + + infinite(pA) + + finite(pB)) + require = finite(pC, lambda pc: constraints(zero={pc.x - pb.x : 'c.x=b.x', pc.y - pb.y : 'c.y=b.y'})) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_b(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + on_weierstrass_curve(A, B, pa) + + infinite(pB) + + finite(pA)) + require = finite(pC, lambda pc: constraints(zero={pc.x - pa.x : 'c.x=a.x', pc.y - pa.y : 'c.y=a.y'})) + return (assumeLaw, require) + + +def law_jacobian_weierstrass_add_infinite_ab(A, B, pa, pb, pA, pB, pC): + assumeLaw = (good_affine_point(pa) + + good_affine_point(pb) + + good_jacobian_point(pA) + + good_jacobian_point(pB) + + infinite(pA) + + infinite(pB)) + require = infinite(pC) + return (assumeLaw, require) + + +laws_jacobian_weierstrass = { + 'add': law_jacobian_weierstrass_add, + 'double': law_jacobian_weierstrass_double, + 'add_opposite': law_jacobian_weierstrass_add_opposites, + 'add_infinite_a': law_jacobian_weierstrass_add_infinite_a, + 'add_infinite_b': law_jacobian_weierstrass_add_infinite_b, + 'add_infinite_ab': law_jacobian_weierstrass_add_infinite_ab +} + + +def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p): + """Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field""" + F = Integers(p) + print "Formula %s on Z%i:" % (name, p) + points = [] + for x in xrange(0, p): + for y in xrange(0, p): + point = affinepoint(F(x), F(y)) + r, e = concrete_verify(on_weierstrass_curve(A, B, point)) + if r: + points.append(point) + + for za in xrange(1, p): + for zb in xrange(1, p): + for pa in points: + for pb in points: + for ia in xrange(2): + for ib in xrange(2): + pA = jacobianpoint(pa.x * F(za)^2, pa.y * F(za)^3, F(za), ia) + pB = jacobianpoint(pb.x * F(zb)^2, pb.y * F(zb)^3, F(zb), ib) + for branch in xrange(0, branches): + assumeAssert, assumeBranch, pC = formula(branch, pA, pB) + pC.X = F(pC.X) + pC.Y = F(pC.Y) + pC.Z = F(pC.Z) + pC.Infinity = F(pC.Infinity) + r, e = concrete_verify(assumeAssert + assumeBranch) + if r: + match = False + for key in laws_jacobian_weierstrass: + assumeLaw, require = laws_jacobian_weierstrass[key](A, B, pa, pb, pA, pB, pC) + r, e = concrete_verify(assumeLaw) + if r: + if match: + print " multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity) + else: + match = True + r, e = concrete_verify(require) + if not r: + print " failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e) + print + + +def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC): + assumeLaw, require = f(A, B, pa, pb, pA, pB, pC) + return check_symbolic(R, assumeLaw, assumeAssert, assumeBranch, require) + +def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): + """Verify an implementation of addition of Jacobian points on a Weierstrass curve symbolically""" + R. = PolynomialRing(QQ,8,order='invlex') + lift = lambda x: fastfrac(R,x) + ax = lift(ax) + ay = lift(ay) + Az = lift(Az) + bx = lift(bx) + by = lift(by) + Bz = lift(Bz) + Ai = lift(Ai) + Bi = lift(Bi) + + pa = affinepoint(ax, ay, Ai) + pb = affinepoint(bx, by, Bi) + pA = jacobianpoint(ax * Az^2, ay * Az^3, Az, Ai) + pB = jacobianpoint(bx * Bz^2, by * Bz^3, Bz, Bi) + + res = {} + + for key in laws_jacobian_weierstrass: + res[key] = [] + + print ("Formula " + name + ":") + count = 0 + for branch in xrange(branches): + assumeFormula, assumeBranch, pC = formula(branch, pA, pB) + pC.X = lift(pC.X) + pC.Y = lift(pC.Y) + pC.Z = lift(pC.Z) + pC.Infinity = lift(pC.Infinity) + + for key in laws_jacobian_weierstrass: + res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch)) + + for key in res: + print " %s:" % key + val = res[key] + for x in val: + if x[0] is not None: + print " branch %i: %s" % (x[1], x[0]) + + print diff --git a/libsecp256k1/src/asm/field_10x26_arm.s b/libsecp256k1/src/asm/field_10x26_arm.s new file mode 100644 index 0000000..9a5bd06 --- /dev/null +++ b/libsecp256k1/src/asm/field_10x26_arm.s @@ -0,0 +1,913 @@ +@ vim: set tabstop=8 softtabstop=8 shiftwidth=8 noexpandtab syntax=armasm: +/********************************************************************** + * Copyright (c) 2014 Wladimir J. van der Laan * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ +/* +ARM implementation of field_10x26 inner loops. + +Note: + +- To avoid unnecessary loads and make use of available registers, two + 'passes' have every time been interleaved, with the odd passes accumulating c' and d' + which will be added to c and d respectively in the even passes + +*/ + + .syntax unified + @ eabi attributes - see readelf -A + .eabi_attribute 24, 1 @ Tag_ABI_align_needed = 8-byte + .eabi_attribute 25, 1 @ Tag_ABI_align_preserved = 8-byte, except leaf SP + .text + + @ Field constants + .set field_R0, 0x3d10 + .set field_R1, 0x400 + .set field_not_M, 0xfc000000 @ ~M = ~0x3ffffff + + .align 2 + .global secp256k1_fe_mul_inner + .type secp256k1_fe_mul_inner, %function + @ Arguments: + @ r0 r Restrict: can overlap with a, not with b + @ r1 a + @ r2 b + @ Stack (total 4+10*4 = 44) + @ sp + #0 saved 'r' pointer + @ sp + #4 + 4*X t0,t1,t2,t3,t4,t5,t6,t7,u8,t9 +secp256k1_fe_mul_inner: + stmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14} + sub sp, sp, #48 @ frame=44 + alignment + str r0, [sp, #0] @ save result address, we need it only at the end + + /****************************************** + * Main computation code. + ****************************************** + + Allocation: + r0,r14,r7,r8 scratch + r1 a (pointer) + r2 b (pointer) + r3:r4 c + r5:r6 d + r11:r12 c' + r9:r10 d' + + Note: do not write to r[] here, it may overlap with a[] + */ + + /* A - interleaved with B */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #9*4] @ b[9] + ldr r0, [r1, #1*4] @ a[1] + umull r5, r6, r7, r8 @ d = a[0] * b[9] + ldr r14, [r2, #8*4] @ b[8] + umull r9, r10, r0, r8 @ d' = a[1] * b[9] + ldr r7, [r1, #2*4] @ a[2] + umlal r5, r6, r0, r14 @ d += a[1] * b[8] + ldr r8, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r14 @ d' += a[2] * b[8] + ldr r0, [r1, #3*4] @ a[3] + umlal r5, r6, r7, r8 @ d += a[2] * b[7] + ldr r14, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r8 @ d' += a[3] * b[7] + ldr r7, [r1, #4*4] @ a[4] + umlal r5, r6, r0, r14 @ d += a[3] * b[6] + ldr r8, [r2, #5*4] @ b[5] + umlal r9, r10, r7, r14 @ d' += a[4] * b[6] + ldr r0, [r1, #5*4] @ a[5] + umlal r5, r6, r7, r8 @ d += a[4] * b[5] + ldr r14, [r2, #4*4] @ b[4] + umlal r9, r10, r0, r8 @ d' += a[5] * b[5] + ldr r7, [r1, #6*4] @ a[6] + umlal r5, r6, r0, r14 @ d += a[5] * b[4] + ldr r8, [r2, #3*4] @ b[3] + umlal r9, r10, r7, r14 @ d' += a[6] * b[4] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r8 @ d += a[6] * b[3] + ldr r14, [r2, #2*4] @ b[2] + umlal r9, r10, r0, r8 @ d' += a[7] * b[3] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r14 @ d += a[7] * b[2] + ldr r8, [r2, #1*4] @ b[1] + umlal r9, r10, r7, r14 @ d' += a[8] * b[2] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r8 @ d += a[8] * b[1] + ldr r14, [r2, #0*4] @ b[0] + umlal r9, r10, r0, r8 @ d' += a[9] * b[1] + ldr r7, [r1, #0*4] @ a[0] + umlal r5, r6, r0, r14 @ d += a[9] * b[0] + @ r7,r14 used in B + + bic r0, r5, field_not_M @ t9 = d & M + str r0, [sp, #4 + 4*9] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + /* B */ + umull r3, r4, r7, r14 @ c = a[0] * b[0] + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u0 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u0 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t0 = c & M + str r14, [sp, #4 + 0*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u0 * R1 + umlal r3, r4, r0, r14 + + /* C - interleaved with D */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #2*4] @ b[2] + ldr r14, [r2, #1*4] @ b[1] + umull r11, r12, r7, r8 @ c' = a[0] * b[2] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[1] * b[1] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[2] * b[0] + ldr r0, [r1, #3*4] @ a[3] + umlal r5, r6, r7, r14 @ d += a[2] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[3] * b[9] + ldr r7, [r1, #4*4] @ a[4] + umlal r5, r6, r0, r8 @ d += a[3] * b[8] + ldr r14, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r8 @ d' += a[4] * b[8] + ldr r0, [r1, #5*4] @ a[5] + umlal r5, r6, r7, r14 @ d += a[4] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r14 @ d' += a[5] * b[7] + ldr r7, [r1, #6*4] @ a[6] + umlal r5, r6, r0, r8 @ d += a[5] * b[6] + ldr r14, [r2, #5*4] @ b[5] + umlal r9, r10, r7, r8 @ d' += a[6] * b[6] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r14 @ d += a[6] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r9, r10, r0, r14 @ d' += a[7] * b[5] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r8 @ d += a[7] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r9, r10, r7, r8 @ d' += a[8] * b[4] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r9, r10, r0, r14 @ d' += a[9] * b[3] + umlal r5, r6, r0, r8 @ d += a[9] * b[2] + + bic r0, r5, field_not_M @ u1 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u1 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t1 = c & M + str r14, [sp, #4 + 1*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u1 * R1 + umlal r3, r4, r0, r14 + + /* D */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u2 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u2 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t2 = c & M + str r14, [sp, #4 + 2*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u2 * R1 + umlal r3, r4, r0, r14 + + /* E - interleaved with F */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #4*4] @ b[4] + umull r11, r12, r7, r8 @ c' = a[0] * b[4] + ldr r8, [r2, #3*4] @ b[3] + umlal r3, r4, r7, r8 @ c += a[0] * b[3] + ldr r7, [r1, #1*4] @ a[1] + umlal r11, r12, r7, r8 @ c' += a[1] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r3, r4, r7, r8 @ c += a[1] * b[2] + ldr r7, [r1, #2*4] @ a[2] + umlal r11, r12, r7, r8 @ c' += a[2] * b[2] + ldr r8, [r2, #1*4] @ b[1] + umlal r3, r4, r7, r8 @ c += a[2] * b[1] + ldr r7, [r1, #3*4] @ a[3] + umlal r11, r12, r7, r8 @ c' += a[3] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r3, r4, r7, r8 @ c += a[3] * b[0] + ldr r7, [r1, #4*4] @ a[4] + umlal r11, r12, r7, r8 @ c' += a[4] * b[0] + ldr r8, [r2, #9*4] @ b[9] + umlal r5, r6, r7, r8 @ d += a[4] * b[9] + ldr r7, [r1, #5*4] @ a[5] + umull r9, r10, r7, r8 @ d' = a[5] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umlal r5, r6, r7, r8 @ d += a[5] * b[8] + ldr r7, [r1, #6*4] @ a[6] + umlal r9, r10, r7, r8 @ d' += a[6] * b[8] + ldr r8, [r2, #7*4] @ b[7] + umlal r5, r6, r7, r8 @ d += a[6] * b[7] + ldr r7, [r1, #7*4] @ a[7] + umlal r9, r10, r7, r8 @ d' += a[7] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r5, r6, r7, r8 @ d += a[7] * b[6] + ldr r7, [r1, #8*4] @ a[8] + umlal r9, r10, r7, r8 @ d' += a[8] * b[6] + ldr r8, [r2, #5*4] @ b[5] + umlal r5, r6, r7, r8 @ d += a[8] * b[5] + ldr r7, [r1, #9*4] @ a[9] + umlal r9, r10, r7, r8 @ d' += a[9] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r5, r6, r7, r8 @ d += a[9] * b[4] + + bic r0, r5, field_not_M @ u3 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u3 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t3 = c & M + str r14, [sp, #4 + 3*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u3 * R1 + umlal r3, r4, r0, r14 + + /* F */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u4 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u4 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t4 = c & M + str r14, [sp, #4 + 4*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u4 * R1 + umlal r3, r4, r0, r14 + + /* G - interleaved with H */ + ldr r7, [r1, #0*4] @ a[0] + ldr r8, [r2, #6*4] @ b[6] + ldr r14, [r2, #5*4] @ b[5] + umull r11, r12, r7, r8 @ c' = a[0] * b[6] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r11, r12, r0, r14 @ c' += a[1] * b[5] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r11, r12, r7, r8 @ c' += a[2] * b[4] + ldr r0, [r1, #3*4] @ a[3] + umlal r3, r4, r7, r14 @ c += a[2] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r11, r12, r0, r14 @ c' += a[3] * b[3] + ldr r7, [r1, #4*4] @ a[4] + umlal r3, r4, r0, r8 @ c += a[3] * b[2] + ldr r14, [r2, #1*4] @ b[1] + umlal r11, r12, r7, r8 @ c' += a[4] * b[2] + ldr r0, [r1, #5*4] @ a[5] + umlal r3, r4, r7, r14 @ c += a[4] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[5] * b[1] + ldr r7, [r1, #6*4] @ a[6] + umlal r3, r4, r0, r8 @ c += a[5] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[6] * b[0] + ldr r0, [r1, #7*4] @ a[7] + umlal r5, r6, r7, r14 @ d += a[6] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[7] * b[9] + ldr r7, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r8 @ d += a[7] * b[8] + ldr r14, [r2, #7*4] @ b[7] + umlal r9, r10, r7, r8 @ d' += a[8] * b[8] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r9, r10, r0, r14 @ d' += a[9] * b[7] + umlal r5, r6, r0, r8 @ d += a[9] * b[6] + + bic r0, r5, field_not_M @ u5 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u5 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t5 = c & M + str r14, [sp, #4 + 5*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u5 * R1 + umlal r3, r4, r0, r14 + + /* H */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u6 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u6 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t6 = c & M + str r14, [sp, #4 + 6*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u6 * R1 + umlal r3, r4, r0, r14 + + /* I - interleaved with J */ + ldr r8, [r2, #8*4] @ b[8] + ldr r7, [r1, #0*4] @ a[0] + ldr r14, [r2, #7*4] @ b[7] + umull r11, r12, r7, r8 @ c' = a[0] * b[8] + ldr r0, [r1, #1*4] @ a[1] + umlal r3, r4, r7, r14 @ c += a[0] * b[7] + ldr r8, [r2, #6*4] @ b[6] + umlal r11, r12, r0, r14 @ c' += a[1] * b[7] + ldr r7, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r8 @ c += a[1] * b[6] + ldr r14, [r2, #5*4] @ b[5] + umlal r11, r12, r7, r8 @ c' += a[2] * b[6] + ldr r0, [r1, #3*4] @ a[3] + umlal r3, r4, r7, r14 @ c += a[2] * b[5] + ldr r8, [r2, #4*4] @ b[4] + umlal r11, r12, r0, r14 @ c' += a[3] * b[5] + ldr r7, [r1, #4*4] @ a[4] + umlal r3, r4, r0, r8 @ c += a[3] * b[4] + ldr r14, [r2, #3*4] @ b[3] + umlal r11, r12, r7, r8 @ c' += a[4] * b[4] + ldr r0, [r1, #5*4] @ a[5] + umlal r3, r4, r7, r14 @ c += a[4] * b[3] + ldr r8, [r2, #2*4] @ b[2] + umlal r11, r12, r0, r14 @ c' += a[5] * b[3] + ldr r7, [r1, #6*4] @ a[6] + umlal r3, r4, r0, r8 @ c += a[5] * b[2] + ldr r14, [r2, #1*4] @ b[1] + umlal r11, r12, r7, r8 @ c' += a[6] * b[2] + ldr r0, [r1, #7*4] @ a[7] + umlal r3, r4, r7, r14 @ c += a[6] * b[1] + ldr r8, [r2, #0*4] @ b[0] + umlal r11, r12, r0, r14 @ c' += a[7] * b[1] + ldr r7, [r1, #8*4] @ a[8] + umlal r3, r4, r0, r8 @ c += a[7] * b[0] + ldr r14, [r2, #9*4] @ b[9] + umlal r11, r12, r7, r8 @ c' += a[8] * b[0] + ldr r0, [r1, #9*4] @ a[9] + umlal r5, r6, r7, r14 @ d += a[8] * b[9] + ldr r8, [r2, #8*4] @ b[8] + umull r9, r10, r0, r14 @ d' = a[9] * b[9] + umlal r5, r6, r0, r8 @ d += a[9] * b[8] + + bic r0, r5, field_not_M @ u7 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u7 * R0 + umlal r3, r4, r0, r14 + + bic r14, r3, field_not_M @ t7 = c & M + str r14, [sp, #4 + 7*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u7 * R1 + umlal r3, r4, r0, r14 + + /* J */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u8 = d & M + str r0, [sp, #4 + 8*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u8 * R0 + umlal r3, r4, r0, r14 + + /****************************************** + * compute and write back result + ****************************************** + Allocation: + r0 r + r3:r4 c + r5:r6 d + r7 t0 + r8 t1 + r9 t2 + r11 u8 + r12 t9 + r1,r2,r10,r14 scratch + + Note: do not read from a[] after here, it may overlap with r[] + */ + ldr r0, [sp, #0] + add r1, sp, #4 + 3*4 @ r[3..7] = t3..7, r11=u8, r12=t9 + ldmia r1, {r2,r7,r8,r9,r10,r11,r12} + add r1, r0, #3*4 + stmia r1, {r2,r7,r8,r9,r10} + + bic r2, r3, field_not_M @ r[8] = c & M + str r2, [r0, #8*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u8 * R1 + umlal r3, r4, r11, r14 + movw r14, field_R0 @ c += d * R0 + umlal r3, r4, r5, r14 + adds r3, r3, r12 @ c += t9 + adc r4, r4, #0 + + add r1, sp, #4 + 0*4 @ r7,r8,r9 = t0,t1,t2 + ldmia r1, {r7,r8,r9} + + ubfx r2, r3, #0, #22 @ r[9] = c & (M >> 4) + str r2, [r0, #9*4] + mov r3, r3, lsr #22 @ c >>= 22 + orr r3, r3, r4, asl #10 + mov r4, r4, lsr #22 + movw r14, field_R1 << 4 @ c += d * (R1 << 4) + umlal r3, r4, r5, r14 + + movw r14, field_R0 >> 4 @ d = c * (R0 >> 4) + t0 (64x64 multiply+add) + umull r5, r6, r3, r14 @ d = c.lo * (R0 >> 4) + adds r5, r5, r7 @ d.lo += t0 + mla r6, r14, r4, r6 @ d.hi += c.hi * (R0 >> 4) + adc r6, r6, 0 @ d.hi += carry + + bic r2, r5, field_not_M @ r[0] = d & M + str r2, [r0, #0*4] + + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + movw r14, field_R1 >> 4 @ d += c * (R1 >> 4) + t1 (64x64 multiply+add) + umull r1, r2, r3, r14 @ tmp = c.lo * (R1 >> 4) + adds r5, r5, r8 @ d.lo += t1 + adc r6, r6, #0 @ d.hi += carry + adds r5, r5, r1 @ d.lo += tmp.lo + mla r2, r14, r4, r2 @ tmp.hi += c.hi * (R1 >> 4) + adc r6, r6, r2 @ d.hi += carry + tmp.hi + + bic r2, r5, field_not_M @ r[1] = d & M + str r2, [r0, #1*4] + mov r5, r5, lsr #26 @ d >>= 26 (ignore hi) + orr r5, r5, r6, asl #6 + + add r5, r5, r9 @ d += t2 + str r5, [r0, #2*4] @ r[2] = d + + add sp, sp, #48 + ldmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc} + .size secp256k1_fe_mul_inner, .-secp256k1_fe_mul_inner + + .align 2 + .global secp256k1_fe_sqr_inner + .type secp256k1_fe_sqr_inner, %function + @ Arguments: + @ r0 r Can overlap with a + @ r1 a + @ Stack (total 4+10*4 = 44) + @ sp + #0 saved 'r' pointer + @ sp + #4 + 4*X t0,t1,t2,t3,t4,t5,t6,t7,u8,t9 +secp256k1_fe_sqr_inner: + stmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14} + sub sp, sp, #48 @ frame=44 + alignment + str r0, [sp, #0] @ save result address, we need it only at the end + /****************************************** + * Main computation code. + ****************************************** + + Allocation: + r0,r14,r2,r7,r8 scratch + r1 a (pointer) + r3:r4 c + r5:r6 d + r11:r12 c' + r9:r10 d' + + Note: do not write to r[] here, it may overlap with a[] + */ + /* A interleaved with B */ + ldr r0, [r1, #1*4] @ a[1]*2 + ldr r7, [r1, #0*4] @ a[0] + mov r0, r0, asl #1 + ldr r14, [r1, #9*4] @ a[9] + umull r3, r4, r7, r7 @ c = a[0] * a[0] + ldr r8, [r1, #8*4] @ a[8] + mov r7, r7, asl #1 + umull r5, r6, r7, r14 @ d = a[0]*2 * a[9] + ldr r7, [r1, #2*4] @ a[2]*2 + umull r9, r10, r0, r14 @ d' = a[1]*2 * a[9] + ldr r14, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r8 @ d += a[1]*2 * a[8] + mov r7, r7, asl #1 + ldr r0, [r1, #3*4] @ a[3]*2 + umlal r9, r10, r7, r8 @ d' += a[2]*2 * a[8] + ldr r8, [r1, #6*4] @ a[6] + umlal r5, r6, r7, r14 @ d += a[2]*2 * a[7] + mov r0, r0, asl #1 + ldr r7, [r1, #4*4] @ a[4]*2 + umlal r9, r10, r0, r14 @ d' += a[3]*2 * a[7] + ldr r14, [r1, #5*4] @ a[5] + mov r7, r7, asl #1 + umlal r5, r6, r0, r8 @ d += a[3]*2 * a[6] + umlal r9, r10, r7, r8 @ d' += a[4]*2 * a[6] + umlal r5, r6, r7, r14 @ d += a[4]*2 * a[5] + umlal r9, r10, r14, r14 @ d' += a[5] * a[5] + + bic r0, r5, field_not_M @ t9 = d & M + str r0, [sp, #4 + 9*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + /* B */ + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u0 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u0 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t0 = c & M + str r14, [sp, #4 + 0*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u0 * R1 + umlal r3, r4, r0, r14 + + /* C interleaved with D */ + ldr r0, [r1, #0*4] @ a[0]*2 + ldr r14, [r1, #1*4] @ a[1] + mov r0, r0, asl #1 + ldr r8, [r1, #2*4] @ a[2] + umlal r3, r4, r0, r14 @ c += a[0]*2 * a[1] + mov r7, r8, asl #1 @ a[2]*2 + umull r11, r12, r14, r14 @ c' = a[1] * a[1] + ldr r14, [r1, #9*4] @ a[9] + umlal r11, r12, r0, r8 @ c' += a[0]*2 * a[2] + ldr r0, [r1, #3*4] @ a[3]*2 + ldr r8, [r1, #8*4] @ a[8] + umlal r5, r6, r7, r14 @ d += a[2]*2 * a[9] + mov r0, r0, asl #1 + ldr r7, [r1, #4*4] @ a[4]*2 + umull r9, r10, r0, r14 @ d' = a[3]*2 * a[9] + ldr r14, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r8 @ d += a[3]*2 * a[8] + mov r7, r7, asl #1 + ldr r0, [r1, #5*4] @ a[5]*2 + umlal r9, r10, r7, r8 @ d' += a[4]*2 * a[8] + ldr r8, [r1, #6*4] @ a[6] + mov r0, r0, asl #1 + umlal r5, r6, r7, r14 @ d += a[4]*2 * a[7] + umlal r9, r10, r0, r14 @ d' += a[5]*2 * a[7] + umlal r5, r6, r0, r8 @ d += a[5]*2 * a[6] + umlal r9, r10, r8, r8 @ d' += a[6] * a[6] + + bic r0, r5, field_not_M @ u1 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u1 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t1 = c & M + str r14, [sp, #4 + 1*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u1 * R1 + umlal r3, r4, r0, r14 + + /* D */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u2 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u2 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t2 = c & M + str r14, [sp, #4 + 2*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u2 * R1 + umlal r3, r4, r0, r14 + + /* E interleaved with F */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + ldr r14, [r1, #2*4] @ a[2] + mov r7, r7, asl #1 + ldr r8, [r1, #3*4] @ a[3] + ldr r2, [r1, #4*4] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[3] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[4] + mov r2, r2, asl #1 @ a[4]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[3] + ldr r8, [r1, #9*4] @ a[9] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[2] + ldr r0, [r1, #5*4] @ a[5]*2 + umlal r11, r12, r14, r14 @ c' += a[2] * a[2] + ldr r14, [r1, #8*4] @ a[8] + mov r0, r0, asl #1 + umlal r5, r6, r2, r8 @ d += a[4]*2 * a[9] + ldr r7, [r1, #6*4] @ a[6]*2 + umull r9, r10, r0, r8 @ d' = a[5]*2 * a[9] + mov r7, r7, asl #1 + ldr r8, [r1, #7*4] @ a[7] + umlal r5, r6, r0, r14 @ d += a[5]*2 * a[8] + umlal r9, r10, r7, r14 @ d' += a[6]*2 * a[8] + umlal r5, r6, r7, r8 @ d += a[6]*2 * a[7] + umlal r9, r10, r8, r8 @ d' += a[7] * a[7] + + bic r0, r5, field_not_M @ u3 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u3 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t3 = c & M + str r14, [sp, #4 + 3*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u3 * R1 + umlal r3, r4, r0, r14 + + /* F */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u4 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u4 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t4 = c & M + str r14, [sp, #4 + 4*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u4 * R1 + umlal r3, r4, r0, r14 + + /* G interleaved with H */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + mov r7, r7, asl #1 + ldr r8, [r1, #5*4] @ a[5] + ldr r2, [r1, #6*4] @ a[6] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[5] + ldr r14, [r1, #4*4] @ a[4] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[6] + ldr r7, [r1, #2*4] @ a[2]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[5] + mov r7, r7, asl #1 + ldr r8, [r1, #3*4] @ a[3] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[4] + mov r0, r2, asl #1 @ a[6]*2 + umlal r11, r12, r7, r14 @ c' += a[2]*2 * a[4] + ldr r14, [r1, #9*4] @ a[9] + umlal r3, r4, r7, r8 @ c += a[2]*2 * a[3] + ldr r7, [r1, #7*4] @ a[7]*2 + umlal r11, r12, r8, r8 @ c' += a[3] * a[3] + mov r7, r7, asl #1 + ldr r8, [r1, #8*4] @ a[8] + umlal r5, r6, r0, r14 @ d += a[6]*2 * a[9] + umull r9, r10, r7, r14 @ d' = a[7]*2 * a[9] + umlal r5, r6, r7, r8 @ d += a[7]*2 * a[8] + umlal r9, r10, r8, r8 @ d' += a[8] * a[8] + + bic r0, r5, field_not_M @ u5 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u5 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t5 = c & M + str r14, [sp, #4 + 5*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u5 * R1 + umlal r3, r4, r0, r14 + + /* H */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + adds r5, r5, r9 @ d += d' + adc r6, r6, r10 + + bic r0, r5, field_not_M @ u6 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u6 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t6 = c & M + str r14, [sp, #4 + 6*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u6 * R1 + umlal r3, r4, r0, r14 + + /* I interleaved with J */ + ldr r7, [r1, #0*4] @ a[0]*2 + ldr r0, [r1, #1*4] @ a[1]*2 + mov r7, r7, asl #1 + ldr r8, [r1, #7*4] @ a[7] + ldr r2, [r1, #8*4] @ a[8] + umlal r3, r4, r7, r8 @ c += a[0]*2 * a[7] + ldr r14, [r1, #6*4] @ a[6] + mov r0, r0, asl #1 + umull r11, r12, r7, r2 @ c' = a[0]*2 * a[8] + ldr r7, [r1, #2*4] @ a[2]*2 + umlal r11, r12, r0, r8 @ c' += a[1]*2 * a[7] + ldr r8, [r1, #5*4] @ a[5] + umlal r3, r4, r0, r14 @ c += a[1]*2 * a[6] + ldr r0, [r1, #3*4] @ a[3]*2 + mov r7, r7, asl #1 + umlal r11, r12, r7, r14 @ c' += a[2]*2 * a[6] + ldr r14, [r1, #4*4] @ a[4] + mov r0, r0, asl #1 + umlal r3, r4, r7, r8 @ c += a[2]*2 * a[5] + mov r2, r2, asl #1 @ a[8]*2 + umlal r11, r12, r0, r8 @ c' += a[3]*2 * a[5] + umlal r3, r4, r0, r14 @ c += a[3]*2 * a[4] + umlal r11, r12, r14, r14 @ c' += a[4] * a[4] + ldr r8, [r1, #9*4] @ a[9] + umlal r5, r6, r2, r8 @ d += a[8]*2 * a[9] + @ r8 will be used in J + + bic r0, r5, field_not_M @ u7 = d & M + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u7 * R0 + umlal r3, r4, r0, r14 + bic r14, r3, field_not_M @ t7 = c & M + str r14, [sp, #4 + 7*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u7 * R1 + umlal r3, r4, r0, r14 + + /* J */ + adds r3, r3, r11 @ c += c' + adc r4, r4, r12 + umlal r5, r6, r8, r8 @ d += a[9] * a[9] + + bic r0, r5, field_not_M @ u8 = d & M + str r0, [sp, #4 + 8*4] + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + movw r14, field_R0 @ c += u8 * R0 + umlal r3, r4, r0, r14 + + /****************************************** + * compute and write back result + ****************************************** + Allocation: + r0 r + r3:r4 c + r5:r6 d + r7 t0 + r8 t1 + r9 t2 + r11 u8 + r12 t9 + r1,r2,r10,r14 scratch + + Note: do not read from a[] after here, it may overlap with r[] + */ + ldr r0, [sp, #0] + add r1, sp, #4 + 3*4 @ r[3..7] = t3..7, r11=u8, r12=t9 + ldmia r1, {r2,r7,r8,r9,r10,r11,r12} + add r1, r0, #3*4 + stmia r1, {r2,r7,r8,r9,r10} + + bic r2, r3, field_not_M @ r[8] = c & M + str r2, [r0, #8*4] + mov r3, r3, lsr #26 @ c >>= 26 + orr r3, r3, r4, asl #6 + mov r4, r4, lsr #26 + mov r14, field_R1 @ c += u8 * R1 + umlal r3, r4, r11, r14 + movw r14, field_R0 @ c += d * R0 + umlal r3, r4, r5, r14 + adds r3, r3, r12 @ c += t9 + adc r4, r4, #0 + + add r1, sp, #4 + 0*4 @ r7,r8,r9 = t0,t1,t2 + ldmia r1, {r7,r8,r9} + + ubfx r2, r3, #0, #22 @ r[9] = c & (M >> 4) + str r2, [r0, #9*4] + mov r3, r3, lsr #22 @ c >>= 22 + orr r3, r3, r4, asl #10 + mov r4, r4, lsr #22 + movw r14, field_R1 << 4 @ c += d * (R1 << 4) + umlal r3, r4, r5, r14 + + movw r14, field_R0 >> 4 @ d = c * (R0 >> 4) + t0 (64x64 multiply+add) + umull r5, r6, r3, r14 @ d = c.lo * (R0 >> 4) + adds r5, r5, r7 @ d.lo += t0 + mla r6, r14, r4, r6 @ d.hi += c.hi * (R0 >> 4) + adc r6, r6, 0 @ d.hi += carry + + bic r2, r5, field_not_M @ r[0] = d & M + str r2, [r0, #0*4] + + mov r5, r5, lsr #26 @ d >>= 26 + orr r5, r5, r6, asl #6 + mov r6, r6, lsr #26 + + movw r14, field_R1 >> 4 @ d += c * (R1 >> 4) + t1 (64x64 multiply+add) + umull r1, r2, r3, r14 @ tmp = c.lo * (R1 >> 4) + adds r5, r5, r8 @ d.lo += t1 + adc r6, r6, #0 @ d.hi += carry + adds r5, r5, r1 @ d.lo += tmp.lo + mla r2, r14, r4, r2 @ tmp.hi += c.hi * (R1 >> 4) + adc r6, r6, r2 @ d.hi += carry + tmp.hi + + bic r2, r5, field_not_M @ r[1] = d & M + str r2, [r0, #1*4] + mov r5, r5, lsr #26 @ d >>= 26 (ignore hi) + orr r5, r5, r6, asl #6 + + add r5, r5, r9 @ d += t2 + str r5, [r0, #2*4] @ r[2] = d + + add sp, sp, #48 + ldmfd sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc} + .size secp256k1_fe_sqr_inner, .-secp256k1_fe_sqr_inner + diff --git a/libsecp256k1/src/basic-config.h b/libsecp256k1/src/basic-config.h new file mode 100644 index 0000000..e9be39d --- /dev/null +++ b/libsecp256k1/src/basic-config.h @@ -0,0 +1,38 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_BASIC_CONFIG_H +#define SECP256K1_BASIC_CONFIG_H + +#ifdef USE_BASIC_CONFIG + +#undef USE_ASM_X86_64 +#undef USE_ECMULT_STATIC_PRECOMPUTATION +#undef USE_ENDOMORPHISM +#undef USE_EXTERNAL_ASM +#undef USE_EXTERNAL_DEFAULT_CALLBACKS +#undef USE_FIELD_10X26 +#undef USE_FIELD_5X52 +#undef USE_FIELD_INV_BUILTIN +#undef USE_FIELD_INV_NUM +#undef USE_NUM_GMP +#undef USE_NUM_NONE +#undef USE_SCALAR_4X64 +#undef USE_SCALAR_8X32 +#undef USE_SCALAR_INV_BUILTIN +#undef USE_SCALAR_INV_NUM +#undef ECMULT_WINDOW_SIZE + +#define USE_NUM_NONE 1 +#define USE_FIELD_INV_BUILTIN 1 +#define USE_SCALAR_INV_BUILTIN 1 +#define USE_FIELD_10X26 1 +#define USE_SCALAR_8X32 1 +#define ECMULT_WINDOW_SIZE 15 + +#endif /* USE_BASIC_CONFIG */ + +#endif /* SECP256K1_BASIC_CONFIG_H */ diff --git a/libsecp256k1/src/bench.h b/libsecp256k1/src/bench.h new file mode 100644 index 0000000..9bfed90 --- /dev/null +++ b/libsecp256k1/src/bench.h @@ -0,0 +1,133 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_BENCH_H +#define SECP256K1_BENCH_H + +#include +#include +#include +#include "sys/time.h" + +static int64_t gettime_i64(void) { + struct timeval tv; + gettimeofday(&tv, NULL); + return (int64_t)tv.tv_usec + (int64_t)tv.tv_sec * 1000000LL; +} + +#define FP_EXP (6) +#define FP_MULT (1000000LL) + +/* Format fixed point number. */ +void print_number(const int64_t x) { + int64_t x_abs, y; + int c, i, rounding; + size_t ptr; + char buffer[30]; + + if (x == INT64_MIN) { + /* Prevent UB. */ + printf("ERR"); + return; + } + x_abs = x < 0 ? -x : x; + + /* Determine how many decimals we want to show (more than FP_EXP makes no + * sense). */ + y = x_abs; + c = 0; + while (y > 0LL && y < 100LL * FP_MULT && c < FP_EXP) { + y *= 10LL; + c++; + } + + /* Round to 'c' decimals. */ + y = x_abs; + rounding = 0; + for (i = c; i < FP_EXP; ++i) { + rounding = (y % 10) >= 5; + y /= 10; + } + y += rounding; + + /* Format and print the number. */ + ptr = sizeof(buffer) - 1; + buffer[ptr] = 0; + if (c != 0) { + for (i = 0; i < c; ++i) { + buffer[--ptr] = '0' + (y % 10); + y /= 10; + } + buffer[--ptr] = '.'; + } + do { + buffer[--ptr] = '0' + (y % 10); + y /= 10; + } while (y != 0); + if (x < 0) { + buffer[--ptr] = '-'; + } + printf("%s", &buffer[ptr]); +} + +void run_benchmark(char *name, void (*benchmark)(void*, int), void (*setup)(void*), void (*teardown)(void*, int), void* data, int count, int iter) { + int i; + int64_t min = INT64_MAX; + int64_t sum = 0; + int64_t max = 0; + for (i = 0; i < count; i++) { + int64_t begin, total; + if (setup != NULL) { + setup(data); + } + begin = gettime_i64(); + benchmark(data, iter); + total = gettime_i64() - begin; + if (teardown != NULL) { + teardown(data, iter); + } + if (total < min) { + min = total; + } + if (total > max) { + max = total; + } + sum += total; + } + printf("%s: min ", name); + print_number(min * FP_MULT / iter); + printf("us / avg "); + print_number(((sum * FP_MULT) / count) / iter); + printf("us / max "); + print_number(max * FP_MULT / iter); + printf("us\n"); +} + +int have_flag(int argc, char** argv, char *flag) { + char** argm = argv + argc; + argv++; + if (argv == argm) { + return 1; + } + while (argv != NULL && argv != argm) { + if (strcmp(*argv, flag) == 0) { + return 1; + } + argv++; + } + return 0; +} + +int get_iters(int default_iters) { + char* env = getenv("SECP256K1_BENCH_ITERS"); + if (env) { + return strtol(env, NULL, 0); + } else { + return default_iters; + } +} + +#endif /* SECP256K1_BENCH_H */ diff --git a/libsecp256k1/src/bench_ecdh.c b/libsecp256k1/src/bench_ecdh.c new file mode 100644 index 0000000..f099d33 --- /dev/null +++ b/libsecp256k1/src/bench_ecdh.c @@ -0,0 +1,59 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include + +#include "include/secp256k1.h" +#include "include/secp256k1_ecdh.h" +#include "util.h" +#include "bench.h" + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point; + unsigned char scalar[32]; +} bench_ecdh_data; + +static void bench_ecdh_setup(void* arg) { + int i; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + const unsigned char point[] = { + 0x03, + 0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06, + 0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd, + 0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb, + 0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f + }; + + for (i = 0; i < 32; i++) { + data->scalar[i] = i + 1; + } + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1); +} + +static void bench_ecdh(void* arg, int iters) { + int i; + unsigned char res[32]; + bench_ecdh_data *data = (bench_ecdh_data*)arg; + + for (i = 0; i < iters; i++) { + CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar, NULL, NULL) == 1); + } +} + +int main(void) { + bench_ecdh_data data; + + int iters = get_iters(20000); + + /* create a context with no capabilities */ + data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT); + + run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); + return 0; +} diff --git a/libsecp256k1/src/bench_ecmult.c b/libsecp256k1/src/bench_ecmult.c new file mode 100644 index 0000000..facd07e --- /dev/null +++ b/libsecp256k1/src/bench_ecmult.c @@ -0,0 +1,214 @@ +/********************************************************************** + * Copyright (c) 2017 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ +#include + +#include "include/secp256k1.h" + +#include "util.h" +#include "hash_impl.h" +#include "num_impl.h" +#include "field_impl.h" +#include "group_impl.h" +#include "scalar_impl.h" +#include "ecmult_impl.h" +#include "bench.h" +#include "secp256k1.c" + +#define POINTS 32768 + +typedef struct { + /* Setup once in advance */ + secp256k1_context* ctx; + secp256k1_scratch_space* scratch; + secp256k1_scalar* scalars; + secp256k1_ge* pubkeys; + secp256k1_scalar* seckeys; + secp256k1_gej* expected_output; + secp256k1_ecmult_multi_func ecmult_multi; + + /* Changes per test */ + size_t count; + int includes_g; + + /* Changes per test iteration */ + size_t offset1; + size_t offset2; + + /* Test output. */ + secp256k1_gej* output; +} bench_data; + +static int bench_callback(secp256k1_scalar* sc, secp256k1_ge* ge, size_t idx, void* arg) { + bench_data* data = (bench_data*)arg; + if (data->includes_g) ++idx; + if (idx == 0) { + *sc = data->scalars[data->offset1]; + *ge = secp256k1_ge_const_g; + } else { + *sc = data->scalars[(data->offset1 + idx) % POINTS]; + *ge = data->pubkeys[(data->offset2 + idx - 1) % POINTS]; + } + return 1; +} + +static void bench_ecmult(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + + int includes_g = data->includes_g; + int iter; + int count = data->count; + iters = iters / data->count; + + for (iter = 0; iter < iters; ++iter) { + data->ecmult_multi(&data->ctx->error_callback, &data->ctx->ecmult_ctx, data->scratch, &data->output[iter], data->includes_g ? &data->scalars[data->offset1] : NULL, bench_callback, arg, count - includes_g); + data->offset1 = (data->offset1 + count) % POINTS; + data->offset2 = (data->offset2 + count - 1) % POINTS; + } +} + +static void bench_ecmult_setup(void* arg) { + bench_data* data = (bench_data*)arg; + data->offset1 = (data->count * 0x537b7f6f + 0x8f66a481) % POINTS; + data->offset2 = (data->count * 0x7f6f537b + 0x6a1a8f49) % POINTS; +} + +static void bench_ecmult_teardown(void* arg, int iters) { + bench_data* data = (bench_data*)arg; + int iter; + iters = iters / data->count; + /* Verify the results in teardown, to avoid doing comparisons while benchmarking. */ + for (iter = 0; iter < iters; ++iter) { + secp256k1_gej tmp; + secp256k1_gej_add_var(&tmp, &data->output[iter], &data->expected_output[iter], NULL); + CHECK(secp256k1_gej_is_infinity(&tmp)); + } +} + +static void generate_scalar(uint32_t num, secp256k1_scalar* scalar) { + secp256k1_sha256 sha256; + unsigned char c[11] = {'e', 'c', 'm', 'u', 'l', 't', 0, 0, 0, 0}; + unsigned char buf[32]; + int overflow = 0; + c[6] = num; + c[7] = num >> 8; + c[8] = num >> 16; + c[9] = num >> 24; + secp256k1_sha256_initialize(&sha256); + secp256k1_sha256_write(&sha256, c, sizeof(c)); + secp256k1_sha256_finalize(&sha256, buf); + secp256k1_scalar_set_b32(scalar, buf, &overflow); + CHECK(!overflow); +} + +static void run_test(bench_data* data, size_t count, int includes_g, int num_iters) { + char str[32]; + static const secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + size_t iters = 1 + num_iters / count; + size_t iter; + + data->count = count; + data->includes_g = includes_g; + + /* Compute (the negation of) the expected results directly. */ + data->offset1 = (data->count * 0x537b7f6f + 0x8f66a481) % POINTS; + data->offset2 = (data->count * 0x7f6f537b + 0x6a1a8f49) % POINTS; + for (iter = 0; iter < iters; ++iter) { + secp256k1_scalar tmp; + secp256k1_scalar total = data->scalars[(data->offset1++) % POINTS]; + size_t i = 0; + for (i = 0; i + 1 < count; ++i) { + secp256k1_scalar_mul(&tmp, &data->seckeys[(data->offset2++) % POINTS], &data->scalars[(data->offset1++) % POINTS]); + secp256k1_scalar_add(&total, &total, &tmp); + } + secp256k1_scalar_negate(&total, &total); + secp256k1_ecmult(&data->ctx->ecmult_ctx, &data->expected_output[iter], NULL, &zero, &total); + } + + /* Run the benchmark. */ + sprintf(str, includes_g ? "ecmult_%ig" : "ecmult_%i", (int)count); + run_benchmark(str, bench_ecmult, bench_ecmult_setup, bench_ecmult_teardown, data, 10, count * iters); +} + +int main(int argc, char **argv) { + bench_data data; + int i, p; + secp256k1_gej* pubkeys_gej; + size_t scratch_size; + + int iters = get_iters(10000); + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + scratch_size = secp256k1_strauss_scratch_size(POINTS) + STRAUSS_SCRATCH_OBJECTS*16; + data.scratch = secp256k1_scratch_space_create(data.ctx, scratch_size); + data.ecmult_multi = secp256k1_ecmult_multi_var; + + if (argc > 1) { + if(have_flag(argc, argv, "pippenger_wnaf")) { + printf("Using pippenger_wnaf:\n"); + data.ecmult_multi = secp256k1_ecmult_pippenger_batch_single; + } else if(have_flag(argc, argv, "strauss_wnaf")) { + printf("Using strauss_wnaf:\n"); + data.ecmult_multi = secp256k1_ecmult_strauss_batch_single; + } else if(have_flag(argc, argv, "simple")) { + printf("Using simple algorithm:\n"); + data.ecmult_multi = secp256k1_ecmult_multi_var; + secp256k1_scratch_space_destroy(data.ctx, data.scratch); + data.scratch = NULL; + } else { + fprintf(stderr, "%s: unrecognized argument '%s'.\n", argv[0], argv[1]); + fprintf(stderr, "Use 'pippenger_wnaf', 'strauss_wnaf', 'simple' or no argument to benchmark a combined algorithm.\n"); + return 1; + } + } + + /* Allocate stuff */ + data.scalars = malloc(sizeof(secp256k1_scalar) * POINTS); + data.seckeys = malloc(sizeof(secp256k1_scalar) * POINTS); + data.pubkeys = malloc(sizeof(secp256k1_ge) * POINTS); + data.expected_output = malloc(sizeof(secp256k1_gej) * (iters + 1)); + data.output = malloc(sizeof(secp256k1_gej) * (iters + 1)); + + /* Generate a set of scalars, and private/public keypairs. */ + pubkeys_gej = malloc(sizeof(secp256k1_gej) * POINTS); + secp256k1_gej_set_ge(&pubkeys_gej[0], &secp256k1_ge_const_g); + secp256k1_scalar_set_int(&data.seckeys[0], 1); + for (i = 0; i < POINTS; ++i) { + generate_scalar(i, &data.scalars[i]); + if (i) { + secp256k1_gej_double_var(&pubkeys_gej[i], &pubkeys_gej[i - 1], NULL); + secp256k1_scalar_add(&data.seckeys[i], &data.seckeys[i - 1], &data.seckeys[i - 1]); + } + } + secp256k1_ge_set_all_gej_var(data.pubkeys, pubkeys_gej, POINTS); + free(pubkeys_gej); + + for (i = 1; i <= 8; ++i) { + run_test(&data, i, 1, iters); + } + + /* This is disabled with low count of iterations because the loop runs 77 times even with iters=1 + * and the higher it goes the longer the computation takes(more points) + * So we don't run this benchmark with low iterations to prevent slow down */ + if (iters > 2) { + for (p = 0; p <= 11; ++p) { + for (i = 9; i <= 16; ++i) { + run_test(&data, i << p, 1, iters); + } + } + } + + if (data.scratch != NULL) { + secp256k1_scratch_space_destroy(data.ctx, data.scratch); + } + secp256k1_context_destroy(data.ctx); + free(data.scalars); + free(data.pubkeys); + free(data.seckeys); + free(data.output); + free(data.expected_output); + + return(0); +} diff --git a/libsecp256k1/src/bench_internal.c b/libsecp256k1/src/bench_internal.c new file mode 100644 index 0000000..2075912 --- /dev/null +++ b/libsecp256k1/src/bench_internal.c @@ -0,0 +1,381 @@ +/********************************************************************** + * Copyright (c) 2014-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ +#include + +#include "include/secp256k1.h" + +#include "util.h" +#include "hash_impl.h" +#include "num_impl.h" +#include "field_impl.h" +#include "group_impl.h" +#include "scalar_impl.h" +#include "ecmult_const_impl.h" +#include "ecmult_impl.h" +#include "bench.h" +#include "secp256k1.c" + +typedef struct { + secp256k1_scalar scalar_x, scalar_y; + secp256k1_fe fe_x, fe_y; + secp256k1_ge ge_x, ge_y; + secp256k1_gej gej_x, gej_y; + unsigned char data[64]; + int wnaf[256]; +} bench_inv; + +void bench_setup(void* arg) { + bench_inv *data = (bench_inv*)arg; + + static const unsigned char init_x[32] = { + 0x02, 0x03, 0x05, 0x07, 0x0b, 0x0d, 0x11, 0x13, + 0x17, 0x1d, 0x1f, 0x25, 0x29, 0x2b, 0x2f, 0x35, + 0x3b, 0x3d, 0x43, 0x47, 0x49, 0x4f, 0x53, 0x59, + 0x61, 0x65, 0x67, 0x6b, 0x6d, 0x71, 0x7f, 0x83 + }; + + static const unsigned char init_y[32] = { + 0x82, 0x83, 0x85, 0x87, 0x8b, 0x8d, 0x81, 0x83, + 0x97, 0xad, 0xaf, 0xb5, 0xb9, 0xbb, 0xbf, 0xc5, + 0xdb, 0xdd, 0xe3, 0xe7, 0xe9, 0xef, 0xf3, 0xf9, + 0x11, 0x15, 0x17, 0x1b, 0x1d, 0xb1, 0xbf, 0xd3 + }; + + secp256k1_scalar_set_b32(&data->scalar_x, init_x, NULL); + secp256k1_scalar_set_b32(&data->scalar_y, init_y, NULL); + secp256k1_fe_set_b32(&data->fe_x, init_x); + secp256k1_fe_set_b32(&data->fe_y, init_y); + CHECK(secp256k1_ge_set_xo_var(&data->ge_x, &data->fe_x, 0)); + CHECK(secp256k1_ge_set_xo_var(&data->ge_y, &data->fe_y, 1)); + secp256k1_gej_set_ge(&data->gej_x, &data->ge_x); + secp256k1_gej_set_ge(&data->gej_y, &data->ge_y); + memcpy(data->data, init_x, 32); + memcpy(data->data + 32, init_y, 32); +} + +void bench_scalar_add(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + j += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(j <= iters); +} + +void bench_scalar_negate(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_negate(&data->scalar_x, &data->scalar_x); + } +} + +void bench_scalar_sqr(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_sqr(&data->scalar_x, &data->scalar_x); + } +} + +void bench_scalar_mul(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_mul(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } +} + +#ifdef USE_ENDOMORPHISM +void bench_scalar_split(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_split_lambda(&data->scalar_x, &data->scalar_y, &data->scalar_x); + j += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(j <= iters); +} +#endif + +void bench_scalar_inverse(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_inverse(&data->scalar_x, &data->scalar_x); + j += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(j <= iters); +} + +void bench_scalar_inverse_var(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_scalar_inverse_var(&data->scalar_x, &data->scalar_x); + j += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(j <= iters); +} + +void bench_field_normalize(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_normalize(&data->fe_x); + } +} + +void bench_field_normalize_weak(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_normalize_weak(&data->fe_x); + } +} + +void bench_field_mul(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_mul(&data->fe_x, &data->fe_x, &data->fe_y); + } +} + +void bench_field_sqr(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_sqr(&data->fe_x, &data->fe_x); + } +} + +void bench_field_inverse(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_inv(&data->fe_x, &data->fe_x); + secp256k1_fe_add(&data->fe_x, &data->fe_y); + } +} + +void bench_field_inverse_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_fe_inv_var(&data->fe_x, &data->fe_x); + secp256k1_fe_add(&data->fe_x, &data->fe_y); + } +} + +void bench_field_sqrt(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + secp256k1_fe t; + + for (i = 0; i < iters; i++) { + t = data->fe_x; + j += secp256k1_fe_sqrt(&data->fe_x, &t); + secp256k1_fe_add(&data->fe_x, &data->fe_y); + } + CHECK(j <= iters); +} + +void bench_group_double_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_double_var(&data->gej_x, &data->gej_x, NULL); + } +} + +void bench_group_add_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_var(&data->gej_x, &data->gej_x, &data->gej_y, NULL); + } +} + +void bench_group_add_affine(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_ge(&data->gej_x, &data->gej_x, &data->ge_y); + } +} + +void bench_group_add_affine_var(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_gej_add_ge_var(&data->gej_x, &data->gej_x, &data->ge_y, NULL); + } +} + +void bench_group_jacobi_var(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + j += secp256k1_gej_has_quad_y_var(&data->gej_x); + } + CHECK(j == iters); +} + +void bench_ecmult_wnaf(void* arg, int iters) { + int i, bits = 0, overflow = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + bits += secp256k1_ecmult_wnaf(data->wnaf, 256, &data->scalar_x, WINDOW_A); + overflow += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(overflow >= 0); + CHECK(bits <= 256*iters); +} + +void bench_wnaf_const(void* arg, int iters) { + int i, bits = 0, overflow = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + bits += secp256k1_wnaf_const(data->wnaf, &data->scalar_x, WINDOW_A, 256); + overflow += secp256k1_scalar_add(&data->scalar_x, &data->scalar_x, &data->scalar_y); + } + CHECK(overflow >= 0); + CHECK(bits <= 256*iters); +} + + +void bench_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_sha256 sha; + + for (i = 0; i < iters; i++) { + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, data->data, 32); + secp256k1_sha256_finalize(&sha, data->data); + } +} + +void bench_hmac_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_hmac_sha256 hmac; + + for (i = 0; i < iters; i++) { + secp256k1_hmac_sha256_initialize(&hmac, data->data, 32); + secp256k1_hmac_sha256_write(&hmac, data->data, 32); + secp256k1_hmac_sha256_finalize(&hmac, data->data); + } +} + +void bench_rfc6979_hmac_sha256(void* arg, int iters) { + int i; + bench_inv *data = (bench_inv*)arg; + secp256k1_rfc6979_hmac_sha256 rng; + + for (i = 0; i < iters; i++) { + secp256k1_rfc6979_hmac_sha256_initialize(&rng, data->data, 64); + secp256k1_rfc6979_hmac_sha256_generate(&rng, data->data, 32); + } +} + +void bench_context_verify(void* arg, int iters) { + int i; + (void)arg; + for (i = 0; i < iters; i++) { + secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_VERIFY)); + } +} + +void bench_context_sign(void* arg, int iters) { + int i; + (void)arg; + for (i = 0; i < iters; i++) { + secp256k1_context_destroy(secp256k1_context_create(SECP256K1_CONTEXT_SIGN)); + } +} + +#ifndef USE_NUM_NONE +void bench_num_jacobi(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + secp256k1_num nx, norder; + + secp256k1_scalar_get_num(&nx, &data->scalar_x); + secp256k1_scalar_order_get_num(&norder); + secp256k1_scalar_get_num(&norder, &data->scalar_y); + + for (i = 0; i < iters; i++) { + j += secp256k1_num_jacobi(&nx, &norder); + } + CHECK(j <= iters); +} +#endif + +int main(int argc, char **argv) { + bench_inv data; + int iters = get_iters(20000); + + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "add")) run_benchmark("scalar_add", bench_scalar_add, bench_setup, NULL, &data, 10, iters*100); + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "negate")) run_benchmark("scalar_negate", bench_scalar_negate, bench_setup, NULL, &data, 10, iters*100); + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "sqr")) run_benchmark("scalar_sqr", bench_scalar_sqr, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "mul")) run_benchmark("scalar_mul", bench_scalar_mul, bench_setup, NULL, &data, 10, iters*10); +#ifdef USE_ENDOMORPHISM + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "split")) run_benchmark("scalar_split", bench_scalar_split, bench_setup, NULL, &data, 10, iters); +#endif + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse", bench_scalar_inverse, bench_setup, NULL, &data, 10, 2000); + if (have_flag(argc, argv, "scalar") || have_flag(argc, argv, "inverse")) run_benchmark("scalar_inverse_var", bench_scalar_inverse_var, bench_setup, NULL, &data, 10, 2000); + + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize", bench_field_normalize, bench_setup, NULL, &data, 10, iters*100); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "normalize")) run_benchmark("field_normalize_weak", bench_field_normalize_weak, bench_setup, NULL, &data, 10, iters*100); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqr")) run_benchmark("field_sqr", bench_field_sqr, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, iters); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, iters); + if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, iters); + + if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine", bench_group_add_affine, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_affine_var", bench_group_add_affine_var, bench_setup, NULL, &data, 10, iters*10); + if (have_flag(argc, argv, "group") || have_flag(argc, argv, "jacobi")) run_benchmark("group_jacobi_var", bench_group_jacobi_var, bench_setup, NULL, &data, 10, iters); + + if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("wnaf_const", bench_wnaf_const, bench_setup, NULL, &data, 10, iters); + if (have_flag(argc, argv, "ecmult") || have_flag(argc, argv, "wnaf")) run_benchmark("ecmult_wnaf", bench_ecmult_wnaf, bench_setup, NULL, &data, 10, iters); + + if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "sha256")) run_benchmark("hash_sha256", bench_sha256, bench_setup, NULL, &data, 10, iters); + if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "hmac")) run_benchmark("hash_hmac_sha256", bench_hmac_sha256, bench_setup, NULL, &data, 10, iters); + if (have_flag(argc, argv, "hash") || have_flag(argc, argv, "rng6979")) run_benchmark("hash_rfc6979_hmac_sha256", bench_rfc6979_hmac_sha256, bench_setup, NULL, &data, 10, iters); + + if (have_flag(argc, argv, "context") || have_flag(argc, argv, "verify")) run_benchmark("context_verify", bench_context_verify, bench_setup, NULL, &data, 10, 1 + iters/1000); + if (have_flag(argc, argv, "context") || have_flag(argc, argv, "sign")) run_benchmark("context_sign", bench_context_sign, bench_setup, NULL, &data, 10, 1 + iters/100); + +#ifndef USE_NUM_NONE + if (have_flag(argc, argv, "num") || have_flag(argc, argv, "jacobi")) run_benchmark("num_jacobi", bench_num_jacobi, bench_setup, NULL, &data, 10, iters*10); +#endif + return 0; +} diff --git a/libsecp256k1/src/bench_recover.c b/libsecp256k1/src/bench_recover.c new file mode 100644 index 0000000..e952ed1 --- /dev/null +++ b/libsecp256k1/src/bench_recover.c @@ -0,0 +1,62 @@ +/********************************************************************** + * Copyright (c) 2014-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include "include/secp256k1.h" +#include "include/secp256k1_recovery.h" +#include "util.h" +#include "bench.h" + +typedef struct { + secp256k1_context *ctx; + unsigned char msg[32]; + unsigned char sig[64]; +} bench_recover_data; + +void bench_recover(void* arg, int iters) { + int i; + bench_recover_data *data = (bench_recover_data*)arg; + secp256k1_pubkey pubkey; + unsigned char pubkeyc[33]; + + for (i = 0; i < iters; i++) { + int j; + size_t pubkeylen = 33; + secp256k1_ecdsa_recoverable_signature sig; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(data->ctx, &sig, data->sig, i % 2)); + CHECK(secp256k1_ecdsa_recover(data->ctx, &pubkey, &sig, data->msg)); + CHECK(secp256k1_ec_pubkey_serialize(data->ctx, pubkeyc, &pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED)); + for (j = 0; j < 32; j++) { + data->sig[j + 32] = data->msg[j]; /* Move former message to S. */ + data->msg[j] = data->sig[j]; /* Move former R to message. */ + data->sig[j] = pubkeyc[j + 1]; /* Move recovered pubkey X coordinate to R (which must be a valid X coordinate). */ + } + } +} + +void bench_recover_setup(void* arg) { + int i; + bench_recover_data *data = (bench_recover_data*)arg; + + for (i = 0; i < 32; i++) { + data->msg[i] = 1 + i; + } + for (i = 0; i < 64; i++) { + data->sig[i] = 65 + i; + } +} + +int main(void) { + bench_recover_data data; + + int iters = get_iters(20000); + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY); + + run_benchmark("ecdsa_recover", bench_recover, bench_recover_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); + return 0; +} diff --git a/libsecp256k1/src/bench_sign.c b/libsecp256k1/src/bench_sign.c new file mode 100644 index 0000000..c6b2942 --- /dev/null +++ b/libsecp256k1/src/bench_sign.c @@ -0,0 +1,58 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include "include/secp256k1.h" +#include "util.h" +#include "bench.h" + +typedef struct { + secp256k1_context* ctx; + unsigned char msg[32]; + unsigned char key[32]; +} bench_sign; + +static void bench_sign_setup(void* arg) { + int i; + bench_sign *data = (bench_sign*)arg; + + for (i = 0; i < 32; i++) { + data->msg[i] = i + 1; + } + for (i = 0; i < 32; i++) { + data->key[i] = i + 65; + } +} + +static void bench_sign_run(void* arg, int iters) { + int i; + bench_sign *data = (bench_sign*)arg; + + unsigned char sig[74]; + for (i = 0; i < iters; i++) { + size_t siglen = 74; + int j; + secp256k1_ecdsa_signature signature; + CHECK(secp256k1_ecdsa_sign(data->ctx, &signature, data->msg, data->key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data->ctx, sig, &siglen, &signature)); + for (j = 0; j < 32; j++) { + data->msg[j] = sig[j]; + data->key[j] = sig[j + 32]; + } + } +} + +int main(void) { + bench_sign data; + + int iters = get_iters(20000); + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); + + run_benchmark("ecdsa_sign", bench_sign_run, bench_sign_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); + return 0; +} diff --git a/libsecp256k1/src/bench_verify.c b/libsecp256k1/src/bench_verify.c new file mode 100644 index 0000000..272d3e5 --- /dev/null +++ b/libsecp256k1/src/bench_verify.c @@ -0,0 +1,115 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include + +#include "include/secp256k1.h" +#include "util.h" +#include "bench.h" + +#ifdef ENABLE_OPENSSL_TESTS +#include +#include +#include +#endif + + +typedef struct { + secp256k1_context *ctx; + unsigned char msg[32]; + unsigned char key[32]; + unsigned char sig[72]; + size_t siglen; + unsigned char pubkey[33]; + size_t pubkeylen; +#ifdef ENABLE_OPENSSL_TESTS + EC_GROUP* ec_group; +#endif +} benchmark_verify_t; + +static void benchmark_verify(void* arg, int iters) { + int i; + benchmark_verify_t* data = (benchmark_verify_t*)arg; + + for (i = 0; i < iters; i++) { + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &pubkey, data->pubkey, data->pubkeylen) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(data->ctx, &sig, data->sig, data->siglen) == 1); + CHECK(secp256k1_ecdsa_verify(data->ctx, &sig, data->msg, &pubkey) == (i == 0)); + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + } +} + +#ifdef ENABLE_OPENSSL_TESTS +static void benchmark_verify_openssl(void* arg, int iters) { + int i; + benchmark_verify_t* data = (benchmark_verify_t*)arg; + + for (i = 0; i < iters; i++) { + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + { + EC_KEY *pkey = EC_KEY_new(); + const unsigned char *pubkey = &data->pubkey[0]; + int result; + + CHECK(pkey != NULL); + result = EC_KEY_set_group(pkey, data->ec_group); + CHECK(result); + result = (o2i_ECPublicKey(&pkey, &pubkey, data->pubkeylen)) != NULL; + CHECK(result); + result = ECDSA_verify(0, &data->msg[0], sizeof(data->msg), &data->sig[0], data->siglen, pkey) == (i == 0); + CHECK(result); + EC_KEY_free(pkey); + } + data->sig[data->siglen - 1] ^= (i & 0xFF); + data->sig[data->siglen - 2] ^= ((i >> 8) & 0xFF); + data->sig[data->siglen - 3] ^= ((i >> 16) & 0xFF); + } +} +#endif + +int main(void) { + int i; + secp256k1_pubkey pubkey; + secp256k1_ecdsa_signature sig; + benchmark_verify_t data; + + int iters = get_iters(20000); + + data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + + for (i = 0; i < 32; i++) { + data.msg[i] = 1 + i; + } + for (i = 0; i < 32; i++) { + data.key[i] = 33 + i; + } + data.siglen = 72; + CHECK(secp256k1_ecdsa_sign(data.ctx, &sig, data.msg, data.key, NULL, NULL)); + CHECK(secp256k1_ecdsa_signature_serialize_der(data.ctx, data.sig, &data.siglen, &sig)); + CHECK(secp256k1_ec_pubkey_create(data.ctx, &pubkey, data.key)); + data.pubkeylen = 33; + CHECK(secp256k1_ec_pubkey_serialize(data.ctx, data.pubkey, &data.pubkeylen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + + run_benchmark("ecdsa_verify", benchmark_verify, NULL, NULL, &data, 10, iters); +#ifdef ENABLE_OPENSSL_TESTS + data.ec_group = EC_GROUP_new_by_curve_name(NID_secp256k1); + run_benchmark("ecdsa_verify_openssl", benchmark_verify_openssl, NULL, NULL, &data, 10, iters); + EC_GROUP_free(data.ec_group); +#endif + + secp256k1_context_destroy(data.ctx); + return 0; +} diff --git a/libsecp256k1/src/dummy.go b/libsecp256k1/src/dummy.go new file mode 100644 index 0000000..65868f3 --- /dev/null +++ b/libsecp256k1/src/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package src diff --git a/libsecp256k1/src/ecdsa.h b/libsecp256k1/src/ecdsa.h new file mode 100644 index 0000000..80590c7 --- /dev/null +++ b/libsecp256k1/src/ecdsa.h @@ -0,0 +1,21 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECDSA_H +#define SECP256K1_ECDSA_H + +#include + +#include "scalar.h" +#include "group.h" +#include "ecmult.h" + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size); +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s); +static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message); +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid); + +#endif /* SECP256K1_ECDSA_H */ diff --git a/libsecp256k1/src/ecdsa_impl.h b/libsecp256k1/src/ecdsa_impl.h new file mode 100644 index 0000000..5f54b59 --- /dev/null +++ b/libsecp256k1/src/ecdsa_impl.h @@ -0,0 +1,315 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + + +#ifndef SECP256K1_ECDSA_IMPL_H +#define SECP256K1_ECDSA_IMPL_H + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult.h" +#include "ecmult_gen.h" +#include "ecdsa.h" + +/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1 + * sage: for t in xrange(1023, -1, -1): + * .. p = 2**256 - 2**32 - t + * .. if p.is_prime(): + * .. print '%x'%p + * .. break + * 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f' + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (EllipticCurve ([F (a), F (b)]).order()) + * 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141' + */ +static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL +); + +/** Difference between field and order, values 'p' and 'n' values defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + * sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F + * sage: a = 0 + * sage: b = 7 + * sage: F = FiniteField (p) + * sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order()) + * '14551231950b75fc4402da1722fc9baee' + */ +static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST( + 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL +); + +static int secp256k1_der_read_len(size_t *len, const unsigned char **sigp, const unsigned char *sigend) { + size_t lenleft; + unsigned char b1; + VERIFY_CHECK(len != NULL); + *len = 0; + if (*sigp >= sigend) { + return 0; + } + b1 = *((*sigp)++); + if (b1 == 0xFF) { + /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */ + return 0; + } + if ((b1 & 0x80) == 0) { + /* X.690-0207 8.1.3.4 short form length octets */ + *len = b1; + return 1; + } + if (b1 == 0x80) { + /* Indefinite length is not allowed in DER. */ + return 0; + } + /* X.690-207 8.1.3.5 long form length octets */ + lenleft = b1 & 0x7F; /* lenleft is at least 1 */ + if (lenleft > (size_t)(sigend - *sigp)) { + return 0; + } + if (**sigp == 0) { + /* Not the shortest possible length encoding. */ + return 0; + } + if (lenleft > sizeof(size_t)) { + /* The resulting length would exceed the range of a size_t, so + * certainly longer than the passed array size. + */ + return 0; + } + while (lenleft > 0) { + *len = (*len << 8) | **sigp; + (*sigp)++; + lenleft--; + } + if (*len > (size_t)(sigend - *sigp)) { + /* Result exceeds the length of the passed array. */ + return 0; + } + if (*len < 128) { + /* Not the shortest possible length encoding. */ + return 0; + } + return 1; +} + +static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) { + int overflow = 0; + unsigned char ra[32] = {0}; + size_t rlen; + + if (*sig == sigend || **sig != 0x02) { + /* Not a primitive integer (X.690-0207 8.3.1). */ + return 0; + } + (*sig)++; + if (secp256k1_der_read_len(&rlen, sig, sigend) == 0) { + return 0; + } + if (rlen == 0 || *sig + rlen > sigend) { + /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1). */ + return 0; + } + if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) { + /* Excessive 0x00 padding. */ + return 0; + } + if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) { + /* Excessive 0xFF padding. */ + return 0; + } + if ((**sig & 0x80) == 0x80) { + /* Negative. */ + overflow = 1; + } + /* There is at most one leading zero byte: + * if there were two leading zero bytes, we would have failed and returned 0 + * because of excessive 0x00 padding already. */ + if (rlen > 0 && **sig == 0) { + /* Skip leading zero byte */ + rlen--; + (*sig)++; + } + if (rlen > 32) { + overflow = 1; + } + if (!overflow) { + memcpy(ra + 32 - rlen, *sig, rlen); + secp256k1_scalar_set_b32(r, ra, &overflow); + } + if (overflow) { + secp256k1_scalar_set_int(r, 0); + } + (*sig) += rlen; + return 1; +} + +static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) { + const unsigned char *sigend = sig + size; + size_t rlen; + if (sig == sigend || *(sig++) != 0x30) { + /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */ + return 0; + } + if (secp256k1_der_read_len(&rlen, &sig, sigend) == 0) { + return 0; + } + if (rlen != (size_t)(sigend - sig)) { + /* Tuple exceeds bounds or garage after tuple. */ + return 0; + } + + if (!secp256k1_der_parse_integer(rr, &sig, sigend)) { + return 0; + } + if (!secp256k1_der_parse_integer(rs, &sig, sigend)) { + return 0; + } + + if (sig != sigend) { + /* Trailing garbage inside tuple. */ + return 0; + } + + return 1; +} + +static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) { + unsigned char r[33] = {0}, s[33] = {0}; + unsigned char *rp = r, *sp = s; + size_t lenR = 33, lenS = 33; + secp256k1_scalar_get_b32(&r[1], ar); + secp256k1_scalar_get_b32(&s[1], as); + while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; } + while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; } + if (*size < 6+lenS+lenR) { + *size = 6 + lenS + lenR; + return 0; + } + *size = 6 + lenS + lenR; + sig[0] = 0x30; + sig[1] = 4 + lenS + lenR; + sig[2] = 0x02; + sig[3] = lenR; + memcpy(sig+4, rp, lenR); + sig[4+lenR] = 0x02; + sig[5+lenR] = lenS; + memcpy(sig+lenR+6, sp, lenS); + return 1; +} + +static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) { + unsigned char c[32]; + secp256k1_scalar sn, u1, u2; +#if !defined(EXHAUSTIVE_TEST_ORDER) + secp256k1_fe xr; +#endif + secp256k1_gej pubkeyj; + secp256k1_gej pr; + + if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) { + return 0; + } + + secp256k1_scalar_inverse_var(&sn, sigs); + secp256k1_scalar_mul(&u1, &sn, message); + secp256k1_scalar_mul(&u2, &sn, sigr); + secp256k1_gej_set_ge(&pubkeyj, pubkey); + secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1); + if (secp256k1_gej_is_infinity(&pr)) { + return 0; + } + +#if defined(EXHAUSTIVE_TEST_ORDER) +{ + secp256k1_scalar computed_r; + secp256k1_ge pr_ge; + secp256k1_ge_set_gej(&pr_ge, &pr); + secp256k1_fe_normalize(&pr_ge.x); + + secp256k1_fe_get_b32(c, &pr_ge.x); + secp256k1_scalar_set_b32(&computed_r, c, NULL); + return secp256k1_scalar_eq(sigr, &computed_r); +} +#else + secp256k1_scalar_get_b32(c, sigr); + secp256k1_fe_set_b32(&xr, c); + + /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n) + * in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p), + * compute the remainder modulo n, and compare it to xr. However: + * + * xr == X(pr) mod n + * <=> exists h. (xr + h * n < p && xr + h * n == X(pr)) + * [Since 2 * n > p, h can only be 0 or 1] + * <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr)) + * [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p] + * <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p) + * [Multiplying both sides of the equations by pr.z^2 mod p] + * <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x) + * + * Thus, we can avoid the inversion, but we have to check both cases separately. + * secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test. + */ + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) { + /* xr + n >= p, so we can skip testing the second case. */ + return 0; + } + secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe); + if (secp256k1_gej_eq_x_var(&xr, &pr)) { + /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */ + return 1; + } + return 0; +#endif +} + +static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) { + unsigned char b[32]; + secp256k1_gej rp; + secp256k1_ge r; + secp256k1_scalar n; + int overflow = 0; + int high; + + secp256k1_ecmult_gen(ctx, &rp, nonce); + secp256k1_ge_set_gej(&r, &rp); + secp256k1_fe_normalize(&r.x); + secp256k1_fe_normalize(&r.y); + secp256k1_fe_get_b32(b, &r.x); + secp256k1_scalar_set_b32(sigr, b, &overflow); + if (recid) { + /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log + * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria. + */ + *recid = (overflow << 1) | secp256k1_fe_is_odd(&r.y); + } + secp256k1_scalar_mul(&n, sigr, seckey); + secp256k1_scalar_add(&n, &n, message); + secp256k1_scalar_inverse(sigs, nonce); + secp256k1_scalar_mul(sigs, sigs, &n); + secp256k1_scalar_clear(&n); + secp256k1_gej_clear(&rp); + secp256k1_ge_clear(&r); + high = secp256k1_scalar_is_high(sigs); + secp256k1_scalar_cond_negate(sigs, high); + if (recid) { + *recid ^= high; + } + /* P.x = order is on the curve, so technically sig->r could end up being zero, which would be an invalid signature. + * This is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N. + */ + return !secp256k1_scalar_is_zero(sigr) & !secp256k1_scalar_is_zero(sigs); +} + +#endif /* SECP256K1_ECDSA_IMPL_H */ diff --git a/libsecp256k1/src/eckey.h b/libsecp256k1/src/eckey.h new file mode 100644 index 0000000..b621f1e --- /dev/null +++ b/libsecp256k1/src/eckey.h @@ -0,0 +1,25 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECKEY_H +#define SECP256K1_ECKEY_H + +#include + +#include "group.h" +#include "scalar.h" +#include "ecmult.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size); +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed); + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak); +static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak); + +#endif /* SECP256K1_ECKEY_H */ diff --git a/libsecp256k1/src/eckey_impl.h b/libsecp256k1/src/eckey_impl.h new file mode 100644 index 0000000..e2e72d9 --- /dev/null +++ b/libsecp256k1/src/eckey_impl.h @@ -0,0 +1,96 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECKEY_IMPL_H +#define SECP256K1_ECKEY_IMPL_H + +#include "eckey.h" + +#include "scalar.h" +#include "field.h" +#include "group.h" +#include "ecmult_gen.h" + +static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) { + if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) { + secp256k1_fe x; + return secp256k1_fe_set_b32(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD); + } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + secp256k1_fe x, y; + if (!secp256k1_fe_set_b32(&x, pub+1) || !secp256k1_fe_set_b32(&y, pub+33)) { + return 0; + } + secp256k1_ge_set_xy(elem, &x, &y); + if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) && + secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) { + return 0; + } + return secp256k1_ge_is_valid_var(elem); + } else { + return 0; + } +} + +static int secp256k1_eckey_pubkey_serialize(secp256k1_ge *elem, unsigned char *pub, size_t *size, int compressed) { + if (secp256k1_ge_is_infinity(elem)) { + return 0; + } + secp256k1_fe_normalize_var(&elem->x); + secp256k1_fe_normalize_var(&elem->y); + secp256k1_fe_get_b32(&pub[1], &elem->x); + if (compressed) { + *size = 33; + pub[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN; + } else { + *size = 65; + pub[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED; + secp256k1_fe_get_b32(&pub[33], &elem->y); + } + return 1; +} + +static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + secp256k1_scalar_add(key, key, tweak); + return !secp256k1_scalar_is_zero(key); +} + +static int secp256k1_eckey_pubkey_tweak_add(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_gej pt; + secp256k1_scalar one; + secp256k1_gej_set_ge(&pt, key); + secp256k1_scalar_set_int(&one, 1); + secp256k1_ecmult(ctx, &pt, &pt, &one, tweak); + + if (secp256k1_gej_is_infinity(&pt)) { + return 0; + } + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) { + int ret; + ret = !secp256k1_scalar_is_zero(tweak); + + secp256k1_scalar_mul(key, key, tweak); + return ret; +} + +static int secp256k1_eckey_pubkey_tweak_mul(const secp256k1_ecmult_context *ctx, secp256k1_ge *key, const secp256k1_scalar *tweak) { + secp256k1_scalar zero; + secp256k1_gej pt; + if (secp256k1_scalar_is_zero(tweak)) { + return 0; + } + + secp256k1_scalar_set_int(&zero, 0); + secp256k1_gej_set_ge(&pt, key); + secp256k1_ecmult(ctx, &pt, &pt, tweak, &zero); + secp256k1_ge_set_gej(key, &pt); + return 1; +} + +#endif /* SECP256K1_ECKEY_IMPL_H */ diff --git a/libsecp256k1/src/ecmult.h b/libsecp256k1/src/ecmult.h new file mode 100644 index 0000000..c9b1982 --- /dev/null +++ b/libsecp256k1/src/ecmult.h @@ -0,0 +1,48 @@ +/********************************************************************** + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_H +#define SECP256K1_ECMULT_H + +#include "num.h" +#include "group.h" +#include "scalar.h" +#include "scratch.h" + +typedef struct { + /* For accelerating the computation of a*P + b*G: */ + secp256k1_ge_storage (*pre_g)[]; /* odd multiples of the generator */ +#ifdef USE_ENDOMORPHISM + secp256k1_ge_storage (*pre_g_128)[]; /* odd multiples of 2^128*generator */ +#endif +} secp256k1_ecmult_context; + +static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE; +static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx); +static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc); +static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src); +static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx); +static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx); + +/** Double multiply: R = na*A + ng*G */ +static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng); + +typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data); + +/** + * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai. + * Chooses the right algorithm for a given number of points and scratch space + * size. Resets and overwrites the given scratch space. If the points do not + * fit in the scratch space the algorithm is repeatedly run with batches of + * points. If no scratch space is given then a simple algorithm is used that + * simply multiplies the points with the corresponding scalars and adds them up. + * Returns: 1 on success (including when inp_g_sc is NULL and n is 0) + * 0 if there is not enough scratch space for a single point or + * callback returns 0 + */ +static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n); + +#endif /* SECP256K1_ECMULT_H */ diff --git a/libsecp256k1/src/ecmult_const.h b/libsecp256k1/src/ecmult_const.h new file mode 100644 index 0000000..03bb332 --- /dev/null +++ b/libsecp256k1/src/ecmult_const.h @@ -0,0 +1,20 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_H +#define SECP256K1_ECMULT_CONST_H + +#include "scalar.h" +#include "group.h" + +/** + * Multiply: R = q*A (in constant-time) + * Here `bits` should be set to the maximum bitlength of the _absolute value_ of `q`, plus + * one because we internally sometimes add 2 to the number during the WNAF conversion. + */ +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q, int bits); + +#endif /* SECP256K1_ECMULT_CONST_H */ diff --git a/libsecp256k1/src/ecmult_const_impl.h b/libsecp256k1/src/ecmult_const_impl.h new file mode 100644 index 0000000..011ccf0 --- /dev/null +++ b/libsecp256k1/src/ecmult_const_impl.h @@ -0,0 +1,264 @@ +/********************************************************************** + * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_CONST_IMPL_H +#define SECP256K1_ECMULT_CONST_IMPL_H + +#include "scalar.h" +#include "group.h" +#include "ecmult_const.h" +#include "ecmult_impl.h" + +/* This is like `ECMULT_TABLE_GET_GE` but is constant time */ +#define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \ + int m; \ + /* Extract the sign-bit for a constant time absolute-value. */ \ + int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \ + int abs_n = ((n) + mask) ^ mask; \ + int idx_n = abs_n >> 1; \ + secp256k1_fe neg_y; \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \ + VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \ + for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \ + /* This loop is used to avoid secret data in array indices. See + * the comment in ecmult_gen_impl.h for rationale. */ \ + secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \ + secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == idx_n); \ + } \ + (r)->infinity = 0; \ + secp256k1_fe_negate(&neg_y, &(r)->y, 1); \ + secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \ +} while(0) + + +/** Convert a number to WNAF notation. + * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. + * It has the following guarantees: + * - each wnaf[i] an odd integer between -(1 << w) and (1 << w) + * - each wnaf[i] is nonzero + * - the number of words set is always WNAF_SIZE(w) + 1 + * + * Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar + * Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.) + * CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlag Berlin Heidelberg 2003 + * + * Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335 + */ +static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) { + int global_sign; + int skew = 0; + int word = 0; + + /* 1 2 3 */ + int u_last; + int u; + + int flip; + int bit; + secp256k1_scalar s; + int not_neg_one; + + VERIFY_CHECK(w > 0); + VERIFY_CHECK(size > 0); + + /* Note that we cannot handle even numbers by negating them to be odd, as is + * done in other implementations, since if our scalars were specified to have + * width < 256 for performance reasons, their negations would have width 256 + * and we'd lose any performance benefit. Instead, we use a technique from + * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even) + * or 2 (for odd) to the number we are encoding, returning a skew value indicating + * this, and having the caller compensate after doing the multiplication. + * + * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in + * particular, to ensure that the outputs from the endomorphism-split fit into + * 128 bits). If we negate, the parity of our number flips, inverting which of + * {1, 2} we want to add to the scalar when ensuring that it's odd. Further + * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and + * we need to special-case it in this logic. */ + flip = secp256k1_scalar_is_high(scalar); + /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ + bit = flip ^ !secp256k1_scalar_is_even(scalar); + /* We check for negative one, since adding 2 to it will cause an overflow */ + secp256k1_scalar_negate(&s, scalar); + not_neg_one = !secp256k1_scalar_is_one(&s); + s = *scalar; + secp256k1_scalar_cadd_bit(&s, bit, not_neg_one); + /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects + * that we added two to it and flipped it. In fact for -1 these operations are + * identical. We only flipped, but since skewing is required (in the sense that + * the skew must be 1 or 2, never zero) and flipping is not, we need to change + * our flags to claim that we only skewed. */ + global_sign = secp256k1_scalar_cond_negate(&s, flip); + global_sign *= not_neg_one * 2 - 1; + skew = 1 << bit; + + /* 4 */ + u_last = secp256k1_scalar_shr_int(&s, w); + do { + int sign; + int even; + + /* 4.1 4.4 */ + u = secp256k1_scalar_shr_int(&s, w); + /* 4.2 */ + even = ((u & 1) == 0); + sign = 2 * (u_last > 0) - 1; + u += sign * even; + u_last -= sign * even * (1 << w); + + /* 4.3, adapted for global sign change */ + wnaf[word++] = u_last * global_sign; + + u_last = u; + } while (word * w < size); + wnaf[word] = u * global_sign; + + VERIFY_CHECK(secp256k1_scalar_is_zero(&s)); + VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w)); + return skew; +} + +static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *scalar, int size) { + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge tmpa; + secp256k1_fe Z; + + int skew_1; +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + int wnaf_lam[1 + WNAF_SIZE(WINDOW_A - 1)]; + int skew_lam; + secp256k1_scalar q_1, q_lam; +#endif + int wnaf_1[1 + WNAF_SIZE(WINDOW_A - 1)]; + + int i; + + /* build wnaf representation for q. */ + int rsize = size; +#ifdef USE_ENDOMORPHISM + if (size > 128) { + rsize = 128; + /* split q into q_1 and q_lam (where q = q_1 + q_lam*lambda, and q_1 and q_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&q_1, &q_lam, scalar); + skew_1 = secp256k1_wnaf_const(wnaf_1, &q_1, WINDOW_A - 1, 128); + skew_lam = secp256k1_wnaf_const(wnaf_lam, &q_lam, WINDOW_A - 1, 128); + } else +#endif + { + skew_1 = secp256k1_wnaf_const(wnaf_1, scalar, WINDOW_A - 1, size); +#ifdef USE_ENDOMORPHISM + skew_lam = 0; +#endif + } + + /* Calculate odd multiples of a. + * All multiples are brought to the same Z 'denominator', which is stored + * in Z. Due to secp256k1' isomorphism we can do all operations pretending + * that the Z coordinate was 1, use affine addition formulae, and correct + * the Z coordinate of the result once at the end. + */ + secp256k1_gej_set_ge(r, a); + secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, r); + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_fe_normalize_weak(&pre_a[i].y); + } +#ifdef USE_ENDOMORPHISM + if (size > 128) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); + } + + } +#endif + + /* first loop iteration (separated out so we can directly set r, rather + * than having it start at infinity, get doubled several times, then have + * its new value added to it) */ + i = wnaf_1[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, i, WINDOW_A); + secp256k1_gej_set_ge(r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + i = wnaf_lam[WNAF_SIZE_BITS(rsize, WINDOW_A - 1)]; + VERIFY_CHECK(i != 0); + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, i, WINDOW_A); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + /* remaining loop iterations */ + for (i = WNAF_SIZE_BITS(rsize, WINDOW_A - 1) - 1; i >= 0; i--) { + int n; + int j; + for (j = 0; j < WINDOW_A - 1; ++j) { + secp256k1_gej_double_nonzero(r, r); + } + + n = wnaf_1[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + n = wnaf_lam[i]; + ECMULT_CONST_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A); + VERIFY_CHECK(n != 0); + secp256k1_gej_add_ge(r, r, &tmpa); + } +#endif + } + + secp256k1_fe_mul(&r->z, &r->z, &Z); + + { + /* Correct for wNAF skew */ + secp256k1_ge correction = *a; + secp256k1_ge_storage correction_1_stor; +#ifdef USE_ENDOMORPHISM + secp256k1_ge_storage correction_lam_stor; +#endif + secp256k1_ge_storage a2_stor; + secp256k1_gej tmpj; + secp256k1_gej_set_ge(&tmpj, &correction); + secp256k1_gej_double_var(&tmpj, &tmpj, NULL); + secp256k1_ge_set_gej(&correction, &tmpj); + secp256k1_ge_to_storage(&correction_1_stor, a); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_to_storage(&correction_lam_stor, a); + } +#endif + secp256k1_ge_to_storage(&a2_stor, &correction); + + /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */ + secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2); +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2); + } +#endif + + /* Apply the correction */ + secp256k1_ge_from_storage(&correction, &correction_1_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + +#ifdef USE_ENDOMORPHISM + if (size > 128) { + secp256k1_ge_from_storage(&correction, &correction_lam_stor); + secp256k1_ge_neg(&correction, &correction); + secp256k1_ge_mul_lambda(&correction, &correction); + secp256k1_gej_add_ge(r, r, &correction); + } +#endif + } +} + +#endif /* SECP256K1_ECMULT_CONST_IMPL_H */ diff --git a/libsecp256k1/src/ecmult_gen.h b/libsecp256k1/src/ecmult_gen.h new file mode 100644 index 0000000..30815e5 --- /dev/null +++ b/libsecp256k1/src/ecmult_gen.h @@ -0,0 +1,50 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_H +#define SECP256K1_ECMULT_GEN_H + +#include "scalar.h" +#include "group.h" + +#if ECMULT_GEN_PREC_BITS != 2 && ECMULT_GEN_PREC_BITS != 4 && ECMULT_GEN_PREC_BITS != 8 +# error "Set ECMULT_GEN_PREC_BITS to 2, 4 or 8." +#endif +#define ECMULT_GEN_PREC_B ECMULT_GEN_PREC_BITS +#define ECMULT_GEN_PREC_G (1 << ECMULT_GEN_PREC_B) +#define ECMULT_GEN_PREC_N (256 / ECMULT_GEN_PREC_B) + +typedef struct { + /* For accelerating the computation of a*G: + * To harden against timing attacks, use the following mechanism: + * * Break up the multiplicand into groups of PREC_B bits, called n_0, n_1, n_2, ..., n_(PREC_N-1). + * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where: + * * U_i = U * 2^i, for i=0 ... PREC_N-2 + * * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1 + * where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0. + * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is + * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1). + * None of the resulting prec group elements have a known scalar, and neither do any of + * the intermediate sums while computing a*G. + */ + secp256k1_ge_storage (*prec)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G]; /* prec[j][i] = (PREC_G)^j * i * G + U_i */ + secp256k1_scalar blind; + secp256k1_gej initial; +} secp256k1_ecmult_gen_context; + +static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE; +static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context* ctx); +static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, void **prealloc); +static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context* src); +static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx); +static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx); + +/** Multiply with the generator: R = a*G */ +static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a); + +static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32); + +#endif /* SECP256K1_ECMULT_GEN_H */ diff --git a/libsecp256k1/src/ecmult_gen_impl.h b/libsecp256k1/src/ecmult_gen_impl.h new file mode 100644 index 0000000..30ac165 --- /dev/null +++ b/libsecp256k1/src/ecmult_gen_impl.h @@ -0,0 +1,208 @@ +/********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_ECMULT_GEN_IMPL_H +#define SECP256K1_ECMULT_GEN_IMPL_H + +#include "util.h" +#include "scalar.h" +#include "group.h" +#include "ecmult_gen.h" +#include "hash_impl.h" +#ifdef USE_ECMULT_STATIC_PRECOMPUTATION +#include "ecmult_static_context.h" +#endif + +#ifndef USE_ECMULT_STATIC_PRECOMPUTATION + static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = ROUND_TO_ALIGN(sizeof(*((secp256k1_ecmult_gen_context*) NULL)->prec)); +#else + static const size_t SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE = 0; +#endif + +static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx) { + ctx->prec = NULL; +} + +static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, void **prealloc) { +#ifndef USE_ECMULT_STATIC_PRECOMPUTATION + secp256k1_ge prec[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G]; + secp256k1_gej gj; + secp256k1_gej nums_gej; + int i, j; + size_t const prealloc_size = SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE; + void* const base = *prealloc; +#endif + + if (ctx->prec != NULL) { + return; + } +#ifndef USE_ECMULT_STATIC_PRECOMPUTATION + ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])manual_alloc(prealloc, prealloc_size, base, prealloc_size); + + /* get the generator */ + secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g); + + /* Construct a group element with no known corresponding scalar (nothing up my sleeve). */ + { + static const unsigned char nums_b32[33] = "The scalar for this x is unknown"; + secp256k1_fe nums_x; + secp256k1_ge nums_ge; + int r; + r = secp256k1_fe_set_b32(&nums_x, nums_b32); + (void)r; + VERIFY_CHECK(r); + r = secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0); + (void)r; + VERIFY_CHECK(r); + secp256k1_gej_set_ge(&nums_gej, &nums_ge); + /* Add G to make the bits in x uniformly distributed. */ + secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g, NULL); + } + + /* compute prec. */ + { + secp256k1_gej precj[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G]; /* Jacobian versions of prec. */ + secp256k1_gej gbase; + secp256k1_gej numsbase; + gbase = gj; /* PREC_G^j * G */ + numsbase = nums_gej; /* 2^j * nums. */ + for (j = 0; j < ECMULT_GEN_PREC_N; j++) { + /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */ + precj[j*ECMULT_GEN_PREC_G] = numsbase; + for (i = 1; i < ECMULT_GEN_PREC_G; i++) { + secp256k1_gej_add_var(&precj[j*ECMULT_GEN_PREC_G + i], &precj[j*ECMULT_GEN_PREC_G + i - 1], &gbase, NULL); + } + /* Multiply gbase by PREC_G. */ + for (i = 0; i < ECMULT_GEN_PREC_B; i++) { + secp256k1_gej_double_var(&gbase, &gbase, NULL); + } + /* Multiply numbase by 2. */ + secp256k1_gej_double_var(&numsbase, &numsbase, NULL); + if (j == ECMULT_GEN_PREC_N - 2) { + /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */ + secp256k1_gej_neg(&numsbase, &numsbase); + secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL); + } + } + secp256k1_ge_set_all_gej_var(prec, precj, ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G); + } + for (j = 0; j < ECMULT_GEN_PREC_N; j++) { + for (i = 0; i < ECMULT_GEN_PREC_G; i++) { + secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*ECMULT_GEN_PREC_G + i]); + } + } +#else + (void)prealloc; + ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])secp256k1_ecmult_static_context; +#endif + secp256k1_ecmult_gen_blind(ctx, NULL); +} + +static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) { + return ctx->prec != NULL; +} + +static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_context *dst, const secp256k1_ecmult_gen_context *src) { +#ifndef USE_ECMULT_STATIC_PRECOMPUTATION + if (src->prec != NULL) { + /* We cast to void* first to suppress a -Wcast-align warning. */ + dst->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])(void*)((unsigned char*)dst + ((unsigned char*)src->prec - (unsigned char*)src)); + } +#else + (void)dst, (void)src; +#endif +} + +static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) { + secp256k1_scalar_clear(&ctx->blind); + secp256k1_gej_clear(&ctx->initial); + ctx->prec = NULL; +} + +static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) { + secp256k1_ge add; + secp256k1_ge_storage adds; + secp256k1_scalar gnb; + int bits; + int i, j; + memset(&adds, 0, sizeof(adds)); + *r = ctx->initial; + /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */ + secp256k1_scalar_add(&gnb, gn, &ctx->blind); + add.infinity = 0; + for (j = 0; j < ECMULT_GEN_PREC_N; j++) { + bits = secp256k1_scalar_get_bits(&gnb, j * ECMULT_GEN_PREC_B, ECMULT_GEN_PREC_B); + for (i = 0; i < ECMULT_GEN_PREC_G; i++) { + /** This uses a conditional move to avoid any secret data in array indexes. + * _Any_ use of secret indexes has been demonstrated to result in timing + * sidechannels, even when the cache-line access patterns are uniform. + * See also: + * "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe + * (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and + * "Cache Attacks and Countermeasures: the Case of AES", RSA 2006, + * by Dag Arne Osvik, Adi Shamir, and Eran Tromer + * (http://www.tau.ac.il/~tromer/papers/cache.pdf) + */ + secp256k1_ge_storage_cmov(&adds, &(*ctx->prec)[j][i], i == bits); + } + secp256k1_ge_from_storage(&add, &adds); + secp256k1_gej_add_ge(r, r, &add); + } + bits = 0; + secp256k1_ge_clear(&add); + secp256k1_scalar_clear(&gnb); +} + +/* Setup blinding values for secp256k1_ecmult_gen. */ +static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const unsigned char *seed32) { + secp256k1_scalar b; + secp256k1_gej gb; + secp256k1_fe s; + unsigned char nonce32[32]; + secp256k1_rfc6979_hmac_sha256 rng; + int overflow; + unsigned char keydata[64] = {0}; + if (seed32 == NULL) { + /* When seed is NULL, reset the initial point and blinding value. */ + secp256k1_gej_set_ge(&ctx->initial, &secp256k1_ge_const_g); + secp256k1_gej_neg(&ctx->initial, &ctx->initial); + secp256k1_scalar_set_int(&ctx->blind, 1); + } + /* The prior blinding value (if not reset) is chained forward by including it in the hash. */ + secp256k1_scalar_get_b32(nonce32, &ctx->blind); + /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data, + * and guards against weak or adversarial seeds. This is a simpler and safer interface than + * asking the caller for blinding values directly and expecting them to retry on failure. + */ + memcpy(keydata, nonce32, 32); + if (seed32 != NULL) { + memcpy(keydata + 32, seed32, 32); + } + secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, seed32 ? 64 : 32); + memset(keydata, 0, sizeof(keydata)); + /* Accept unobservably small non-uniformity. */ + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + overflow = !secp256k1_fe_set_b32(&s, nonce32); + overflow |= secp256k1_fe_is_zero(&s); + secp256k1_fe_cmov(&s, &secp256k1_fe_one, overflow); + /* Randomize the projection to defend against multiplier sidechannels. */ + secp256k1_gej_rescale(&ctx->initial, &s); + secp256k1_fe_clear(&s); + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + secp256k1_scalar_set_b32(&b, nonce32, NULL); + /* A blinding value of 0 works, but would undermine the projection hardening. */ + secp256k1_scalar_cmov(&b, &secp256k1_scalar_one, secp256k1_scalar_is_zero(&b)); + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + memset(nonce32, 0, 32); + secp256k1_ecmult_gen(ctx, &gb, &b); + secp256k1_scalar_negate(&b, &b); + ctx->blind = b; + ctx->initial = gb; + secp256k1_scalar_clear(&b); + secp256k1_gej_clear(&gb); +} + +#endif /* SECP256K1_ECMULT_GEN_IMPL_H */ diff --git a/libsecp256k1/src/ecmult_impl.h b/libsecp256k1/src/ecmult_impl.h new file mode 100644 index 0000000..f03fa94 --- /dev/null +++ b/libsecp256k1/src/ecmult_impl.h @@ -0,0 +1,1216 @@ +/***************************************************************************** + * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************/ + +#ifndef SECP256K1_ECMULT_IMPL_H +#define SECP256K1_ECMULT_IMPL_H + +#include +#include + +#include "util.h" +#include "group.h" +#include "scalar.h" +#include "ecmult.h" + +#if defined(EXHAUSTIVE_TEST_ORDER) +/* We need to lower these values for exhaustive tests because + * the tables cannot have infinities in them (this breaks the + * affine-isomorphism stuff which tracks z-ratios) */ +# if EXHAUSTIVE_TEST_ORDER > 128 +# define WINDOW_A 5 +# define WINDOW_G 8 +# elif EXHAUSTIVE_TEST_ORDER > 8 +# define WINDOW_A 4 +# define WINDOW_G 4 +# else +# define WINDOW_A 2 +# define WINDOW_G 2 +# endif +#else +/* optimal for 128-bit and 256-bit exponents. */ +# define WINDOW_A 5 +/** Larger values for ECMULT_WINDOW_SIZE result in possibly better + * performance at the cost of an exponentially larger precomputed + * table. The exact table size is + * (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage) bytes, + * where sizeof(secp256k1_ge_storage) is typically 64 bytes but can + * be larger due to platform-specific padding and alignment. + * If the endomorphism optimization is enabled (USE_ENDOMORMPHSIM) + * two tables of this size are used instead of only one. + */ +# define WINDOW_G ECMULT_WINDOW_SIZE +#endif + +/* Noone will ever need more than a window size of 24. The code might + * be correct for larger values of ECMULT_WINDOW_SIZE but this is not + * not tested. + * + * The following limitations are known, and there are probably more: + * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect + * because the size of the memory object that we allocate (in bytes) + * will not fit in a size_t. + * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect + * because certain expressions will overflow. + */ +#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24 +# error Set ECMULT_WINDOW_SIZE to an integer in range [2..24]. +#endif + +#ifdef USE_ENDOMORPHISM + #define WNAF_BITS 128 +#else + #define WNAF_BITS 256 +#endif +#define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w)) +#define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w) + +/** The number of entries a table with precomputed multiples needs to have. */ +#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2)) + +/* The number of objects allocated on the scratch space for ecmult_multi algorithms */ +#define PIPPENGER_SCRATCH_OBJECTS 6 +#define STRAUSS_SCRATCH_OBJECTS 6 + +#define PIPPENGER_MAX_BUCKET_WINDOW 12 + +/* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */ +#ifdef USE_ENDOMORPHISM + #define ECMULT_PIPPENGER_THRESHOLD 88 +#else + #define ECMULT_PIPPENGER_THRESHOLD 160 +#endif + +#ifdef USE_ENDOMORPHISM + #define ECMULT_MAX_POINTS_PER_BATCH 5000000 +#else + #define ECMULT_MAX_POINTS_PER_BATCH 10000000 +#endif + +/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain + * the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will + * contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z. + * Prej's Z values are undefined, except for the last value. + */ +static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) { + secp256k1_gej d; + secp256k1_ge a_ge, d_ge; + int i; + + VERIFY_CHECK(!a->infinity); + + secp256k1_gej_double_var(&d, a, NULL); + + /* + * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate + * of 'd', and scale the 1P starting value's x/y coordinates without changing its z. + */ + d_ge.x = d.x; + d_ge.y = d.y; + d_ge.infinity = 0; + + secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z); + prej[0].x = a_ge.x; + prej[0].y = a_ge.y; + prej[0].z = a->z; + prej[0].infinity = 0; + + zr[0] = d.z; + for (i = 1; i < n; i++) { + secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]); + } + + /* + * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only + * the final point's z coordinate is actually used though, so just update that. + */ + secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z); +} + +/** Fill a table 'pre' with precomputed odd multiples of a. + * + * There are two versions of this function: + * - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its + * resulting point set to a single constant Z denominator, stores the X and Y + * coordinates as ge_storage points in pre, and stores the global Z in rz. + * It only operates on tables sized for WINDOW_A wnaf multiples. + * - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its + * resulting point set to actually affine points, and stores those in pre. + * It operates on tables of any size. + * + * To compute a*P + b*G, we compute a table for P using the first function, + * and for G using the second (which requires an inverse, but it only needs to + * happen once). + */ +static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) { + secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; + + /* Compute the odd multiples in Jacobian form. */ + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a); + /* Bring them to the same Z denominator. */ + secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr); +} + +static void secp256k1_ecmult_odd_multiples_table_storage_var(const int n, secp256k1_ge_storage *pre, const secp256k1_gej *a) { + secp256k1_gej d; + secp256k1_ge d_ge, p_ge; + secp256k1_gej pj; + secp256k1_fe zi; + secp256k1_fe zr; + secp256k1_fe dx_over_dz_squared; + int i; + + VERIFY_CHECK(!a->infinity); + + secp256k1_gej_double_var(&d, a, NULL); + + /* First, we perform all the additions in an isomorphic curve obtained by multiplying + * all `z` coordinates by 1/`d.z`. In these coordinates `d` is affine so we can use + * `secp256k1_gej_add_ge_var` to perform the additions. For each addition, we store + * the resulting y-coordinate and the z-ratio, since we only have enough memory to + * store two field elements. These are sufficient to efficiently undo the isomorphism + * and recompute all the `x`s. + */ + d_ge.x = d.x; + d_ge.y = d.y; + d_ge.infinity = 0; + + secp256k1_ge_set_gej_zinv(&p_ge, a, &d.z); + pj.x = p_ge.x; + pj.y = p_ge.y; + pj.z = a->z; + pj.infinity = 0; + + for (i = 0; i < (n - 1); i++) { + secp256k1_fe_normalize_var(&pj.y); + secp256k1_fe_to_storage(&pre[i].y, &pj.y); + secp256k1_gej_add_ge_var(&pj, &pj, &d_ge, &zr); + secp256k1_fe_normalize_var(&zr); + secp256k1_fe_to_storage(&pre[i].x, &zr); + } + + /* Invert d.z in the same batch, preserving pj.z so we can extract 1/d.z */ + secp256k1_fe_mul(&zi, &pj.z, &d.z); + secp256k1_fe_inv_var(&zi, &zi); + + /* Directly set `pre[n - 1]` to `pj`, saving the inverted z-coordinate so + * that we can combine it with the saved z-ratios to compute the other zs + * without any more inversions. */ + secp256k1_ge_set_gej_zinv(&p_ge, &pj, &zi); + secp256k1_ge_to_storage(&pre[n - 1], &p_ge); + + /* Compute the actual x-coordinate of D, which will be needed below. */ + secp256k1_fe_mul(&d.z, &zi, &pj.z); /* d.z = 1/d.z */ + secp256k1_fe_sqr(&dx_over_dz_squared, &d.z); + secp256k1_fe_mul(&dx_over_dz_squared, &dx_over_dz_squared, &d.x); + + /* Going into the second loop, we have set `pre[n-1]` to its final affine + * form, but still need to set `pre[i]` for `i` in 0 through `n-2`. We + * have `zi = (p.z * d.z)^-1`, where + * + * `p.z` is the z-coordinate of the point on the isomorphic curve + * which was ultimately assigned to `pre[n-1]`. + * `d.z` is the multiplier that must be applied to all z-coordinates + * to move from our isomorphic curve back to secp256k1; so the + * product `p.z * d.z` is the z-coordinate of the secp256k1 + * point assigned to `pre[n-1]`. + * + * All subsequent inverse-z-coordinates can be obtained by multiplying this + * factor by successive z-ratios, which is much more efficient than directly + * computing each one. + * + * Importantly, these inverse-zs will be coordinates of points on secp256k1, + * while our other stored values come from computations on the isomorphic + * curve. So in the below loop, we will take care not to actually use `zi` + * or any derived values until we're back on secp256k1. + */ + i = n - 1; + while (i > 0) { + secp256k1_fe zi2, zi3; + const secp256k1_fe *rzr; + i--; + + secp256k1_ge_from_storage(&p_ge, &pre[i]); + + /* For each remaining point, we extract the z-ratio from the stored + * x-coordinate, compute its z^-1 from that, and compute the full + * point from that. */ + rzr = &p_ge.x; + secp256k1_fe_mul(&zi, &zi, rzr); + secp256k1_fe_sqr(&zi2, &zi); + secp256k1_fe_mul(&zi3, &zi2, &zi); + /* To compute the actual x-coordinate, we use the stored z ratio and + * y-coordinate, which we obtained from `secp256k1_gej_add_ge_var` + * in the loop above, as well as the inverse of the square of its + * z-coordinate. We store the latter in the `zi2` variable, which is + * computed iteratively starting from the overall Z inverse then + * multiplying by each z-ratio in turn. + * + * Denoting the z-ratio as `rzr`, we observe that it is equal to `h` + * from the inside of the above `gej_add_ge_var` call. This satisfies + * + * rzr = d_x * z^2 - x * d_z^2 + * + * where (`d_x`, `d_z`) are Jacobian coordinates of `D` and `(x, z)` + * are Jacobian coordinates of our desired point -- except both are on + * the isomorphic curve that we were using when we called `gej_add_ge_var`. + * To get back to secp256k1, we must multiply both `z`s by `d_z`, or + * equivalently divide both `x`s by `d_z^2`. Our equation then becomes + * + * rzr = d_x * z^2 / d_z^2 - x + * + * (The left-hand-side, being a ratio of z-coordinates, is unaffected + * by the isomorphism.) + * + * Rearranging to solve for `x`, we have + * + * x = d_x * z^2 / d_z^2 - rzr + * + * But what we actually want is the affine coordinate `X = x/z^2`, + * which will satisfy + * + * X = d_x / d_z^2 - rzr / z^2 + * = dx_over_dz_squared - rzr * zi2 + */ + secp256k1_fe_mul(&p_ge.x, rzr, &zi2); + secp256k1_fe_negate(&p_ge.x, &p_ge.x, 1); + secp256k1_fe_add(&p_ge.x, &dx_over_dz_squared); + /* y is stored_y/z^3, as we expect */ + secp256k1_fe_mul(&p_ge.y, &p_ge.y, &zi3); + /* Store */ + secp256k1_ge_to_storage(&pre[i], &p_ge); + } +} + +/** The following two macro retrieves a particular odd multiple from a table + * of precomputed multiples. */ +#define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + if ((n) > 0) { \ + *(r) = (pre)[((n)-1)/2]; \ + } else { \ + *(r) = (pre)[(-(n)-1)/2]; \ + secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \ + } \ +} while(0) + +#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + if ((n) > 0) { \ + secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \ + } else { \ + secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \ + secp256k1_fe_negate(&((r)->y), &((r)->y), 1); \ + } \ +} while(0) + +static const size_t SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE = + ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G)) +#ifdef USE_ENDOMORPHISM + + ROUND_TO_ALIGN(sizeof((*((secp256k1_ecmult_context*) NULL)->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G)) +#endif + ; + +static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) { + ctx->pre_g = NULL; +#ifdef USE_ENDOMORPHISM + ctx->pre_g_128 = NULL; +#endif +} + +static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, void **prealloc) { + secp256k1_gej gj; + void* const base = *prealloc; + size_t const prealloc_size = SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE; + + if (ctx->pre_g != NULL) { + return; + } + + /* get the generator */ + secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g); + + { + size_t size = sizeof((*ctx->pre_g)[0]) * ((size_t)ECMULT_TABLE_SIZE(WINDOW_G)); + /* check for overflow */ + VERIFY_CHECK(size / sizeof((*ctx->pre_g)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G))); + ctx->pre_g = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size); + } + + /* precompute the tables with odd multiples */ + secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj); + +#ifdef USE_ENDOMORPHISM + { + secp256k1_gej g_128j; + int i; + + size_t size = sizeof((*ctx->pre_g_128)[0]) * ((size_t) ECMULT_TABLE_SIZE(WINDOW_G)); + /* check for overflow */ + VERIFY_CHECK(size / sizeof((*ctx->pre_g_128)[0]) == ((size_t)ECMULT_TABLE_SIZE(WINDOW_G))); + ctx->pre_g_128 = (secp256k1_ge_storage (*)[])manual_alloc(prealloc, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G), base, prealloc_size); + + /* calculate 2^128*generator */ + g_128j = gj; + for (i = 0; i < 128; i++) { + secp256k1_gej_double_var(&g_128j, &g_128j, NULL); + } + secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j); + } +#endif +} + +static void secp256k1_ecmult_context_finalize_memcpy(secp256k1_ecmult_context *dst, const secp256k1_ecmult_context *src) { + if (src->pre_g != NULL) { + /* We cast to void* first to suppress a -Wcast-align warning. */ + dst->pre_g = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g) - (unsigned char*)src)); + } +#ifdef USE_ENDOMORPHISM + if (src->pre_g_128 != NULL) { + dst->pre_g_128 = (secp256k1_ge_storage (*)[])(void*)((unsigned char*)dst + ((unsigned char*)(src->pre_g_128) - (unsigned char*)src)); + } +#endif +} + +static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) { + return ctx->pre_g != NULL; +} + +static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) { + secp256k1_ecmult_context_init(ctx); +} + +/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), + * with the following guarantees: + * - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1) + * - two non-zero entries in wnaf are separated by at least w-1 zeroes. + * - the number of set values in wnaf is returned. This number is at most 256, and at most one more + * than the number of bits in the (absolute value) of the input. + */ +static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) { + secp256k1_scalar s; + int last_set_bit = -1; + int bit = 0; + int sign = 1; + int carry = 0; + + VERIFY_CHECK(wnaf != NULL); + VERIFY_CHECK(0 <= len && len <= 256); + VERIFY_CHECK(a != NULL); + VERIFY_CHECK(2 <= w && w <= 31); + + memset(wnaf, 0, len * sizeof(wnaf[0])); + + s = *a; + if (secp256k1_scalar_get_bits(&s, 255, 1)) { + secp256k1_scalar_negate(&s, &s); + sign = -1; + } + + while (bit < len) { + int now; + int word; + if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) { + bit++; + continue; + } + + now = w; + if (now > len - bit) { + now = len - bit; + } + + word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry; + + carry = (word >> (w-1)) & 1; + word -= carry << w; + + wnaf[bit] = sign * word; + last_set_bit = bit; + + bit += now; + } +#ifdef VERIFY + CHECK(carry == 0); + while (bit < 256) { + CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0); + } +#endif + return last_set_bit + 1; +} + +struct secp256k1_strauss_point_state { +#ifdef USE_ENDOMORPHISM + secp256k1_scalar na_1, na_lam; + int wnaf_na_1[130]; + int wnaf_na_lam[130]; + int bits_na_1; + int bits_na_lam; +#else + int wnaf_na[256]; + int bits_na; +#endif + size_t input_pos; +}; + +struct secp256k1_strauss_state { + secp256k1_gej* prej; + secp256k1_fe* zr; + secp256k1_ge* pre_a; +#ifdef USE_ENDOMORPHISM + secp256k1_ge* pre_a_lam; +#endif + struct secp256k1_strauss_point_state* ps; +}; + +static void secp256k1_ecmult_strauss_wnaf(const secp256k1_ecmult_context *ctx, const struct secp256k1_strauss_state *state, secp256k1_gej *r, int num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { + secp256k1_ge tmpa; + secp256k1_fe Z; +#ifdef USE_ENDOMORPHISM + /* Splitted G factors. */ + secp256k1_scalar ng_1, ng_128; + int wnaf_ng_1[129]; + int bits_ng_1 = 0; + int wnaf_ng_128[129]; + int bits_ng_128 = 0; +#else + int wnaf_ng[256]; + int bits_ng = 0; +#endif + int i; + int bits = 0; + int np; + int no = 0; + + for (np = 0; np < num; ++np) { + if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) { + continue; + } + state->ps[no].input_pos = np; +#ifdef USE_ENDOMORPHISM + /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */ + secp256k1_scalar_split_lambda(&state->ps[no].na_1, &state->ps[no].na_lam, &na[np]); + + /* build wnaf representation for na_1 and na_lam. */ + state->ps[no].bits_na_1 = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_1, 130, &state->ps[no].na_1, WINDOW_A); + state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na_lam, 130, &state->ps[no].na_lam, WINDOW_A); + VERIFY_CHECK(state->ps[no].bits_na_1 <= 130); + VERIFY_CHECK(state->ps[no].bits_na_lam <= 130); + if (state->ps[no].bits_na_1 > bits) { + bits = state->ps[no].bits_na_1; + } + if (state->ps[no].bits_na_lam > bits) { + bits = state->ps[no].bits_na_lam; + } +#else + /* build wnaf representation for na. */ + state->ps[no].bits_na = secp256k1_ecmult_wnaf(state->ps[no].wnaf_na, 256, &na[np], WINDOW_A); + if (state->ps[no].bits_na > bits) { + bits = state->ps[no].bits_na; + } +#endif + ++no; + } + + /* Calculate odd multiples of a. + * All multiples are brought to the same Z 'denominator', which is stored + * in Z. Due to secp256k1' isomorphism we can do all operations pretending + * that the Z coordinate was 1, use affine addition formulae, and correct + * the Z coordinate of the result once at the end. + * The exception is the precomputed G table points, which are actually + * affine. Compared to the base used for other points, they have a Z ratio + * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same + * isomorphism to efficiently add with a known Z inverse. + */ + if (no > 0) { + /* Compute the odd multiples in Jacobian form. */ + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej, state->zr, &a[state->ps[0].input_pos]); + for (np = 1; np < no; ++np) { + secp256k1_gej tmp = a[state->ps[np].input_pos]; +#ifdef VERIFY + secp256k1_fe_normalize_var(&(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z)); +#endif + secp256k1_gej_rescale(&tmp, &(state->prej[(np - 1) * ECMULT_TABLE_SIZE(WINDOW_A) + ECMULT_TABLE_SIZE(WINDOW_A) - 1].z)); + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->prej + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &tmp); + secp256k1_fe_mul(state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), state->zr + np * ECMULT_TABLE_SIZE(WINDOW_A), &(a[state->ps[np].input_pos].z)); + } + /* Bring them to the same Z denominator. */ + secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, &Z, state->prej, state->zr); + } else { + secp256k1_fe_set_int(&Z, 1); + } + +#ifdef USE_ENDOMORPHISM + for (np = 0; np < no; ++np) { + for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { + secp256k1_ge_mul_lambda(&state->pre_a_lam[np * ECMULT_TABLE_SIZE(WINDOW_A) + i], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + i]); + } + } + + if (ng) { + /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */ + secp256k1_scalar_split_128(&ng_1, &ng_128, ng); + + /* Build wnaf representation for ng_1 and ng_128 */ + bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G); + bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G); + if (bits_ng_1 > bits) { + bits = bits_ng_1; + } + if (bits_ng_128 > bits) { + bits = bits_ng_128; + } + } +#else + if (ng) { + bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G); + if (bits_ng > bits) { + bits = bits_ng; + } + } +#endif + + secp256k1_gej_set_infinity(r); + + for (i = bits - 1; i >= 0; i--) { + int n; + secp256k1_gej_double_var(r, r, NULL); +#ifdef USE_ENDOMORPHISM + for (np = 0; np < no; ++np) { + if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a_lam + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + } + if (i < bits_ng_1 && (n = wnaf_ng_1[i])) { + ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G); + secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); + } + if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { + ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G); + secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); + } +#else + for (np = 0; np < no; ++np) { + if (i < state->ps[np].bits_na && (n = state->ps[np].wnaf_na[i])) { + ECMULT_TABLE_GET_GE(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A); + secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); + } + } + if (i < bits_ng && (n = wnaf_ng[i])) { + ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G); + secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); + } +#endif + } + + if (!r->infinity) { + secp256k1_fe_mul(&r->z, &r->z, &Z); + } +} + +static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { + secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + struct secp256k1_strauss_point_state ps[1]; +#ifdef USE_ENDOMORPHISM + secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; +#endif + struct secp256k1_strauss_state state; + + state.prej = prej; + state.zr = zr; + state.pre_a = pre_a; +#ifdef USE_ENDOMORPHISM + state.pre_a_lam = pre_a_lam; +#endif + state.ps = ps; + secp256k1_ecmult_strauss_wnaf(ctx, &state, r, 1, a, na, ng); +} + +static size_t secp256k1_strauss_scratch_size(size_t n_points) { +#ifdef USE_ENDOMORPHISM + static const size_t point_size = (2 * sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); +#else + static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_gej) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar); +#endif + return n_points*point_size; +} + +static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { + secp256k1_gej* points; + secp256k1_scalar* scalars; + struct secp256k1_strauss_state state; + size_t i; + const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); + + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n_points == 0) { + return 1; + } + + points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej)); + scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar)); + state.prej = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_gej)); + state.zr = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe)); +#ifdef USE_ENDOMORPHISM + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * 2 * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); + state.pre_a_lam = state.pre_a + n_points * ECMULT_TABLE_SIZE(WINDOW_A); +#else + state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge)); +#endif + state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state)); + + if (points == NULL || scalars == NULL || state.prej == NULL || state.zr == NULL || state.pre_a == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + + for (i = 0; i < n_points; i++) { + secp256k1_ge point; + if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + secp256k1_gej_set_ge(&points[i], &point); + } + secp256k1_ecmult_strauss_wnaf(ctx, &state, r, n_points, points, scalars, inp_g_sc); + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 1; +} + +/* Wrapper for secp256k1_ecmult_multi_func interface */ +static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *actx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + return secp256k1_ecmult_strauss_batch(error_callback, actx, scratch, r, inp_g_sc, cb, cbdata, n, 0); +} + +static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) { + return secp256k1_scratch_max_allocation(error_callback, scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1); +} + +/** Convert a number to WNAF notation. + * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. + * It has the following guarantees: + * - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w) + * - the number of words set is always WNAF_SIZE(w) + * - the returned skew is 0 or 1 + */ +static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) { + int skew = 0; + int pos; + int max_pos; + int last_w; + const secp256k1_scalar *work = s; + + if (secp256k1_scalar_is_zero(s)) { + for (pos = 0; pos < WNAF_SIZE(w); pos++) { + wnaf[pos] = 0; + } + return 0; + } + + if (secp256k1_scalar_is_even(s)) { + skew = 1; + } + + wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew; + /* Compute last window size. Relevant when window size doesn't divide the + * number of bits in the scalar */ + last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w; + + /* Store the position of the first nonzero word in max_pos to allow + * skipping leading zeros when calculating the wnaf. */ + for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) { + int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); + if(val != 0) { + break; + } + wnaf[pos] = 0; + } + max_pos = pos; + pos = 1; + + while (pos <= max_pos) { + int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w); + if ((val & 1) == 0) { + wnaf[pos - 1] -= (1 << w); + wnaf[pos] = (val + 1); + } else { + wnaf[pos] = val; + } + /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit + * is strictly negative or strictly positive respectively. Only change + * coefficients at previous positions because above code assumes that + * wnaf[pos - 1] is odd. + */ + if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) { + if (wnaf[pos - 1] == 1) { + wnaf[pos - 2] += 1 << w; + } else { + wnaf[pos - 2] -= 1 << w; + } + wnaf[pos - 1] = 0; + } + ++pos; + } + + return skew; +} + +struct secp256k1_pippenger_point_state { + int skew_na; + size_t input_pos; +}; + +struct secp256k1_pippenger_state { + int *wnaf_na; + struct secp256k1_pippenger_point_state* ps; +}; + +/* + * pippenger_wnaf computes the result of a multi-point multiplication as + * follows: The scalars are brought into wnaf with n_wnaf elements each. Then + * for every i < n_wnaf, first each point is added to a "bucket" corresponding + * to the point's wnaf[i]. Second, the buckets are added together such that + * r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ... + */ +static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) { + size_t n_wnaf = WNAF_SIZE(bucket_window+1); + size_t np; + size_t no = 0; + int i; + int j; + + for (np = 0; np < num; ++np) { + if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) { + continue; + } + state->ps[no].input_pos = np; + state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1); + no++; + } + secp256k1_gej_set_infinity(r); + + if (no == 0) { + return 1; + } + + for (i = n_wnaf - 1; i >= 0; i--) { + secp256k1_gej running_sum; + + for(j = 0; j < ECMULT_TABLE_SIZE(bucket_window+2); j++) { + secp256k1_gej_set_infinity(&buckets[j]); + } + + for (np = 0; np < no; ++np) { + int n = state->wnaf_na[np*n_wnaf + i]; + struct secp256k1_pippenger_point_state point_state = state->ps[np]; + secp256k1_ge tmp; + int idx; + + if (i == 0) { + /* correct for wnaf skew */ + int skew = point_state.skew_na; + if (skew) { + secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); + secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL); + } + } + if (n > 0) { + idx = (n - 1)/2; + secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &pt[point_state.input_pos], NULL); + } else if (n < 0) { + idx = -(n + 1)/2; + secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]); + secp256k1_gej_add_ge_var(&buckets[idx], &buckets[idx], &tmp, NULL); + } + } + + for(j = 0; j < bucket_window; j++) { + secp256k1_gej_double_var(r, r, NULL); + } + + secp256k1_gej_set_infinity(&running_sum); + /* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ... + * = bucket[0] + bucket[1] + bucket[2] + bucket[3] + ... + * + 2 * (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...) + * using an intermediate running sum: + * running_sum = bucket[0] + bucket[1] + bucket[2] + ... + * + * The doubling is done implicitly by deferring the final window doubling (of 'r'). + */ + for(j = ECMULT_TABLE_SIZE(bucket_window+2) - 1; j > 0; j--) { + secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[j], NULL); + secp256k1_gej_add_var(r, r, &running_sum, NULL); + } + + secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL); + secp256k1_gej_double_var(r, r, NULL); + secp256k1_gej_add_var(r, r, &running_sum, NULL); + } + return 1; +} + +/** + * Returns optimal bucket_window (number of bits of a scalar represented by a + * set of buckets) for a given number of points. + */ +static int secp256k1_pippenger_bucket_window(size_t n) { +#ifdef USE_ENDOMORPHISM + if (n <= 1) { + return 1; + } else if (n <= 4) { + return 2; + } else if (n <= 20) { + return 3; + } else if (n <= 57) { + return 4; + } else if (n <= 136) { + return 5; + } else if (n <= 235) { + return 6; + } else if (n <= 1260) { + return 7; + } else if (n <= 4420) { + return 9; + } else if (n <= 7880) { + return 10; + } else if (n <= 16050) { + return 11; + } else { + return PIPPENGER_MAX_BUCKET_WINDOW; + } +#else + if (n <= 1) { + return 1; + } else if (n <= 11) { + return 2; + } else if (n <= 45) { + return 3; + } else if (n <= 100) { + return 4; + } else if (n <= 275) { + return 5; + } else if (n <= 625) { + return 6; + } else if (n <= 1850) { + return 7; + } else if (n <= 3400) { + return 8; + } else if (n <= 9630) { + return 9; + } else if (n <= 17900) { + return 10; + } else if (n <= 32800) { + return 11; + } else { + return PIPPENGER_MAX_BUCKET_WINDOW; + } +#endif +} + +/** + * Returns the maximum optimal number of points for a bucket_window. + */ +static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) { + switch(bucket_window) { +#ifdef USE_ENDOMORPHISM + case 1: return 1; + case 2: return 4; + case 3: return 20; + case 4: return 57; + case 5: return 136; + case 6: return 235; + case 7: return 1260; + case 8: return 1260; + case 9: return 4420; + case 10: return 7880; + case 11: return 16050; + case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX; +#else + case 1: return 1; + case 2: return 11; + case 3: return 45; + case 4: return 100; + case 5: return 275; + case 6: return 625; + case 7: return 1850; + case 8: return 3400; + case 9: return 9630; + case 10: return 17900; + case 11: return 32800; + case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX; +#endif + } + return 0; +} + + +#ifdef USE_ENDOMORPHISM +SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) { + secp256k1_scalar tmp = *s1; + secp256k1_scalar_split_lambda(s1, s2, &tmp); + secp256k1_ge_mul_lambda(p2, p1); + + if (secp256k1_scalar_is_high(s1)) { + secp256k1_scalar_negate(s1, s1); + secp256k1_ge_neg(p1, p1); + } + if (secp256k1_scalar_is_high(s2)) { + secp256k1_scalar_negate(s2, s2); + secp256k1_ge_neg(p2, p2); + } +} +#endif + +/** + * Returns the scratch size required for a given number of points (excluding + * base point G) without considering alignment. + */ +static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) { +#ifdef USE_ENDOMORPHISM + size_t entries = 2*n_points + 2; +#else + size_t entries = n_points + 1; +#endif + size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int); + return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size; +} + +static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) { + const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch); + /* Use 2(n+1) with the endomorphism, n+1 without, when calculating batch + * sizes. The reason for +1 is that we add the G scalar to the list of + * other scalars. */ +#ifdef USE_ENDOMORPHISM + size_t entries = 2*n_points + 2; +#else + size_t entries = n_points + 1; +#endif + secp256k1_ge *points; + secp256k1_scalar *scalars; + secp256k1_gej *buckets; + struct secp256k1_pippenger_state *state_space; + size_t idx = 0; + size_t point_idx = 0; + int i, j; + int bucket_window; + + (void)ctx; + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n_points == 0) { + return 1; + } + + bucket_window = secp256k1_pippenger_bucket_window(n_points); + points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points)); + scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars)); + state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space)); + if (points == NULL || scalars == NULL || state_space == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + + state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps)); + state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int)); + buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, (1<ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + + if (inp_g_sc != NULL) { + scalars[0] = *inp_g_sc; + points[0] = secp256k1_ge_const_g; + idx++; +#ifdef USE_ENDOMORPHISM + secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]); + idx++; +#endif + } + + while (point_idx < n_points) { + if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) { + secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint); + return 0; + } + idx++; +#ifdef USE_ENDOMORPHISM + secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]); + idx++; +#endif + point_idx++; + } + + secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx); + + /* Clear data */ + for(i = 0; (size_t)i < idx; i++) { + secp256k1_scalar_clear(&scalars[i]); + state_space->ps[i].skew_na = 0; + for(j = 0; j < WNAF_SIZE(bucket_window+1); j++) { + state_space->wnaf_na[i * WNAF_SIZE(bucket_window+1) + j] = 0; + } + } + for(i = 0; i < 1< max_alloc) { + break; + } + space_for_points = max_alloc - space_overhead; + + n_points = space_for_points/entry_size; + n_points = n_points > max_points ? max_points : n_points; + if (n_points > res) { + res = n_points; + } + if (n_points < max_points) { + /* A larger bucket_window may support even more points. But if we + * would choose that then the caller couldn't safely use any number + * smaller than what this function returns */ + break; + } + } + return res; +} + +/* Computes ecmult_multi by simply multiplying and adding each point. Does not + * require a scratch space */ +static int secp256k1_ecmult_multi_simple_var(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) { + size_t point_idx; + secp256k1_scalar szero; + secp256k1_gej tmpj; + + secp256k1_scalar_set_int(&szero, 0); + secp256k1_gej_set_infinity(r); + secp256k1_gej_set_infinity(&tmpj); + /* r = inp_g_sc*G */ + secp256k1_ecmult(ctx, r, &tmpj, &szero, inp_g_sc); + for (point_idx = 0; point_idx < n_points; point_idx++) { + secp256k1_ge point; + secp256k1_gej pointj; + secp256k1_scalar scalar; + if (!cb(&scalar, &point, point_idx, cbdata)) { + return 0; + } + /* r += scalar*point */ + secp256k1_gej_set_ge(&pointj, &point); + secp256k1_ecmult(ctx, &tmpj, &pointj, &scalar, NULL); + secp256k1_gej_add_var(r, r, &tmpj, NULL); + } + return 1; +} + +/* Compute the number of batches and the batch size given the maximum batch size and the + * total number of points */ +static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) { + if (max_n_batch_points == 0) { + return 0; + } + if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) { + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + } + if (n == 0) { + *n_batches = 0; + *n_batch_points = 0; + return 1; + } + /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */ + *n_batches = 1 + (n - 1) / max_n_batch_points; + *n_batch_points = 1 + (n - 1) / *n_batches; + return 1; +} + +typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t); +static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, const secp256k1_ecmult_context *ctx, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) { + size_t i; + + int (*f)(const secp256k1_callback* error_callback, const secp256k1_ecmult_context*, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t); + size_t n_batches; + size_t n_batch_points; + + secp256k1_gej_set_infinity(r); + if (inp_g_sc == NULL && n == 0) { + return 1; + } else if (n == 0) { + secp256k1_scalar szero; + secp256k1_scalar_set_int(&szero, 0); + secp256k1_ecmult(ctx, r, r, &szero, inp_g_sc); + return 1; + } + if (scratch == NULL) { + return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n); + } + + /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than + * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm. + * As a first step check if there's enough space for Pippenger's algo (which requires less space + * than Strauss' algo) and if not, use the simple algorithm. */ + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(error_callback, scratch), n)) { + return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n); + } + if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) { + f = secp256k1_ecmult_pippenger_batch; + } else { + if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(error_callback, scratch), n)) { + return secp256k1_ecmult_multi_simple_var(ctx, r, inp_g_sc, cb, cbdata, n); + } + f = secp256k1_ecmult_strauss_batch; + } + for(i = 0; i < n_batches; i++) { + size_t nbp = n < n_batch_points ? n : n_batch_points; + size_t offset = n_batch_points*i; + secp256k1_gej tmp; + if (!f(error_callback, ctx, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) { + return 0; + } + secp256k1_gej_add_var(r, r, &tmp, NULL); + n -= nbp; + } + return 1; +} + +#endif /* SECP256K1_ECMULT_IMPL_H */ diff --git a/libsecp256k1/src/field.h b/libsecp256k1/src/field.h new file mode 100644 index 0000000..8283e4b --- /dev/null +++ b/libsecp256k1/src/field.h @@ -0,0 +1,134 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_H +#define SECP256K1_FIELD_H + +/** Field element module. + * + * Field elements can be represented in several ways, but code accessing + * it (and implementations) need to take certain properties into account: + * - Each field element can be normalized or not. + * - Each field element has a magnitude, which represents how far away + * its representation is away from normalization. Normalized elements + * always have a magnitude of 1, but a magnitude of 1 doesn't imply + * normality. + */ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(USE_FIELD_10X26) +#include "field_10x26.h" +#elif defined(USE_FIELD_5X52) +#include "field_5x52.h" +#else +#error "Please select field implementation" +#endif + +#include "util.h" + +/** Normalize a field element. This brings the field element to a canonical representation, reduces + * its magnitude to 1, and reduces it modulo field size `p`. + */ +static void secp256k1_fe_normalize(secp256k1_fe *r); + +/** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */ +static void secp256k1_fe_normalize_weak(secp256k1_fe *r); + +/** Normalize a field element, without constant-time guarantee. */ +static void secp256k1_fe_normalize_var(secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field + * implementation may optionally normalize the input, but this should not be relied upon. */ +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r); + +/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field + * implementation may optionally normalize the input, but this should not be relied upon. */ +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r); + +/** Set a field element equal to a small integer. Resulting field element is normalized. */ +static void secp256k1_fe_set_int(secp256k1_fe *r, int a); + +/** Sets a field element equal to zero, initializing all fields. */ +static void secp256k1_fe_clear(secp256k1_fe *a); + +/** Verify whether a field element is zero. Requires the input to be normalized. */ +static int secp256k1_fe_is_zero(const secp256k1_fe *a); + +/** Check the "oddness" of a field element. Requires the input to be normalized. */ +static int secp256k1_fe_is_odd(const secp256k1_fe *a); + +/** Compare two field elements. Requires magnitude-1 inputs. */ +static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Same as secp256k1_fe_equal, but may be variable time. */ +static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Compare two field elements. Requires both inputs to be normalized */ +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b); + +/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */ +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a); + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a); + +/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input + * as an argument. The magnitude of the output is one higher. */ +static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m); + +/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that + * small integer. */ +static void secp256k1_fe_mul_int(secp256k1_fe *r, int a); + +/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */ +static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a); + +/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b); + +/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8. + * The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a); + +/** If a has a square root, it is computed in r and 1 is returned. If a does not + * have a square root, the root of its negation is computed and 0 is returned. + * The input's magnitude can be at most 8. The output magnitude is 1 (but not + * guaranteed to be normalized). The result in r will always be a square + * itself. */ +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a); + +/** Checks whether a field element is a quadratic residue. */ +static int secp256k1_fe_is_quad_var(const secp256k1_fe *a); + +/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be + * at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */ +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a); + +/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */ +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a); + +/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be + * at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and + * outputs must not overlap in memory. */ +static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len); + +/** Convert a field element to the storage type. */ +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a); + +/** Convert a field element back from the storage type. */ +static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag); + +#endif /* SECP256K1_FIELD_H */ diff --git a/libsecp256k1/src/field_10x26.h b/libsecp256k1/src/field_10x26.h new file mode 100644 index 0000000..5ff03c8 --- /dev/null +++ b/libsecp256k1/src/field_10x26.h @@ -0,0 +1,50 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_H +#define SECP256K1_FIELD_REPR_H + +#include + +typedef struct { + /* X = sum(i=0..9, n[i]*2^(i*26)) mod p + * where p = 2^256 - 0x1000003D1 + */ + uint32_t n[10]; +#ifdef VERIFY + int magnitude; + int normalized; +#endif +} secp256k1_fe; + +/* Unpacks a constant into a overlapping multi-limbed FE element. */ +#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ + (d0) & 0x3FFFFFFUL, \ + (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \ + (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \ + (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \ + (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \ + (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \ + (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \ + (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \ + (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \ + (((uint32_t)d7) >> 10) \ +} + +#ifdef VERIFY +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} +#else +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} +#endif + +typedef struct { + uint32_t n[8]; +} secp256k1_fe_storage; + +#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }} +#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0] + +#endif /* SECP256K1_FIELD_REPR_H */ diff --git a/libsecp256k1/src/field_10x26_impl.h b/libsecp256k1/src/field_10x26_impl.h new file mode 100644 index 0000000..3930424 --- /dev/null +++ b/libsecp256k1/src/field_10x26_impl.h @@ -0,0 +1,1165 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_IMPL_H +#define SECP256K1_FIELD_REPR_IMPL_H + +#include "util.h" +#include "field.h" + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe *a) { + const uint32_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + r &= (d[0] <= 0x3FFFFFFUL * m); + r &= (d[1] <= 0x3FFFFFFUL * m); + r &= (d[2] <= 0x3FFFFFFUL * m); + r &= (d[3] <= 0x3FFFFFFUL * m); + r &= (d[4] <= 0x3FFFFFFUL * m); + r &= (d[5] <= 0x3FFFFFFUL * m); + r &= (d[6] <= 0x3FFFFFFUL * m); + r &= (d[7] <= 0x3FFFFFFUL * m); + r &= (d[8] <= 0x3FFFFFFUL * m); + r &= (d[9] <= 0x03FFFFFUL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 32); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[9] == 0x03FFFFFUL)) { + uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2]; + if (mid == 0x3FFFFFFUL) { + r &= ((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL); + } + } + } + VERIFY_CHECK(r == 1); +} +#endif + +static void secp256k1_fe_normalize(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t m; + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL) + & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); + + if (x) { + t0 += 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; + + /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */ + VERIFY_CHECK(t9 >> 22 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t9 &= 0x03FFFFFUL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { + uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4], + t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint32_t z0, z1; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; t1 += (x << 6); + t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL; + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { + uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9; + uint32_t z0, z1; + uint32_t x; + + t0 = r->n[0]; + t9 = r->n[9]; + + /* Reduce t9 at the start so there will be at most a single carry from the first pass */ + x = t9 >> 22; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x3D1UL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0x3FFFFFFUL; + z1 = z0 ^ 0x3D0UL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) { + return 0; + } + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + t4 = r->n[4]; + t5 = r->n[5]; + t6 = r->n[6]; + t7 = r->n[7]; + t8 = r->n[8]; + + t9 &= 0x03FFFFFUL; + t1 += (x << 6); + + t1 += (t0 >> 26); + t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL; + t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3; + t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4; + t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5; + t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6; + t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7; + t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8; + z0 |= t9; z1 &= t9 ^ 0x3C00000UL; + + /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t9 >> 23 == 0); + + return (z0 == 0) | (z1 == 0x3FFFFFFUL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { + r->n[0] = a; + r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { + const uint32_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return a->n[0] & 1; +} + +SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { + int i; +#ifdef VERIFY + a->magnitude = 0; + a->normalized = 1; +#endif + for (i=0; i<10; i++) { + a->n[i] = 0; + } +} + +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { + int i; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + VERIFY_CHECK(b->normalized); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); +#endif + for (i = 9; i >= 0; i--) { + if (a->n[i] > b->n[i]) { + return 1; + } + if (a->n[i] < b->n[i]) { + return -1; + } + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { + int ret; + r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24); + r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22); + r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20); + r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18); + r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24); + r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22); + r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20); + r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18); + r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24); + r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14); + + ret = !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL)); +#ifdef VERIFY + r->magnitude = 1; + if (ret) { + r->normalized = 1; + secp256k1_fe_verify(r); + } else { + r->normalized = 0; + } +#endif + return ret; +} + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + r[0] = (a->n[9] >> 14) & 0xff; + r[1] = (a->n[9] >> 6) & 0xff; + r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3); + r[3] = (a->n[8] >> 16) & 0xff; + r[4] = (a->n[8] >> 8) & 0xff; + r[5] = a->n[8] & 0xff; + r[6] = (a->n[7] >> 18) & 0xff; + r[7] = (a->n[7] >> 10) & 0xff; + r[8] = (a->n[7] >> 2) & 0xff; + r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f); + r[10] = (a->n[6] >> 12) & 0xff; + r[11] = (a->n[6] >> 4) & 0xff; + r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf); + r[13] = (a->n[5] >> 14) & 0xff; + r[14] = (a->n[5] >> 6) & 0xff; + r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3); + r[16] = (a->n[4] >> 16) & 0xff; + r[17] = (a->n[4] >> 8) & 0xff; + r[18] = a->n[4] & 0xff; + r[19] = (a->n[3] >> 18) & 0xff; + r[20] = (a->n[3] >> 10) & 0xff; + r[21] = (a->n[3] >> 2) & 0xff; + r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f); + r[23] = (a->n[2] >> 12) & 0xff; + r[24] = (a->n[2] >> 4) & 0xff; + r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf); + r[26] = (a->n[1] >> 14) & 0xff; + r[27] = (a->n[1] >> 6) & 0xff; + r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3); + r[29] = (a->n[0] >> 16) & 0xff; + r[30] = (a->n[0] >> 8) & 0xff; + r[31] = a->n[0] & 0xff; +} + +SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= m); + secp256k1_fe_verify(a); +#endif + r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4]; + r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5]; + r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6]; + r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7]; + r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8]; + r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; + r->n[5] *= a; + r->n[6] *= a; + r->n[7] *= a; + r->n[8] *= a; + r->n[9] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + secp256k1_fe_verify(a); +#endif + r->n[0] += a->n[0]; + r->n[1] += a->n[1]; + r->n[2] += a->n[2]; + r->n[3] += a->n[3]; + r->n[4] += a->n[4]; + r->n[5] += a->n[5]; + r->n[6] += a->n[6]; + r->n[7] += a->n[7]; + r->n[8] += a->n[8]; + r->n[9] += a->n[9]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +#if defined(USE_EXTERNAL_ASM) + +/* External assembler implementation */ +void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b); +void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a); + +#else + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + VERIFY_BITS(b[0], 30); + VERIFY_BITS(b[1], 30); + VERIFY_BITS(b[2], 30); + VERIFY_BITS(b[3], 30); + VERIFY_BITS(b[4], 30); + VERIFY_BITS(b[5], 30); + VERIFY_BITS(b[6], 30); + VERIFY_BITS(b[7], 30); + VERIFY_BITS(b[8], 30); + VERIFY_BITS(b[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * for 0 <= x <= 9, px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * for 9 <= x <= 18, px is a shorthand for sum(a[i]*b[x-i], i=(x-9)..9) + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)a[0] * b[9] + + (uint64_t)a[1] * b[8] + + (uint64_t)a[2] * b[7] + + (uint64_t)a[3] * b[6] + + (uint64_t)a[4] * b[5] + + (uint64_t)a[5] * b[4] + + (uint64_t)a[6] * b[3] + + (uint64_t)a[7] * b[2] + + (uint64_t)a[8] * b[1] + + (uint64_t)a[9] * b[0]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * b[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)a[1] * b[9] + + (uint64_t)a[2] * b[8] + + (uint64_t)a[3] * b[7] + + (uint64_t)a[4] * b[6] + + (uint64_t)a[5] * b[5] + + (uint64_t)a[6] * b[4] + + (uint64_t)a[7] * b[3] + + (uint64_t)a[8] * b[2] + + (uint64_t)a[9] * b[1]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)a[0] * b[1] + + (uint64_t)a[1] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)a[2] * b[9] + + (uint64_t)a[3] * b[8] + + (uint64_t)a[4] * b[7] + + (uint64_t)a[5] * b[6] + + (uint64_t)a[6] * b[5] + + (uint64_t)a[7] * b[4] + + (uint64_t)a[8] * b[3] + + (uint64_t)a[9] * b[2]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)a[0] * b[2] + + (uint64_t)a[1] * b[1] + + (uint64_t)a[2] * b[0]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)a[3] * b[9] + + (uint64_t)a[4] * b[8] + + (uint64_t)a[5] * b[7] + + (uint64_t)a[6] * b[6] + + (uint64_t)a[7] * b[5] + + (uint64_t)a[8] * b[4] + + (uint64_t)a[9] * b[3]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[3] + + (uint64_t)a[1] * b[2] + + (uint64_t)a[2] * b[1] + + (uint64_t)a[3] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)a[4] * b[9] + + (uint64_t)a[5] * b[8] + + (uint64_t)a[6] * b[7] + + (uint64_t)a[7] * b[6] + + (uint64_t)a[8] * b[5] + + (uint64_t)a[9] * b[4]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[4] + + (uint64_t)a[1] * b[3] + + (uint64_t)a[2] * b[2] + + (uint64_t)a[3] * b[1] + + (uint64_t)a[4] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[5] * b[9] + + (uint64_t)a[6] * b[8] + + (uint64_t)a[7] * b[7] + + (uint64_t)a[8] * b[6] + + (uint64_t)a[9] * b[5]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[5] + + (uint64_t)a[1] * b[4] + + (uint64_t)a[2] * b[3] + + (uint64_t)a[3] * b[2] + + (uint64_t)a[4] * b[1] + + (uint64_t)a[5] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[6] * b[9] + + (uint64_t)a[7] * b[8] + + (uint64_t)a[8] * b[7] + + (uint64_t)a[9] * b[6]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[6] + + (uint64_t)a[1] * b[5] + + (uint64_t)a[2] * b[4] + + (uint64_t)a[3] * b[3] + + (uint64_t)a[4] * b[2] + + (uint64_t)a[5] * b[1] + + (uint64_t)a[6] * b[0]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[7] * b[9] + + (uint64_t)a[8] * b[8] + + (uint64_t)a[9] * b[7]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[7] + + (uint64_t)a[1] * b[6] + + (uint64_t)a[2] * b[5] + + (uint64_t)a[3] * b[4] + + (uint64_t)a[4] * b[3] + + (uint64_t)a[5] * b[2] + + (uint64_t)a[6] * b[1] + + (uint64_t)a[7] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[8] * b[9] + + (uint64_t)a[9] * b[8]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)a[0] * b[8] + + (uint64_t)a[1] * b[7] + + (uint64_t)a[2] * b[6] + + (uint64_t)a[3] * b[5] + + (uint64_t)a[4] * b[4] + + (uint64_t)a[5] * b[3] + + (uint64_t)a[6] * b[2] + + (uint64_t)a[7] * b[1] + + (uint64_t)a[8] * b[0]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * b[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) { + uint64_t c, d; + uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8; + uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7; + const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL; + + VERIFY_BITS(a[0], 30); + VERIFY_BITS(a[1], 30); + VERIFY_BITS(a[2], 30); + VERIFY_BITS(a[3], 30); + VERIFY_BITS(a[4], 30); + VERIFY_BITS(a[5], 30); + VERIFY_BITS(a[6], 30); + VERIFY_BITS(a[7], 30); + VERIFY_BITS(a[8], 30); + VERIFY_BITS(a[9], 26); + + /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0]. + */ + + d = (uint64_t)(a[0]*2) * a[9] + + (uint64_t)(a[1]*2) * a[8] + + (uint64_t)(a[2]*2) * a[7] + + (uint64_t)(a[3]*2) * a[6] + + (uint64_t)(a[4]*2) * a[5]; + /* VERIFY_BITS(d, 64); */ + /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + t9 = d & M; d >>= 26; + VERIFY_BITS(t9, 26); + VERIFY_BITS(d, 38); + /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */ + + c = (uint64_t)a[0] * a[0]; + VERIFY_BITS(c, 60); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */ + d += (uint64_t)(a[1]*2) * a[9] + + (uint64_t)(a[2]*2) * a[8] + + (uint64_t)(a[3]*2) * a[7] + + (uint64_t)(a[4]*2) * a[6] + + (uint64_t)a[5] * a[5]; + VERIFY_BITS(d, 63); + /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + u0 = d & M; d >>= 26; c += u0 * R0; + VERIFY_BITS(u0, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 61); + /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + t0 = c & M; c >>= 26; c += u0 * R1; + VERIFY_BITS(t0, 26); + VERIFY_BITS(c, 37); + /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */ + + c += (uint64_t)(a[0]*2) * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */ + d += (uint64_t)(a[2]*2) * a[9] + + (uint64_t)(a[3]*2) * a[8] + + (uint64_t)(a[4]*2) * a[7] + + (uint64_t)(a[5]*2) * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + u1 = d & M; d >>= 26; c += u1 * R0; + VERIFY_BITS(u1, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + t1 = c & M; c >>= 26; c += u1 * R1; + VERIFY_BITS(t1, 26); + VERIFY_BITS(c, 38); + /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[2] + + (uint64_t)a[1] * a[1]; + VERIFY_BITS(c, 62); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + d += (uint64_t)(a[3]*2) * a[9] + + (uint64_t)(a[4]*2) * a[8] + + (uint64_t)(a[5]*2) * a[7] + + (uint64_t)a[6] * a[6]; + VERIFY_BITS(d, 63); + /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + u2 = d & M; d >>= 26; c += u2 * R0; + VERIFY_BITS(u2, 26); + VERIFY_BITS(d, 37); + VERIFY_BITS(c, 63); + /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + t2 = c & M; c >>= 26; c += u2 * R1; + VERIFY_BITS(t2, 26); + VERIFY_BITS(c, 38); + /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[3] + + (uint64_t)(a[1]*2) * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + d += (uint64_t)(a[4]*2) * a[9] + + (uint64_t)(a[5]*2) * a[8] + + (uint64_t)(a[6]*2) * a[7]; + VERIFY_BITS(d, 63); + /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + u3 = d & M; d >>= 26; c += u3 * R0; + VERIFY_BITS(u3, 26); + VERIFY_BITS(d, 37); + /* VERIFY_BITS(c, 64); */ + /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + t3 = c & M; c >>= 26; c += u3 * R1; + VERIFY_BITS(t3, 26); + VERIFY_BITS(c, 39); + /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[4] + + (uint64_t)(a[1]*2) * a[3] + + (uint64_t)a[2] * a[2]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[5]*2) * a[9] + + (uint64_t)(a[6]*2) * a[8] + + (uint64_t)a[7] * a[7]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + u4 = d & M; d >>= 26; c += u4 * R0; + VERIFY_BITS(u4, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + t4 = c & M; c >>= 26; c += u4 * R1; + VERIFY_BITS(t4, 26); + VERIFY_BITS(c, 39); + /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[5] + + (uint64_t)(a[1]*2) * a[4] + + (uint64_t)(a[2]*2) * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[6]*2) * a[9] + + (uint64_t)(a[7]*2) * a[8]; + VERIFY_BITS(d, 62); + /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + u5 = d & M; d >>= 26; c += u5 * R0; + VERIFY_BITS(u5, 26); + VERIFY_BITS(d, 36); + /* VERIFY_BITS(c, 64); */ + /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + t5 = c & M; c >>= 26; c += u5 * R1; + VERIFY_BITS(t5, 26); + VERIFY_BITS(c, 39); + /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[6] + + (uint64_t)(a[1]*2) * a[5] + + (uint64_t)(a[2]*2) * a[4] + + (uint64_t)a[3] * a[3]; + VERIFY_BITS(c, 63); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[7]*2) * a[9] + + (uint64_t)a[8] * a[8]; + VERIFY_BITS(d, 61); + /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + u6 = d & M; d >>= 26; c += u6 * R0; + VERIFY_BITS(u6, 26); + VERIFY_BITS(d, 35); + /* VERIFY_BITS(c, 64); */ + /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + t6 = c & M; c >>= 26; c += u6 * R1; + VERIFY_BITS(t6, 26); + VERIFY_BITS(c, 39); + /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[7] + + (uint64_t)(a[1]*2) * a[6] + + (uint64_t)(a[2]*2) * a[5] + + (uint64_t)(a[3]*2) * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x8000007C00000007ULL); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)(a[8]*2) * a[9]; + VERIFY_BITS(d, 58); + /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + u7 = d & M; d >>= 26; c += u7 * R0; + VERIFY_BITS(u7, 26); + VERIFY_BITS(d, 32); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL); + /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + t7 = c & M; c >>= 26; c += u7 * R1; + VERIFY_BITS(t7, 26); + VERIFY_BITS(c, 38); + /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += (uint64_t)(a[0]*2) * a[8] + + (uint64_t)(a[1]*2) * a[7] + + (uint64_t)(a[2]*2) * a[6] + + (uint64_t)(a[3]*2) * a[5] + + (uint64_t)a[4] * a[4]; + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000007B80000008ULL); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint64_t)a[9] * a[9]; + VERIFY_BITS(d, 57); + /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + u8 = d & M; d >>= 26; c += u8 * R0; + VERIFY_BITS(u8, 26); + VERIFY_BITS(d, 31); + /* VERIFY_BITS(c, 64); */ + VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[3] = t3; + VERIFY_BITS(r[3], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = t4; + VERIFY_BITS(r[4], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[5] = t5; + VERIFY_BITS(r[5], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[6] = t6; + VERIFY_BITS(r[6], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[7] = t7; + VERIFY_BITS(r[7], 26); + /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + r[8] = c & M; c >>= 26; c += u8 * R1; + VERIFY_BITS(r[8], 26); + VERIFY_BITS(c, 39); + /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R0 + t9; + VERIFY_BITS(c, 45); + /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4); + VERIFY_BITS(r[9], 22); + VERIFY_BITS(c, 46); + /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + d = c * (R0 >> 4) + t0; + VERIFY_BITS(d, 56); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[0] = d & M; d >>= 26; + VERIFY_BITS(r[0], 26); + VERIFY_BITS(d, 30); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += c * (R1 >> 4) + t1; + VERIFY_BITS(d, 53); + VERIFY_CHECK(d <= 0x10000003FFFFBFULL); + /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[1] = d & M; d >>= 26; + VERIFY_BITS(r[1], 26); + VERIFY_BITS(d, 27); + VERIFY_CHECK(d <= 0x4000000ULL); + /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + d += t2; + VERIFY_BITS(d, 27); + /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = d; + VERIFY_BITS(r[2], 27); + /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} +#endif + +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + VERIFY_CHECK(b->magnitude <= 8); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); +#endif + secp256k1_fe_mul_inner(r->n, a->n, b->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + secp256k1_fe_verify(a); +#endif + secp256k1_fe_sqr_inner(r->n, a->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { + uint32_t mask0, mask1; + mask0 = flag + ~((uint32_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); + r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1); + r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1); + r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1); + r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1); + r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1); +#ifdef VERIFY + if (flag) { + r->magnitude = a->magnitude; + r->normalized = a->normalized; + } +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { + uint32_t mask0, mask1; + mask0 = flag + ~((uint32_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); + r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1); + r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1); + r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 26; + r->n[1] = a->n[1] >> 6 | a->n[2] << 20; + r->n[2] = a->n[2] >> 12 | a->n[3] << 14; + r->n[3] = a->n[3] >> 18 | a->n[4] << 8; + r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28; + r->n[5] = a->n[6] >> 4 | a->n[7] << 22; + r->n[6] = a->n[7] >> 10 | a->n[8] << 16; + r->n[7] = a->n[8] >> 16 | a->n[9] << 10; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { + r->n[0] = a->n[0] & 0x3FFFFFFUL; + r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL); + r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL); + r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL); + r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL); + r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL; + r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL); + r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL); + r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL); + r->n[9] = a->n[7] >> 10; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; +#endif +} + +#endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/libsecp256k1/src/field_5x52.h b/libsecp256k1/src/field_5x52.h new file mode 100644 index 0000000..fc5bfe3 --- /dev/null +++ b/libsecp256k1/src/field_5x52.h @@ -0,0 +1,49 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_H +#define SECP256K1_FIELD_REPR_H + +#include + +typedef struct { + /* X = sum(i=0..4, n[i]*2^(i*52)) mod p + * where p = 2^256 - 0x1000003D1 + */ + uint64_t n[5]; +#ifdef VERIFY + int magnitude; + int normalized; +#endif +} secp256k1_fe; + +/* Unpacks a constant into a overlapping multi-limbed FE element. */ +#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \ + (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \ + ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \ + ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \ + ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \ + ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \ +} + +#ifdef VERIFY +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1} +#else +#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))} +#endif + +typedef struct { + uint64_t n[4]; +} secp256k1_fe_storage; + +#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \ + (d0) | (((uint64_t)(d1)) << 32), \ + (d2) | (((uint64_t)(d3)) << 32), \ + (d4) | (((uint64_t)(d5)) << 32), \ + (d6) | (((uint64_t)(d7)) << 32) \ +}} + +#endif /* SECP256K1_FIELD_REPR_H */ diff --git a/libsecp256k1/src/field_5x52_asm_impl.h b/libsecp256k1/src/field_5x52_asm_impl.h new file mode 100644 index 0000000..1fc3171 --- /dev/null +++ b/libsecp256k1/src/field_5x52_asm_impl.h @@ -0,0 +1,502 @@ +/********************************************************************** + * Copyright (c) 2013-2014 Diederik Huys, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +/** + * Changelog: + * - March 2013, Diederik Huys: original version + * - November 2014, Pieter Wuille: updated to use Peter Dettman's parallel multiplication algorithm + * - December 2014, Pieter Wuille: converted from YASM to GCC inline assembly + */ + +#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H +#define SECP256K1_FIELD_INNER5X52_IMPL_H + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { +/** + * Registers: rdx:rax = multiplication accumulator + * r9:r8 = c + * r15:rcx = d + * r10-r14 = a0-a4 + * rbx = b + * rdi = r + * rsi = a / t? + */ + uint64_t tmp1, tmp2, tmp3; +__asm__ __volatile__( + "movq 0(%%rsi),%%r10\n" + "movq 8(%%rsi),%%r11\n" + "movq 16(%%rsi),%%r12\n" + "movq 24(%%rsi),%%r13\n" + "movq 32(%%rsi),%%r14\n" + + /* d += a3 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r13\n" + "movq %%rax,%%rcx\n" + "movq %%rdx,%%r15\n" + /* d += a2 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d = a0 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c = a4 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r14\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += (c & M) * R */ + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* t3 (tmp1) = d & M */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + "movq %%rsi,%q1\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* d += a4 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a0 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += c * R */ + "movq %%r8,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* t4 = d & M (%%rsi) */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* tx = t4 >> 48 (tmp3) */ + "movq %%rsi,%%rax\n" + "shrq $48,%%rax\n" + "movq %%rax,%q3\n" + /* t4 &= (M >> 4) (tmp2) */ + "movq $0xffffffffffff,%%rax\n" + "andq %%rax,%%rsi\n" + "movq %%rsi,%q2\n" + /* c = a0 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r10\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += a4 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a1 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* u0 = d & M (%%rsi) */ + "movq %%rcx,%%rsi\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* u0 = (u0 << 4) | tx (%%rsi) */ + "shlq $4,%%rsi\n" + "movq %q3,%%rax\n" + "orq %%rax,%%rsi\n" + /* c += u0 * (R >> 4) */ + "movq $0x1000003d1,%%rax\n" + "mulq %%rsi\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[0] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,0(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a1 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a0 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a4 * b2 */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a2 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c += (d & M) * R */ + "movq %%rcx,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 */ + "shrdq $52,%%r15,%%rcx\n" + "xorq %%r15,%%r15\n" + /* r[1] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,8(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a2 * b0 */ + "movq 0(%%rbx),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a1 * b1 */ + "movq 8(%%rbx),%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* c += a0 * b2 (last use of %%r10 = a0) */ + "movq 16(%%rbx),%%rax\n" + "mulq %%r10\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* fetch t3 (%%r10, overwrites a0), t4 (%%rsi) */ + "movq %q2,%%rsi\n" + "movq %q1,%%r10\n" + /* d += a4 * b3 */ + "movq 24(%%rbx),%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* d += a3 * b4 */ + "movq 32(%%rbx),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rcx\n" + "adcq %%rdx,%%r15\n" + /* c += (d & M) * R */ + "movq %%rcx,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 (%%rcx only) */ + "shrdq $52,%%r15,%%rcx\n" + /* r[2] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,16(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += t3 */ + "addq %%r10,%%r8\n" + /* c += d * R */ + "movq %%rcx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[3] = c & M */ + "movq %%r8,%%rax\n" + "movq $0xfffffffffffff,%%rdx\n" + "andq %%rdx,%%rax\n" + "movq %%rax,24(%%rdi)\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* c += t4 (%%r8 only) */ + "addq %%rsi,%%r8\n" + /* r[4] = c */ + "movq %%r8,32(%%rdi)\n" +: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) +: "b"(b), "D"(r) +: "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" +); +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { +/** + * Registers: rdx:rax = multiplication accumulator + * r9:r8 = c + * rcx:rbx = d + * r10-r14 = a0-a4 + * r15 = M (0xfffffffffffff) + * rdi = r + * rsi = a / t? + */ + uint64_t tmp1, tmp2, tmp3; +__asm__ __volatile__( + "movq 0(%%rsi),%%r10\n" + "movq 8(%%rsi),%%r11\n" + "movq 16(%%rsi),%%r12\n" + "movq 24(%%rsi),%%r13\n" + "movq 32(%%rsi),%%r14\n" + "movq $0xfffffffffffff,%%r15\n" + + /* d = (a0*2) * a3 */ + "leaq (%%r10,%%r10,1),%%rax\n" + "mulq %%r13\n" + "movq %%rax,%%rbx\n" + "movq %%rdx,%%rcx\n" + /* d += (a1*2) * a2 */ + "leaq (%%r11,%%r11,1),%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c = a4 * a4 */ + "movq %%r14,%%rax\n" + "mulq %%r14\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += (c & M) * R */ + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* t3 (tmp1) = d & M */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + "movq %%rsi,%q1\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* a4 *= 2 */ + "addq %%r14,%%r14\n" + /* d += a0 * a4 */ + "movq %%r10,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d+= (a1*2) * a3 */ + "leaq (%%r11,%%r11,1),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += a2 * a2 */ + "movq %%r12,%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += c * R */ + "movq %%r8,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* t4 = d & M (%%rsi) */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* tx = t4 >> 48 (tmp3) */ + "movq %%rsi,%%rax\n" + "shrq $48,%%rax\n" + "movq %%rax,%q3\n" + /* t4 &= (M >> 4) (tmp2) */ + "movq $0xffffffffffff,%%rax\n" + "andq %%rax,%%rsi\n" + "movq %%rsi,%q2\n" + /* c = a0 * a0 */ + "movq %%r10,%%rax\n" + "mulq %%r10\n" + "movq %%rax,%%r8\n" + "movq %%rdx,%%r9\n" + /* d += a1 * a4 */ + "movq %%r11,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += (a2*2) * a3 */ + "leaq (%%r12,%%r12,1),%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* u0 = d & M (%%rsi) */ + "movq %%rbx,%%rsi\n" + "andq %%r15,%%rsi\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* u0 = (u0 << 4) | tx (%%rsi) */ + "shlq $4,%%rsi\n" + "movq %q3,%%rax\n" + "orq %%rax,%%rsi\n" + /* c += u0 * (R >> 4) */ + "movq $0x1000003d1,%%rax\n" + "mulq %%rsi\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[0] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,0(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* a0 *= 2 */ + "addq %%r10,%%r10\n" + /* c += a0 * a1 */ + "movq %%r10,%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a2 * a4 */ + "movq %%r12,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* d += a3 * a3 */ + "movq %%r13,%%rax\n" + "mulq %%r13\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c += (d & M) * R */ + "movq %%rbx,%%rax\n" + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 */ + "shrdq $52,%%rcx,%%rbx\n" + "xorq %%rcx,%%rcx\n" + /* r[1] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,8(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += a0 * a2 (last use of %%r10) */ + "movq %%r10,%%rax\n" + "mulq %%r12\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* fetch t3 (%%r10, overwrites a0),t4 (%%rsi) */ + "movq %q2,%%rsi\n" + "movq %q1,%%r10\n" + /* c += a1 * a1 */ + "movq %%r11,%%rax\n" + "mulq %%r11\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d += a3 * a4 */ + "movq %%r13,%%rax\n" + "mulq %%r14\n" + "addq %%rax,%%rbx\n" + "adcq %%rdx,%%rcx\n" + /* c += (d & M) * R */ + "movq %%rbx,%%rax\n" + "andq %%r15,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* d >>= 52 (%%rbx only) */ + "shrdq $52,%%rcx,%%rbx\n" + /* r[2] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,16(%%rdi)\n" + /* c >>= 52 */ + "shrdq $52,%%r9,%%r8\n" + "xorq %%r9,%%r9\n" + /* c += t3 */ + "addq %%r10,%%r8\n" + /* c += d * R */ + "movq %%rbx,%%rax\n" + "movq $0x1000003d10,%%rdx\n" + "mulq %%rdx\n" + "addq %%rax,%%r8\n" + "adcq %%rdx,%%r9\n" + /* r[3] = c & M */ + "movq %%r8,%%rax\n" + "andq %%r15,%%rax\n" + "movq %%rax,24(%%rdi)\n" + /* c >>= 52 (%%r8 only) */ + "shrdq $52,%%r9,%%r8\n" + /* c += t4 (%%r8 only) */ + "addq %%rsi,%%r8\n" + /* r[4] = c */ + "movq %%r8,32(%%rdi)\n" +: "+S"(a), "=m"(tmp1), "=m"(tmp2), "=m"(tmp3) +: "D"(r) +: "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", "%r14", "%r15", "cc", "memory" +); +} + +#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ diff --git a/libsecp256k1/src/field_5x52_impl.h b/libsecp256k1/src/field_5x52_impl.h new file mode 100644 index 0000000..71aa550 --- /dev/null +++ b/libsecp256k1/src/field_5x52_impl.h @@ -0,0 +1,499 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_REPR_IMPL_H +#define SECP256K1_FIELD_REPR_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "util.h" +#include "field.h" + +#if defined(USE_ASM_X86_64) +#include "field_5x52_asm_impl.h" +#else +#include "field_5x52_int128_impl.h" +#endif + +/** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, + * represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular, + * each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element + * is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations + * accept any input with magnitude at most M, and have different rules for propagating magnitude to their + * output. + */ + +#ifdef VERIFY +static void secp256k1_fe_verify(const secp256k1_fe *a) { + const uint64_t *d = a->n; + int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; + /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m); + r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m); + r &= (a->magnitude >= 0); + r &= (a->magnitude <= 2048); + if (a->normalized) { + r &= (a->magnitude <= 1); + if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) { + r &= (d[0] < 0xFFFFEFFFFFC2FULL); + } + } + VERIFY_CHECK(r == 1); +} +#endif + +static void secp256k1_fe_normalize(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + /* Apply the final reduction (for constant-time behaviour, we do it always) */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_normalize_var(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t m; + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + /* At most a single final reduction is needed; check if the value is >= the field characteristic */ + x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) + & (t0 >= 0xFFFFEFFFFFC2FULL)); + + if (x) { + t0 += 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; + + /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ + VERIFY_CHECK(t4 >> 48 == x); + + /* Mask off the possible multiple of 2^256 from the final reduction */ + t4 &= 0x0FFFFFFFFFFFFULL; + } + + r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; + +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { + uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + uint64_t z0, z1; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL; + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { + uint64_t t0, t1, t2, t3, t4; + uint64_t z0, z1; + uint64_t x; + + t0 = r->n[0]; + t4 = r->n[4]; + + /* Reduce t4 at the start so there will be at most a single carry from the first pass */ + x = t4 >> 48; + + /* The first pass ensures the magnitude is 1, ... */ + t0 += x * 0x1000003D1ULL; + + /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ + z0 = t0 & 0xFFFFFFFFFFFFFULL; + z1 = z0 ^ 0x1000003D0ULL; + + /* Fast return path should catch the majority of cases */ + if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) { + return 0; + } + + t1 = r->n[1]; + t2 = r->n[2]; + t3 = r->n[3]; + + t4 &= 0x0FFFFFFFFFFFFULL; + + t1 += (t0 >> 52); + t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; + t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; + t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; + z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; + + /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ + VERIFY_CHECK(t4 >> 49 == 0); + + return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); +} + +SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { + r->n[0] = a; + r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { + const uint64_t *t = a->n; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0; +} + +SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + return a->n[0] & 1; +} + +SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { + int i; +#ifdef VERIFY + a->magnitude = 0; + a->normalized = 1; +#endif + for (i=0; i<5; i++) { + a->n[i] = 0; + } +} + +static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { + int i; +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + VERIFY_CHECK(b->normalized); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); +#endif + for (i = 4; i >= 0; i--) { + if (a->n[i] > b->n[i]) { + return 1; + } + if (a->n[i] < b->n[i]) { + return -1; + } + } + return 0; +} + +static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { + int ret; + r->n[0] = (uint64_t)a[31] + | ((uint64_t)a[30] << 8) + | ((uint64_t)a[29] << 16) + | ((uint64_t)a[28] << 24) + | ((uint64_t)a[27] << 32) + | ((uint64_t)a[26] << 40) + | ((uint64_t)(a[25] & 0xF) << 48); + r->n[1] = (uint64_t)((a[25] >> 4) & 0xF) + | ((uint64_t)a[24] << 4) + | ((uint64_t)a[23] << 12) + | ((uint64_t)a[22] << 20) + | ((uint64_t)a[21] << 28) + | ((uint64_t)a[20] << 36) + | ((uint64_t)a[19] << 44); + r->n[2] = (uint64_t)a[18] + | ((uint64_t)a[17] << 8) + | ((uint64_t)a[16] << 16) + | ((uint64_t)a[15] << 24) + | ((uint64_t)a[14] << 32) + | ((uint64_t)a[13] << 40) + | ((uint64_t)(a[12] & 0xF) << 48); + r->n[3] = (uint64_t)((a[12] >> 4) & 0xF) + | ((uint64_t)a[11] << 4) + | ((uint64_t)a[10] << 12) + | ((uint64_t)a[9] << 20) + | ((uint64_t)a[8] << 28) + | ((uint64_t)a[7] << 36) + | ((uint64_t)a[6] << 44); + r->n[4] = (uint64_t)a[5] + | ((uint64_t)a[4] << 8) + | ((uint64_t)a[3] << 16) + | ((uint64_t)a[2] << 24) + | ((uint64_t)a[1] << 32) + | ((uint64_t)a[0] << 40); + ret = !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL)); +#ifdef VERIFY + r->magnitude = 1; + if (ret) { + r->normalized = 1; + secp256k1_fe_verify(r); + } else { + r->normalized = 0; + } +#endif + return ret; +} + +/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ +static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); + secp256k1_fe_verify(a); +#endif + r[0] = (a->n[4] >> 40) & 0xFF; + r[1] = (a->n[4] >> 32) & 0xFF; + r[2] = (a->n[4] >> 24) & 0xFF; + r[3] = (a->n[4] >> 16) & 0xFF; + r[4] = (a->n[4] >> 8) & 0xFF; + r[5] = a->n[4] & 0xFF; + r[6] = (a->n[3] >> 44) & 0xFF; + r[7] = (a->n[3] >> 36) & 0xFF; + r[8] = (a->n[3] >> 28) & 0xFF; + r[9] = (a->n[3] >> 20) & 0xFF; + r[10] = (a->n[3] >> 12) & 0xFF; + r[11] = (a->n[3] >> 4) & 0xFF; + r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4); + r[13] = (a->n[2] >> 40) & 0xFF; + r[14] = (a->n[2] >> 32) & 0xFF; + r[15] = (a->n[2] >> 24) & 0xFF; + r[16] = (a->n[2] >> 16) & 0xFF; + r[17] = (a->n[2] >> 8) & 0xFF; + r[18] = a->n[2] & 0xFF; + r[19] = (a->n[1] >> 44) & 0xFF; + r[20] = (a->n[1] >> 36) & 0xFF; + r[21] = (a->n[1] >> 28) & 0xFF; + r[22] = (a->n[1] >> 20) & 0xFF; + r[23] = (a->n[1] >> 12) & 0xFF; + r[24] = (a->n[1] >> 4) & 0xFF; + r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4); + r[26] = (a->n[0] >> 40) & 0xFF; + r[27] = (a->n[0] >> 32) & 0xFF; + r[28] = (a->n[0] >> 24) & 0xFF; + r[29] = (a->n[0] >> 16) & 0xFF; + r[30] = (a->n[0] >> 8) & 0xFF; + r[31] = a->n[0] & 0xFF; +} + +SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= m); + secp256k1_fe_verify(a); +#endif + r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; + r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; + r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2]; + r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3]; + r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4]; +#ifdef VERIFY + r->magnitude = m + 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { + r->n[0] *= a; + r->n[1] *= a; + r->n[2] *= a; + r->n[3] *= a; + r->n[4] *= a; +#ifdef VERIFY + r->magnitude *= a; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + secp256k1_fe_verify(a); +#endif + r->n[0] += a->n[0]; + r->n[1] += a->n[1]; + r->n[2] += a->n[2]; + r->n[3] += a->n[3]; + r->n[4] += a->n[4]; +#ifdef VERIFY + r->magnitude += a->magnitude; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + VERIFY_CHECK(b->magnitude <= 8); + secp256k1_fe_verify(a); + secp256k1_fe_verify(b); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); +#endif + secp256k1_fe_mul_inner(r->n, a->n, b->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->magnitude <= 8); + secp256k1_fe_verify(a); +#endif + secp256k1_fe_sqr_inner(r->n, a->n); +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 0; + secp256k1_fe_verify(r); +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { + uint64_t mask0, mask1; + mask0 = flag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); + r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); +#ifdef VERIFY + if (flag) { + r->magnitude = a->magnitude; + r->normalized = a->normalized; + } +#endif +} + +static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { + uint64_t mask0, mask1; + mask0 = flag + ~((uint64_t)0); + mask1 = ~mask0; + r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); + r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); + r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); + r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); +} + +static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { +#ifdef VERIFY + VERIFY_CHECK(a->normalized); +#endif + r->n[0] = a->n[0] | a->n[1] << 52; + r->n[1] = a->n[1] >> 12 | a->n[2] << 40; + r->n[2] = a->n[2] >> 24 | a->n[3] << 28; + r->n[3] = a->n[3] >> 36 | a->n[4] << 16; +} + +static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { + r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL; + r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL); + r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL); + r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); + r->n[4] = a->n[3] >> 16; +#ifdef VERIFY + r->magnitude = 1; + r->normalized = 1; +#endif +} + +#endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/libsecp256k1/src/field_5x52_int128_impl.h b/libsecp256k1/src/field_5x52_int128_impl.h new file mode 100644 index 0000000..bcbfb92 --- /dev/null +++ b/libsecp256k1/src/field_5x52_int128_impl.h @@ -0,0 +1,279 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H +#define SECP256K1_FIELD_INNER5X52_IMPL_H + +#include + +#ifdef VERIFY +#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0) +#else +#define VERIFY_BITS(x, n) do { } while(0) +#endif + +SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) { + uint128_t c, d; + uint64_t t3, t4, tx, u0; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + VERIFY_BITS(b[0], 56); + VERIFY_BITS(b[1], 56); + VERIFY_BITS(b[2], 56); + VERIFY_BITS(b[3], 56); + VERIFY_BITS(b[4], 52); + VERIFY_CHECK(r != b); + VERIFY_CHECK(a != b); + + /* [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x). + * for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4) + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + d = (uint128_t)a0 * b[3] + + (uint128_t)a1 * b[2] + + (uint128_t)a2 * b[1] + + (uint128_t)a3 * b[0]; + VERIFY_BITS(d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + c = (uint128_t)a4 * b[4]; + VERIFY_BITS(c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + d += (c & M) * R; c >>= 52; + VERIFY_BITS(d, 115); + VERIFY_BITS(c, 60); + /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = d & M; d >>= 52; + VERIFY_BITS(t3, 52); + VERIFY_BITS(d, 63); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + d += (uint128_t)a0 * b[4] + + (uint128_t)a1 * b[3] + + (uint128_t)a2 * b[2] + + (uint128_t)a3 * b[1] + + (uint128_t)a4 * b[0]; + VERIFY_BITS(d, 115); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + d += c * R; + VERIFY_BITS(d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = d & M; d >>= 52; + VERIFY_BITS(t4, 52); + VERIFY_BITS(d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + c = (uint128_t)a0 * b[0]; + VERIFY_BITS(c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + d += (uint128_t)a1 * b[4] + + (uint128_t)a2 * b[3] + + (uint128_t)a3 * b[2] + + (uint128_t)a4 * b[1]; + VERIFY_BITS(d, 115); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = d & M; d >>= 52; + VERIFY_BITS(u0, 52); + VERIFY_BITS(d, 63); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + c += (uint128_t)u0 * (R >> 4); + VERIFY_BITS(c, 115); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = c & M; c >>= 52; + VERIFY_BITS(r[0], 52); + VERIFY_BITS(c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + c += (uint128_t)a0 * b[1] + + (uint128_t)a1 * b[0]; + VERIFY_BITS(c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + d += (uint128_t)a2 * b[4] + + (uint128_t)a3 * b[3] + + (uint128_t)a4 * b[2]; + VERIFY_BITS(d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = c & M; c >>= 52; + VERIFY_BITS(r[1], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + c += (uint128_t)a0 * b[2] + + (uint128_t)a1 * b[1] + + (uint128_t)a2 * b[0]; + VERIFY_BITS(c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint128_t)a3 * b[4] + + (uint128_t)a4 * b[3]; + VERIFY_BITS(d, 114); + /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = c & M; c >>= 52; + VERIFY_BITS(r[2], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += d * R + t3; + VERIFY_BITS(c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = c & M; c >>= 52; + VERIFY_BITS(r[3], 52); + VERIFY_BITS(c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += t4; + VERIFY_BITS(c, 49); + /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = c; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) { + uint128_t c, d; + uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4]; + int64_t t3, t4, tx, u0; + const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL; + + VERIFY_BITS(a[0], 56); + VERIFY_BITS(a[1], 56); + VERIFY_BITS(a[2], 56); + VERIFY_BITS(a[3], 56); + VERIFY_BITS(a[4], 52); + + /** [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n. + * px is a shorthand for sum(a[i]*a[x-i], i=0..x). + * Note that [x 0 0 0 0 0] = [x*R]. + */ + + d = (uint128_t)(a0*2) * a3 + + (uint128_t)(a1*2) * a2; + VERIFY_BITS(d, 114); + /* [d 0 0 0] = [p3 0 0 0] */ + c = (uint128_t)a4 * a4; + VERIFY_BITS(c, 112); + /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + d += (c & M) * R; c >>= 52; + VERIFY_BITS(d, 115); + VERIFY_BITS(c, 60); + /* [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + t3 = d & M; d >>= 52; + VERIFY_BITS(t3, 52); + VERIFY_BITS(d, 63); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */ + + a4 *= 2; + d += (uint128_t)a0 * a4 + + (uint128_t)(a1*2) * a3 + + (uint128_t)a2 * a2; + VERIFY_BITS(d, 115); + /* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + d += c * R; + VERIFY_BITS(d, 116); + /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + t4 = d & M; d >>= 52; + VERIFY_BITS(t4, 52); + VERIFY_BITS(d, 64); + /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + tx = (t4 >> 48); t4 &= (M >> 4); + VERIFY_BITS(tx, 4); + VERIFY_BITS(t4, 48); + /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */ + + c = (uint128_t)a0 * a0; + VERIFY_BITS(c, 112); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */ + d += (uint128_t)a1 * a4 + + (uint128_t)(a2*2) * a3; + VERIFY_BITS(d, 114); + /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = d & M; d >>= 52; + VERIFY_BITS(u0, 52); + VERIFY_BITS(d, 62); + /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + u0 = (u0 << 4) | tx; + VERIFY_BITS(u0, 56); + /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + c += (uint128_t)u0 * (R >> 4); + VERIFY_BITS(c, 113); + /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */ + r[0] = c & M; c >>= 52; + VERIFY_BITS(r[0], 52); + VERIFY_BITS(c, 61); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */ + + a0 *= 2; + c += (uint128_t)a0 * a1; + VERIFY_BITS(c, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */ + d += (uint128_t)a2 * a4 + + (uint128_t)a3 * a3; + VERIFY_BITS(d, 114); + /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + r[1] = c & M; c >>= 52; + VERIFY_BITS(r[1], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */ + + c += (uint128_t)a0 * a2 + + (uint128_t)a1 * a1; + VERIFY_BITS(c, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */ + d += (uint128_t)a3 * a4; + VERIFY_BITS(d, 114); + /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += (d & M) * R; d >>= 52; + VERIFY_BITS(c, 115); + VERIFY_BITS(d, 62); + /* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[2] = c & M; c >>= 52; + VERIFY_BITS(r[2], 52); + VERIFY_BITS(c, 63); + /* [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + + c += d * R + t3; + VERIFY_BITS(c, 100); + /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[3] = c & M; c >>= 52; + VERIFY_BITS(r[3], 52); + VERIFY_BITS(c, 48); + /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + c += t4; + VERIFY_BITS(c, 49); + /* [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ + r[4] = c; + VERIFY_BITS(r[4], 49); + /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */ +} + +#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */ diff --git a/libsecp256k1/src/field_impl.h b/libsecp256k1/src/field_impl.h new file mode 100644 index 0000000..485921a --- /dev/null +++ b/libsecp256k1/src/field_impl.h @@ -0,0 +1,320 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_FIELD_IMPL_H +#define SECP256K1_FIELD_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "util.h" +#include "num.h" + +#if defined(USE_FIELD_10X26) +#include "field_10x26_impl.h" +#elif defined(USE_FIELD_5X52) +#include "field_5x52_impl.h" +#else +#error "Please select field implementation" +#endif + +SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero(&na); +} + +SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe na; + secp256k1_fe_negate(&na, a, 1); + secp256k1_fe_add(&na, b); + return secp256k1_fe_normalizes_to_zero_var(&na); +} + +static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) { + /** Given that p is congruent to 3 mod 4, we can compute the square root of + * a mod p as the (p+1)/4'th power of a. + * + * As (p+1)/4 is an even number, it will have the same result for a and for + * (-a). Only one of these two numbers actually has a square root however, + * so we test at the end by squaring and comparing to the input. + * Also because (p+1)/4 is an even number, the computed square root is + * itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)). + */ + secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; + int j; + + VERIFY_CHECK(r != a); + + /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in + * { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: + * 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + secp256k1_fe_sqr(&x2, a); + secp256k1_fe_mul(&x2, &x2, a); + + secp256k1_fe_sqr(&x3, &x2); + secp256k1_fe_mul(&x3, &x3, a); + + x6 = x3; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x6, &x6); + } + secp256k1_fe_mul(&x6, &x6, &x3); + + x9 = x6; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x9, &x9); + } + secp256k1_fe_mul(&x9, &x9, &x3); + + x11 = x9; + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&x11, &x11); + } + secp256k1_fe_mul(&x11, &x11, &x2); + + x22 = x11; + for (j=0; j<11; j++) { + secp256k1_fe_sqr(&x22, &x22); + } + secp256k1_fe_mul(&x22, &x22, &x11); + + x44 = x22; + for (j=0; j<22; j++) { + secp256k1_fe_sqr(&x44, &x44); + } + secp256k1_fe_mul(&x44, &x44, &x22); + + x88 = x44; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x88, &x88); + } + secp256k1_fe_mul(&x88, &x88, &x44); + + x176 = x88; + for (j=0; j<88; j++) { + secp256k1_fe_sqr(&x176, &x176); + } + secp256k1_fe_mul(&x176, &x176, &x88); + + x220 = x176; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x220, &x220); + } + secp256k1_fe_mul(&x220, &x220, &x44); + + x223 = x220; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x223, &x223); + } + secp256k1_fe_mul(&x223, &x223, &x3); + + /* The final result is then assembled using a sliding window over the blocks. */ + + t1 = x223; + for (j=0; j<23; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x22); + for (j=0; j<6; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x2); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_sqr(r, &t1); + + /* Check that a square root was actually calculated */ + + secp256k1_fe_sqr(&t1, r); + return secp256k1_fe_equal(&t1, a); +} + +static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) { + secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1; + int j; + + /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in + * { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block: + * [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223] + */ + + secp256k1_fe_sqr(&x2, a); + secp256k1_fe_mul(&x2, &x2, a); + + secp256k1_fe_sqr(&x3, &x2); + secp256k1_fe_mul(&x3, &x3, a); + + x6 = x3; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x6, &x6); + } + secp256k1_fe_mul(&x6, &x6, &x3); + + x9 = x6; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x9, &x9); + } + secp256k1_fe_mul(&x9, &x9, &x3); + + x11 = x9; + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&x11, &x11); + } + secp256k1_fe_mul(&x11, &x11, &x2); + + x22 = x11; + for (j=0; j<11; j++) { + secp256k1_fe_sqr(&x22, &x22); + } + secp256k1_fe_mul(&x22, &x22, &x11); + + x44 = x22; + for (j=0; j<22; j++) { + secp256k1_fe_sqr(&x44, &x44); + } + secp256k1_fe_mul(&x44, &x44, &x22); + + x88 = x44; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x88, &x88); + } + secp256k1_fe_mul(&x88, &x88, &x44); + + x176 = x88; + for (j=0; j<88; j++) { + secp256k1_fe_sqr(&x176, &x176); + } + secp256k1_fe_mul(&x176, &x176, &x88); + + x220 = x176; + for (j=0; j<44; j++) { + secp256k1_fe_sqr(&x220, &x220); + } + secp256k1_fe_mul(&x220, &x220, &x44); + + x223 = x220; + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&x223, &x223); + } + secp256k1_fe_mul(&x223, &x223, &x3); + + /* The final result is then assembled using a sliding window over the blocks. */ + + t1 = x223; + for (j=0; j<23; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x22); + for (j=0; j<5; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, a); + for (j=0; j<3; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(&t1, &t1, &x2); + for (j=0; j<2; j++) { + secp256k1_fe_sqr(&t1, &t1); + } + secp256k1_fe_mul(r, a, &t1); +} + +static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) { +#if defined(USE_FIELD_INV_BUILTIN) + secp256k1_fe_inv(r, a); +#elif defined(USE_FIELD_INV_NUM) + secp256k1_num n, m; + static const secp256k1_fe negone = SECP256K1_FE_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL + ); + /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + static const unsigned char prime[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F + }; + unsigned char b[32]; + int res; + secp256k1_fe c = *a; + secp256k1_fe_normalize_var(&c); + secp256k1_fe_get_b32(b, &c); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_num_set_bin(&m, prime, 32); + secp256k1_num_mod_inverse(&n, &n, &m); + secp256k1_num_get_bin(b, 32, &n); + res = secp256k1_fe_set_b32(r, b); + (void)res; + VERIFY_CHECK(res); + /* Verify the result is the (unique) valid inverse using non-GMP code. */ + secp256k1_fe_mul(&c, &c, r); + secp256k1_fe_add(&c, &negone); + CHECK(secp256k1_fe_normalizes_to_zero_var(&c)); +#else +#error "Please select field inverse implementation" +#endif +} + +static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) { + secp256k1_fe u; + size_t i; + if (len < 1) { + return; + } + + VERIFY_CHECK((r + len <= a) || (a + len <= r)); + + r[0] = a[0]; + + i = 0; + while (++i < len) { + secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]); + } + + secp256k1_fe_inv_var(&u, &r[--i]); + + while (i > 0) { + size_t j = i--; + secp256k1_fe_mul(&r[j], &r[i], &u); + secp256k1_fe_mul(&u, &u, &a[j]); + } + + r[0] = u; +} + +static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) { +#ifndef USE_NUM_NONE + unsigned char b[32]; + secp256k1_num n; + secp256k1_num m; + /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ + static const unsigned char prime[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F + }; + + secp256k1_fe c = *a; + secp256k1_fe_normalize_var(&c); + secp256k1_fe_get_b32(b, &c); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_num_set_bin(&m, prime, 32); + return secp256k1_num_jacobi(&n, &m) >= 0; +#else + secp256k1_fe r; + return secp256k1_fe_sqrt(&r, a); +#endif +} + +static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + +#endif /* SECP256K1_FIELD_IMPL_H */ diff --git a/libsecp256k1/src/gen_context.c b/libsecp256k1/src/gen_context.c new file mode 100644 index 0000000..539f574 --- /dev/null +++ b/libsecp256k1/src/gen_context.c @@ -0,0 +1,87 @@ +/********************************************************************** + * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +// Autotools creates libsecp256k1-config.h, of which ECMULT_GEN_PREC_BITS is needed. +// ifndef guard so downstream users can define their own if they do not use autotools. +#if !defined(ECMULT_GEN_PREC_BITS) +#include "libsecp256k1-config.h" +#endif +#define USE_BASIC_CONFIG 1 +#include "basic-config.h" + +#include "include/secp256k1.h" +#include "util.h" +#include "field_impl.h" +#include "scalar_impl.h" +#include "group_impl.h" +#include "ecmult_gen_impl.h" + +static void default_error_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str); + abort(); +} + +static const secp256k1_callback default_error_callback = { + default_error_callback_fn, + NULL +}; + +int main(int argc, char **argv) { + secp256k1_ecmult_gen_context ctx; + void *prealloc, *base; + int inner; + int outer; + FILE* fp; + + (void)argc; + (void)argv; + + fp = fopen("src/ecmult_static_context.h","w"); + if (fp == NULL) { + fprintf(stderr, "Could not open src/ecmult_static_context.h for writing!\n"); + return -1; + } + + fprintf(fp, "#ifndef _SECP256K1_ECMULT_STATIC_CONTEXT_\n"); + fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n"); + fprintf(fp, "#include \"src/group.h\"\n"); + fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n"); + fprintf(fp, "#if ECMULT_GEN_PREC_N != %d || ECMULT_GEN_PREC_G != %d\n", ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G); + fprintf(fp, " #error configuration mismatch, invalid ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G. Try deleting ecmult_static_context.h before the build.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G] = {\n"); + + base = checked_malloc(&default_error_callback, SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE); + prealloc = base; + secp256k1_ecmult_gen_context_init(&ctx); + secp256k1_ecmult_gen_context_build(&ctx, &prealloc); + for(outer = 0; outer != ECMULT_GEN_PREC_N; outer++) { + fprintf(fp,"{\n"); + for(inner = 0; inner != ECMULT_GEN_PREC_G; inner++) { + fprintf(fp," SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner])); + if (inner != ECMULT_GEN_PREC_G - 1) { + fprintf(fp,",\n"); + } else { + fprintf(fp,"\n"); + } + } + if (outer != ECMULT_GEN_PREC_N - 1) { + fprintf(fp,"},\n"); + } else { + fprintf(fp,"}\n"); + } + } + fprintf(fp,"};\n"); + secp256k1_ecmult_gen_context_clear(&ctx); + free(base); + + fprintf(fp, "#undef SC\n"); + fprintf(fp, "#endif\n"); + fclose(fp); + + return 0; +} diff --git a/libsecp256k1/src/group.h b/libsecp256k1/src/group.h new file mode 100644 index 0000000..ded4e1d --- /dev/null +++ b/libsecp256k1/src/group.h @@ -0,0 +1,141 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_GROUP_H +#define SECP256K1_GROUP_H + +#include "num.h" +#include "field.h" + +/** A group element of the secp256k1 curve, in affine coordinates. */ +typedef struct { + secp256k1_fe x; + secp256k1_fe y; + int infinity; /* whether this represents the point at infinity */ +} secp256k1_ge; + +#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0} +#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} + +/** A group element of the secp256k1 curve, in jacobian coordinates. */ +typedef struct { + secp256k1_fe x; /* actual X: x/z^2 */ + secp256k1_fe y; /* actual Y: y/z^3 */ + secp256k1_fe z; + int infinity; /* whether this represents the point at infinity */ +} secp256k1_gej; + +#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0} +#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1} + +typedef struct { + secp256k1_fe_storage x; + secp256k1_fe_storage y; +} secp256k1_ge_storage; + +#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))} + +#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y) + +/** Set a group element equal to the point with given X and Y coordinates */ +static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y); + +/** Set a group element (affine) equal to the point with the given X coordinate + * and a Y coordinate that is a quadratic residue modulo p. The return value + * is true iff a coordinate with the given X coordinate exists. + */ +static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x); + +/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness + * for Y. Return value indicates whether the result is valid. */ +static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_ge_is_infinity(const secp256k1_ge *a); + +/** Check whether a group element is valid (i.e., on the curve). */ +static int secp256k1_ge_is_valid_var(const secp256k1_ge *a); + +static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a); + +/** Set a group element equal to another which is given in jacobian coordinates */ +static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a); + +/** Set a batch of group elements equal to the inputs given in jacobian coordinates */ +static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len); + +/** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to + * the same global z "denominator". zr must contain the known z-ratios such + * that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y + * coordinates of the result are stored in r, the common z coordinate is + * stored in globalz. */ +static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr); + +/** Set a group element (affine) equal to the point at infinity. */ +static void secp256k1_ge_set_infinity(secp256k1_ge *r); + +/** Set a group element (jacobian) equal to the point at infinity. */ +static void secp256k1_gej_set_infinity(secp256k1_gej *r); + +/** Set a group element (jacobian) equal to another which is given in affine coordinates. */ +static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a); + +/** Compare the X coordinate of a group element (jacobian). */ +static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a); + +/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */ +static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a); + +/** Check whether a group element is the point at infinity. */ +static int secp256k1_gej_is_infinity(const secp256k1_gej *a); + +/** Check whether a group element's y coordinate is a quadratic residue. */ +static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a); + +/** Set r equal to the double of a, a cannot be infinity. Constant time. */ +static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a); + +/** Set r equal to the double of a. If rzr is not-NULL this sets *rzr such that r->z == a->z * *rzr (where infinity means an implicit z = 0). */ +static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ +static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */ +static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b); + +/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient + than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time + guarantee, and b is allowed to be infinity. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */ +static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr); + +/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */ +static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv); + +#ifdef USE_ENDOMORPHISM +/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */ +static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a); +#endif + +/** Clear a secp256k1_gej to prevent leaking sensitive information. */ +static void secp256k1_gej_clear(secp256k1_gej *r); + +/** Clear a secp256k1_ge to prevent leaking sensitive information. */ +static void secp256k1_ge_clear(secp256k1_ge *r); + +/** Convert a group element to the storage type. */ +static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a); + +/** Convert a group element back from the storage type. */ +static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag); + +/** Rescale a jacobian point by b which must be non-zero. Constant-time. */ +static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b); + +#endif /* SECP256K1_GROUP_H */ diff --git a/libsecp256k1/src/group_impl.h b/libsecp256k1/src/group_impl.h new file mode 100644 index 0000000..43b039b --- /dev/null +++ b/libsecp256k1/src/group_impl.h @@ -0,0 +1,708 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_GROUP_IMPL_H +#define SECP256K1_GROUP_IMPL_H + +#include "num.h" +#include "field.h" +#include "group.h" + +/* These points can be generated in sage as follows: + * + * 0. Setup a worksheet with the following parameters. + * b = 4 # whatever CURVE_B will be set to + * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F) + * C = EllipticCurve ([F (0), F (b)]) + * + * 1. Determine all the small orders available to you. (If there are + * no satisfactory ones, go back and change b.) + * print C.order().factor(limit=1000) + * + * 2. Choose an order as one of the prime factors listed in the above step. + * (You can also multiply some to get a composite order, though the + * tests will crash trying to invert scalars during signing.) We take a + * random point and scale it to drop its order to the desired value. + * There is some probability this won't work; just try again. + * order = 199 + * P = C.random_point() + * P = (int(P.order()) / int(order)) * P + * assert(P.order() == order) + * + * 3. Print the values. You'll need to use a vim macro or something to + * split the hex output into 4-byte chunks. + * print "%x %x" % P.xy() + */ +#if defined(EXHAUSTIVE_TEST_ORDER) +# if EXHAUSTIVE_TEST_ORDER == 199 +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( + 0xFA7CC9A7, 0x0737F2DB, 0xA749DD39, 0x2B4FB069, + 0x3B017A7D, 0xA808C2F1, 0xFB12940C, 0x9EA66C18, + 0x78AC123A, 0x5ED8AEF3, 0x8732BC91, 0x1F3A2868, + 0x48DF246C, 0x808DAE72, 0xCFE52572, 0x7F0501ED +); + +static const int CURVE_B = 4; +# elif EXHAUSTIVE_TEST_ORDER == 13 +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( + 0xedc60018, 0xa51a786b, 0x2ea91f4d, 0x4c9416c0, + 0x9de54c3b, 0xa1316554, 0x6cf4345c, 0x7277ef15, + 0x54cb1b6b, 0xdc8c1273, 0x087844ea, 0x43f4603e, + 0x0eaf9a43, 0xf6effe55, 0x939f806d, 0x37adf8ac +); +static const int CURVE_B = 2; +# else +# error No known generator for the specified exhaustive test group order. +# endif +#else +/** Generator for secp256k1, value 'g' defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + */ +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( + 0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL, + 0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL, + 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL, + 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL +); + +static const int CURVE_B = 7; +#endif + +static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) { + secp256k1_fe zi2; + secp256k1_fe zi3; + secp256k1_fe_sqr(&zi2, zi); + secp256k1_fe_mul(&zi3, &zi2, zi); + secp256k1_fe_mul(&r->x, &a->x, &zi2); + secp256k1_fe_mul(&r->y, &a->y, &zi3); + r->infinity = a->infinity; +} + +static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) { + r->infinity = 0; + r->x = *x; + r->y = *y; +} + +static int secp256k1_ge_is_infinity(const secp256k1_ge *a) { + return a->infinity; +} + +static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) { + *r = *a; + secp256k1_fe_normalize_weak(&r->y); + secp256k1_fe_negate(&r->y, &r->y, 1); +} + +static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) { + secp256k1_fe z2, z3; + r->infinity = a->infinity; + secp256k1_fe_inv(&a->z, &a->z); + secp256k1_fe_sqr(&z2, &a->z); + secp256k1_fe_mul(&z3, &a->z, &z2); + secp256k1_fe_mul(&a->x, &a->x, &z2); + secp256k1_fe_mul(&a->y, &a->y, &z3); + secp256k1_fe_set_int(&a->z, 1); + r->x = a->x; + r->y = a->y; +} + +static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) { + secp256k1_fe z2, z3; + r->infinity = a->infinity; + if (a->infinity) { + return; + } + secp256k1_fe_inv_var(&a->z, &a->z); + secp256k1_fe_sqr(&z2, &a->z); + secp256k1_fe_mul(&z3, &a->z, &z2); + secp256k1_fe_mul(&a->x, &a->x, &z2); + secp256k1_fe_mul(&a->y, &a->y, &z3); + secp256k1_fe_set_int(&a->z, 1); + r->x = a->x; + r->y = a->y; +} + +static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len) { + secp256k1_fe u; + size_t i; + size_t last_i = SIZE_MAX; + + for (i = 0; i < len; i++) { + if (!a[i].infinity) { + /* Use destination's x coordinates as scratch space */ + if (last_i == SIZE_MAX) { + r[i].x = a[i].z; + } else { + secp256k1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z); + } + last_i = i; + } + } + if (last_i == SIZE_MAX) { + return; + } + secp256k1_fe_inv_var(&u, &r[last_i].x); + + i = last_i; + while (i > 0) { + i--; + if (!a[i].infinity) { + secp256k1_fe_mul(&r[last_i].x, &r[i].x, &u); + secp256k1_fe_mul(&u, &u, &a[last_i].z); + last_i = i; + } + } + VERIFY_CHECK(!a[last_i].infinity); + r[last_i].x = u; + + for (i = 0; i < len; i++) { + r[i].infinity = a[i].infinity; + if (!a[i].infinity) { + secp256k1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x); + } + } +} + +static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr) { + size_t i = len - 1; + secp256k1_fe zs; + + if (len > 0) { + /* The z of the final point gives us the "global Z" for the table. */ + r[i].x = a[i].x; + r[i].y = a[i].y; + /* Ensure all y values are in weak normal form for fast negation of points */ + secp256k1_fe_normalize_weak(&r[i].y); + *globalz = a[i].z; + r[i].infinity = 0; + zs = zr[i]; + + /* Work our way backwards, using the z-ratios to scale the x/y values. */ + while (i > 0) { + if (i != len - 1) { + secp256k1_fe_mul(&zs, &zs, &zr[i]); + } + i--; + secp256k1_ge_set_gej_zinv(&r[i], &a[i], &zs); + } + } +} + +static void secp256k1_gej_set_infinity(secp256k1_gej *r) { + r->infinity = 1; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); + secp256k1_fe_clear(&r->z); +} + +static void secp256k1_ge_set_infinity(secp256k1_ge *r) { + r->infinity = 1; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); +} + +static void secp256k1_gej_clear(secp256k1_gej *r) { + r->infinity = 0; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); + secp256k1_fe_clear(&r->z); +} + +static void secp256k1_ge_clear(secp256k1_ge *r) { + r->infinity = 0; + secp256k1_fe_clear(&r->x); + secp256k1_fe_clear(&r->y); +} + +static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) { + secp256k1_fe x2, x3, c; + r->x = *x; + secp256k1_fe_sqr(&x2, x); + secp256k1_fe_mul(&x3, x, &x2); + r->infinity = 0; + secp256k1_fe_set_int(&c, CURVE_B); + secp256k1_fe_add(&c, &x3); + return secp256k1_fe_sqrt(&r->y, &c); +} + +static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) { + if (!secp256k1_ge_set_xquad(r, x)) { + return 0; + } + secp256k1_fe_normalize_var(&r->y); + if (secp256k1_fe_is_odd(&r->y) != odd) { + secp256k1_fe_negate(&r->y, &r->y, 1); + } + return 1; + +} + +static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) { + r->infinity = a->infinity; + r->x = a->x; + r->y = a->y; + secp256k1_fe_set_int(&r->z, 1); +} + +static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) { + secp256k1_fe r, r2; + VERIFY_CHECK(!a->infinity); + secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x); + r2 = a->x; secp256k1_fe_normalize_weak(&r2); + return secp256k1_fe_equal_var(&r, &r2); +} + +static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) { + r->infinity = a->infinity; + r->x = a->x; + r->y = a->y; + r->z = a->z; + secp256k1_fe_normalize_weak(&r->y); + secp256k1_fe_negate(&r->y, &r->y, 1); +} + +static int secp256k1_gej_is_infinity(const secp256k1_gej *a) { + return a->infinity; +} + +static int secp256k1_gej_is_valid_var(const secp256k1_gej *a) { + secp256k1_fe y2, x3, z2, z6; + if (a->infinity) { + return 0; + } + /** y^2 = x^3 + 7 + * (Y/Z^3)^2 = (X/Z^2)^3 + 7 + * Y^2 / Z^6 = X^3 / Z^6 + 7 + * Y^2 = X^3 + 7*Z^6 + */ + secp256k1_fe_sqr(&y2, &a->y); + secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x); + secp256k1_fe_sqr(&z2, &a->z); + secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2); + secp256k1_fe_mul_int(&z6, CURVE_B); + secp256k1_fe_add(&x3, &z6); + secp256k1_fe_normalize_weak(&x3); + return secp256k1_fe_equal_var(&y2, &x3); +} + +static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) { + secp256k1_fe y2, x3, c; + if (a->infinity) { + return 0; + } + /* y^2 = x^3 + 7 */ + secp256k1_fe_sqr(&y2, &a->y); + secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x); + secp256k1_fe_set_int(&c, CURVE_B); + secp256k1_fe_add(&x3, &c); + secp256k1_fe_normalize_weak(&x3); + return secp256k1_fe_equal_var(&y2, &x3); +} + +static SECP256K1_INLINE void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a) { + /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate. + * + * Note that there is an implementation described at + * https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l + * which trades a multiply for a square, but in practice this is actually slower, + * mainly because it requires more normalizations. + */ + secp256k1_fe t1,t2,t3,t4; + + VERIFY_CHECK(!secp256k1_gej_is_infinity(a)); + r->infinity = 0; + + secp256k1_fe_mul(&r->z, &a->z, &a->y); + secp256k1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */ + secp256k1_fe_sqr(&t1, &a->x); + secp256k1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */ + secp256k1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */ + secp256k1_fe_sqr(&t3, &a->y); + secp256k1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */ + secp256k1_fe_sqr(&t4, &t3); + secp256k1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */ + secp256k1_fe_mul(&t3, &t3, &a->x); /* T3 = 2*X*Y^2 (1) */ + r->x = t3; + secp256k1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */ + secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */ + secp256k1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */ + secp256k1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */ + secp256k1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */ + secp256k1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */ + secp256k1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */ + secp256k1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */ + secp256k1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */ +} + +static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) { + /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity, + * Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have + * y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p. + * + * Having said this, if this function receives a point on a sextic twist, e.g. by + * a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6, + * since -6 does have a cube root mod p. For this point, this function will not set + * the infinity flag even though the point doubles to infinity, and the result + * point will be gibberish (z = 0 but infinity = 0). + */ + if (a->infinity) { + r->infinity = 1; + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + return; + } + + if (rzr != NULL) { + *rzr = a->y; + secp256k1_fe_normalize_weak(rzr); + secp256k1_fe_mul_int(rzr, 2); + } + + secp256k1_gej_double_nonzero(r, a); +} + +static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr) { + /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */ + secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t; + + if (a->infinity) { + VERIFY_CHECK(rzr == NULL); + *r = *b; + return; + } + + if (b->infinity) { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + *r = *a; + return; + } + + r->infinity = 0; + secp256k1_fe_sqr(&z22, &b->z); + secp256k1_fe_sqr(&z12, &a->z); + secp256k1_fe_mul(&u1, &a->x, &z22); + secp256k1_fe_mul(&u2, &b->x, &z12); + secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, rzr); + } else { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 0); + } + r->infinity = 1; + } + return; + } + secp256k1_fe_sqr(&i2, &i); + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_mul(&h3, &h, &h2); + secp256k1_fe_mul(&h, &h, &b->z); + if (rzr != NULL) { + *rzr = h; + } + secp256k1_fe_mul(&r->z, &a->z, &h); + secp256k1_fe_mul(&t, &u1, &h2); + r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2); + secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i); + secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1); + secp256k1_fe_add(&r->y, &h3); +} + +static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) { + /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */ + secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t; + if (a->infinity) { + VERIFY_CHECK(rzr == NULL); + secp256k1_gej_set_ge(r, b); + return; + } + if (b->infinity) { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 1); + } + *r = *a; + return; + } + r->infinity = 0; + + secp256k1_fe_sqr(&z12, &a->z); + u1 = a->x; secp256k1_fe_normalize_weak(&u1); + secp256k1_fe_mul(&u2, &b->x, &z12); + s1 = a->y; secp256k1_fe_normalize_weak(&s1); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, rzr); + } else { + if (rzr != NULL) { + secp256k1_fe_set_int(rzr, 0); + } + r->infinity = 1; + } + return; + } + secp256k1_fe_sqr(&i2, &i); + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_mul(&h3, &h, &h2); + if (rzr != NULL) { + *rzr = h; + } + secp256k1_fe_mul(&r->z, &a->z, &h); + secp256k1_fe_mul(&t, &u1, &h2); + r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2); + secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i); + secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1); + secp256k1_fe_add(&r->y, &h3); +} + +static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) { + /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */ + secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t; + + if (b->infinity) { + *r = *a; + return; + } + if (a->infinity) { + secp256k1_fe bzinv2, bzinv3; + r->infinity = b->infinity; + secp256k1_fe_sqr(&bzinv2, bzinv); + secp256k1_fe_mul(&bzinv3, &bzinv2, bzinv); + secp256k1_fe_mul(&r->x, &b->x, &bzinv2); + secp256k1_fe_mul(&r->y, &b->y, &bzinv3); + secp256k1_fe_set_int(&r->z, 1); + return; + } + r->infinity = 0; + + /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to + * secp256k1's isomorphism we can multiply the Z coordinates on both sides + * by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1). + * This means that (rx,ry,rz) can be calculated as + * (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz. + * The variable az below holds the modified Z coordinate for a, which is used + * for the computation of rx and ry, but not for rz. + */ + secp256k1_fe_mul(&az, &a->z, bzinv); + + secp256k1_fe_sqr(&z12, &az); + u1 = a->x; secp256k1_fe_normalize_weak(&u1); + secp256k1_fe_mul(&u2, &b->x, &z12); + s1 = a->y; secp256k1_fe_normalize_weak(&s1); + secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az); + secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); + secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2); + if (secp256k1_fe_normalizes_to_zero_var(&h)) { + if (secp256k1_fe_normalizes_to_zero_var(&i)) { + secp256k1_gej_double_var(r, a, NULL); + } else { + r->infinity = 1; + } + return; + } + secp256k1_fe_sqr(&i2, &i); + secp256k1_fe_sqr(&h2, &h); + secp256k1_fe_mul(&h3, &h, &h2); + r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h); + secp256k1_fe_mul(&t, &u1, &h2); + r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2); + secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i); + secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1); + secp256k1_fe_add(&r->y, &h3); +} + + +static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) { + /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */ + static const secp256k1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr; + secp256k1_fe m_alt, rr_alt; + int infinity, degenerate; + VERIFY_CHECK(!b->infinity); + VERIFY_CHECK(a->infinity == 0 || a->infinity == 1); + + /** In: + * Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks. + * In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002. + * we find as solution for a unified addition/doubling formula: + * lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation. + * x3 = lambda^2 - (x1 + x2) + * 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2). + * + * Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives: + * U1 = X1*Z2^2, U2 = X2*Z1^2 + * S1 = Y1*Z2^3, S2 = Y2*Z1^3 + * Z = Z1*Z2 + * T = U1+U2 + * M = S1+S2 + * Q = T*M^2 + * R = T^2-U1*U2 + * X3 = 4*(R^2-Q) + * Y3 = 4*(R*(3*Q-2*R^2)-M^4) + * Z3 = 2*M*Z + * (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.) + * + * This formula has the benefit of being the same for both addition + * of distinct points and doubling. However, it breaks down in the + * case that either point is infinity, or that y1 = -y2. We handle + * these cases in the following ways: + * + * - If b is infinity we simply bail by means of a VERIFY_CHECK. + * + * - If a is infinity, we detect this, and at the end of the + * computation replace the result (which will be meaningless, + * but we compute to be constant-time) with b.x : b.y : 1. + * + * - If a = -b, we have y1 = -y2, which is a degenerate case. + * But here the answer is infinity, so we simply set the + * infinity flag of the result, overriding the computed values + * without even needing to cmov. + * + * - If y1 = -y2 but x1 != x2, which does occur thanks to certain + * properties of our curve (specifically, 1 has nontrivial cube + * roots in our field, and the curve equation has no x coefficient) + * then the answer is not infinity but also not given by the above + * equation. In this case, we cmov in place an alternate expression + * for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these + * expressions for lambda are defined, they are equal, and can be + * obtained from each other by multiplication by (y1 + y2)/(y1 + y2) + * then substitution of x^3 + 7 for y^2 (using the curve equation). + * For all pairs of nonzero points (a, b) at least one is defined, + * so this covers everything. + */ + + secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */ + u1 = a->x; secp256k1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */ + secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */ + s1 = a->y; secp256k1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */ + secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */ + secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */ + t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */ + m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */ + secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */ + secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */ + secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */ + secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */ + /** If lambda = R/M = 0/0 we have a problem (except in the "trivial" + * case that Z = z1z2 = 0, and this is special-cased later on). */ + degenerate = secp256k1_fe_normalizes_to_zero(&m) & + secp256k1_fe_normalizes_to_zero(&rr); + /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2. + * This means either x1 == beta*x2 or beta*x1 == x2, where beta is + * a nontrivial cube root of one. In either case, an alternate + * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2), + * so we set R/M equal to this. */ + rr_alt = s1; + secp256k1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */ + secp256k1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */ + + secp256k1_fe_cmov(&rr_alt, &rr, !degenerate); + secp256k1_fe_cmov(&m_alt, &m, !degenerate); + /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0. + * From here on out Ralt and Malt represent the numerator + * and denominator of lambda; R and M represent the explicit + * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */ + secp256k1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */ + secp256k1_fe_mul(&q, &n, &t); /* q = Q = T*Malt^2 (1) */ + /* These two lines use the observation that either M == Malt or M == 0, + * so M^3 * Malt is either Malt^4 (which is computed by squaring), or + * zero (which is "computed" by cmov). So the cost is one squaring + * versus two multiplications. */ + secp256k1_fe_sqr(&n, &n); + secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */ + secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */ + secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Malt*Z (1) */ + infinity = secp256k1_fe_normalizes_to_zero(&r->z) * (1 - a->infinity); + secp256k1_fe_mul_int(&r->z, 2); /* r->z = Z3 = 2*Malt*Z (2) */ + secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */ + secp256k1_fe_add(&t, &q); /* t = Ralt^2-Q (3) */ + secp256k1_fe_normalize_weak(&t); + r->x = t; /* r->x = Ralt^2-Q (1) */ + secp256k1_fe_mul_int(&t, 2); /* t = 2*x3 (2) */ + secp256k1_fe_add(&t, &q); /* t = 2*x3 - Q: (4) */ + secp256k1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*x3 - Q) (1) */ + secp256k1_fe_add(&t, &n); /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */ + secp256k1_fe_negate(&r->y, &t, 3); /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */ + secp256k1_fe_normalize_weak(&r->y); + secp256k1_fe_mul_int(&r->x, 4); /* r->x = X3 = 4*(Ralt^2-Q) */ + secp256k1_fe_mul_int(&r->y, 4); /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */ + + /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */ + secp256k1_fe_cmov(&r->x, &b->x, a->infinity); + secp256k1_fe_cmov(&r->y, &b->y, a->infinity); + secp256k1_fe_cmov(&r->z, &fe_1, a->infinity); + r->infinity = infinity; +} + +static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) { + /* Operations: 4 mul, 1 sqr */ + secp256k1_fe zz; + VERIFY_CHECK(!secp256k1_fe_is_zero(s)); + secp256k1_fe_sqr(&zz, s); + secp256k1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */ + secp256k1_fe_mul(&r->y, &r->y, &zz); + secp256k1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */ + secp256k1_fe_mul(&r->z, &r->z, s); /* r->z *= s */ +} + +static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) { + secp256k1_fe x, y; + VERIFY_CHECK(!a->infinity); + x = a->x; + secp256k1_fe_normalize(&x); + y = a->y; + secp256k1_fe_normalize(&y); + secp256k1_fe_to_storage(&r->x, &x); + secp256k1_fe_to_storage(&r->y, &y); +} + +static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a) { + secp256k1_fe_from_storage(&r->x, &a->x); + secp256k1_fe_from_storage(&r->y, &a->y); + r->infinity = 0; +} + +static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) { + secp256k1_fe_storage_cmov(&r->x, &a->x, flag); + secp256k1_fe_storage_cmov(&r->y, &a->y, flag); +} + +#ifdef USE_ENDOMORPHISM +static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) { + static const secp256k1_fe beta = SECP256K1_FE_CONST( + 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul, + 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul + ); + *r = *a; + secp256k1_fe_mul(&r->x, &r->x, &beta); +} +#endif + +static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a) { + secp256k1_fe yz; + + if (a->infinity) { + return 0; + } + + /* We rely on the fact that the Jacobi symbol of 1 / a->z^3 is the same as + * that of a->z. Thus a->y / a->z^3 is a quadratic residue iff a->y * a->z + is */ + secp256k1_fe_mul(&yz, &a->y, &a->z); + return secp256k1_fe_is_quad_var(&yz); +} + +#endif /* SECP256K1_GROUP_IMPL_H */ diff --git a/libsecp256k1/src/hash.h b/libsecp256k1/src/hash.h new file mode 100644 index 0000000..de26e4b --- /dev/null +++ b/libsecp256k1/src/hash.h @@ -0,0 +1,41 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_HASH_H +#define SECP256K1_HASH_H + +#include +#include + +typedef struct { + uint32_t s[8]; + uint32_t buf[16]; /* In big endian */ + size_t bytes; +} secp256k1_sha256; + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash); +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32); + +typedef struct { + secp256k1_sha256 inner, outer; +} secp256k1_hmac_sha256; + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size); +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size); +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32); + +typedef struct { + unsigned char v[32]; + unsigned char k[32]; + int retry; +} secp256k1_rfc6979_hmac_sha256; + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen); +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen); +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng); + +#endif /* SECP256K1_HASH_H */ diff --git a/libsecp256k1/src/hash_impl.h b/libsecp256k1/src/hash_impl.h new file mode 100644 index 0000000..782f972 --- /dev/null +++ b/libsecp256k1/src/hash_impl.h @@ -0,0 +1,283 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_HASH_IMPL_H +#define SECP256K1_HASH_IMPL_H + +#include "hash.h" + +#include +#include +#include + +#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z)))) +#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y)))) +#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10)) +#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7)) +#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3)) +#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10)) + +#define Round(a,b,c,d,e,f,g,h,k,w) do { \ + uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \ + uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \ + (d) += t1; \ + (h) = t1 + t2; \ +} while(0) + +#ifdef WORDS_BIGENDIAN +#define BE32(x) (x) +#else +#define BE32(p) ((((p) & 0xFF) << 24) | (((p) & 0xFF00) << 8) | (((p) & 0xFF0000) >> 8) | (((p) & 0xFF000000) >> 24)) +#endif + +static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) { + hash->s[0] = 0x6a09e667ul; + hash->s[1] = 0xbb67ae85ul; + hash->s[2] = 0x3c6ef372ul; + hash->s[3] = 0xa54ff53aul; + hash->s[4] = 0x510e527ful; + hash->s[5] = 0x9b05688cul; + hash->s[6] = 0x1f83d9abul; + hash->s[7] = 0x5be0cd19ul; + hash->bytes = 0; +} + +/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */ +static void secp256k1_sha256_transform(uint32_t* s, const uint32_t* chunk) { + uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7]; + uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15; + + Round(a, b, c, d, e, f, g, h, 0x428a2f98, w0 = BE32(chunk[0])); + Round(h, a, b, c, d, e, f, g, 0x71374491, w1 = BE32(chunk[1])); + Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf, w2 = BE32(chunk[2])); + Round(f, g, h, a, b, c, d, e, 0xe9b5dba5, w3 = BE32(chunk[3])); + Round(e, f, g, h, a, b, c, d, 0x3956c25b, w4 = BE32(chunk[4])); + Round(d, e, f, g, h, a, b, c, 0x59f111f1, w5 = BE32(chunk[5])); + Round(c, d, e, f, g, h, a, b, 0x923f82a4, w6 = BE32(chunk[6])); + Round(b, c, d, e, f, g, h, a, 0xab1c5ed5, w7 = BE32(chunk[7])); + Round(a, b, c, d, e, f, g, h, 0xd807aa98, w8 = BE32(chunk[8])); + Round(h, a, b, c, d, e, f, g, 0x12835b01, w9 = BE32(chunk[9])); + Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = BE32(chunk[10])); + Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = BE32(chunk[11])); + Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = BE32(chunk[12])); + Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = BE32(chunk[13])); + Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = BE32(chunk[14])); + Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = BE32(chunk[15])); + + Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0)); + + Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1)); + Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2)); + Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3)); + Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4)); + Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5)); + Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6)); + Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7)); + Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8)); + Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9)); + Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10)); + Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11)); + Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12)); + Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13)); + Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14)); + Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15)); + Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0)); + + s[0] += a; + s[1] += b; + s[2] += c; + s[3] += d; + s[4] += e; + s[5] += f; + s[6] += g; + s[7] += h; +} + +static void secp256k1_sha256_write(secp256k1_sha256 *hash, const unsigned char *data, size_t len) { + size_t bufsize = hash->bytes & 0x3F; + hash->bytes += len; + VERIFY_CHECK(hash->bytes >= len); + while (len >= 64 - bufsize) { + /* Fill the buffer, and process it. */ + size_t chunk_len = 64 - bufsize; + memcpy(((unsigned char*)hash->buf) + bufsize, data, chunk_len); + data += chunk_len; + len -= chunk_len; + secp256k1_sha256_transform(hash->s, hash->buf); + bufsize = 0; + } + if (len) { + /* Fill the buffer with what remains. */ + memcpy(((unsigned char*)hash->buf) + bufsize, data, len); + } +} + +static void secp256k1_sha256_finalize(secp256k1_sha256 *hash, unsigned char *out32) { + static const unsigned char pad[64] = {0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; + uint32_t sizedesc[2]; + uint32_t out[8]; + int i = 0; + sizedesc[0] = BE32(hash->bytes >> 29); + sizedesc[1] = BE32(hash->bytes << 3); + secp256k1_sha256_write(hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64)); + secp256k1_sha256_write(hash, (const unsigned char*)sizedesc, 8); + for (i = 0; i < 8; i++) { + out[i] = BE32(hash->s[i]); + hash->s[i] = 0; + } + memcpy(out32, (const unsigned char*)out, 32); +} + +static void secp256k1_hmac_sha256_initialize(secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) { + size_t n; + unsigned char rkey[64]; + if (keylen <= sizeof(rkey)) { + memcpy(rkey, key, keylen); + memset(rkey + keylen, 0, sizeof(rkey) - keylen); + } else { + secp256k1_sha256 sha256; + secp256k1_sha256_initialize(&sha256); + secp256k1_sha256_write(&sha256, key, keylen); + secp256k1_sha256_finalize(&sha256, rkey); + memset(rkey + 32, 0, 32); + } + + secp256k1_sha256_initialize(&hash->outer); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c; + } + secp256k1_sha256_write(&hash->outer, rkey, sizeof(rkey)); + + secp256k1_sha256_initialize(&hash->inner); + for (n = 0; n < sizeof(rkey); n++) { + rkey[n] ^= 0x5c ^ 0x36; + } + secp256k1_sha256_write(&hash->inner, rkey, sizeof(rkey)); + memset(rkey, 0, sizeof(rkey)); +} + +static void secp256k1_hmac_sha256_write(secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) { + secp256k1_sha256_write(&hash->inner, data, size); +} + +static void secp256k1_hmac_sha256_finalize(secp256k1_hmac_sha256 *hash, unsigned char *out32) { + unsigned char temp[32]; + secp256k1_sha256_finalize(&hash->inner, temp); + secp256k1_sha256_write(&hash->outer, temp, 32); + memset(temp, 0, 32); + secp256k1_sha256_finalize(&hash->outer, out32); +} + + +static void secp256k1_rfc6979_hmac_sha256_initialize(secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) { + secp256k1_hmac_sha256 hmac; + static const unsigned char zero[1] = {0x00}; + static const unsigned char one[1] = {0x01}; + + memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */ + memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */ + + /* RFC6979 3.2.d. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + + /* RFC6979 3.2.f. */ + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, one, 1); + secp256k1_hmac_sha256_write(&hmac, key, keylen); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + rng->retry = 0; +} + +static void secp256k1_rfc6979_hmac_sha256_generate(secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) { + /* RFC6979 3.2.h. */ + static const unsigned char zero[1] = {0x00}; + if (rng->retry) { + secp256k1_hmac_sha256 hmac; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_write(&hmac, zero, 1); + secp256k1_hmac_sha256_finalize(&hmac, rng->k); + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + } + + while (outlen > 0) { + secp256k1_hmac_sha256 hmac; + int now = outlen; + secp256k1_hmac_sha256_initialize(&hmac, rng->k, 32); + secp256k1_hmac_sha256_write(&hmac, rng->v, 32); + secp256k1_hmac_sha256_finalize(&hmac, rng->v); + if (now > 32) { + now = 32; + } + memcpy(out, rng->v, now); + out += now; + outlen -= now; + } + + rng->retry = 1; +} + +static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng) { + memset(rng->k, 0, 32); + memset(rng->v, 0, 32); + rng->retry = 0; +} + +#undef BE32 +#undef Round +#undef sigma1 +#undef sigma0 +#undef Sigma1 +#undef Sigma0 +#undef Maj +#undef Ch + +#endif /* SECP256K1_HASH_IMPL_H */ diff --git a/libsecp256k1/src/modules/dummy.go b/libsecp256k1/src/modules/dummy.go new file mode 100644 index 0000000..3c7a696 --- /dev/null +++ b/libsecp256k1/src/modules/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package module diff --git a/libsecp256k1/src/modules/ecdh/Makefile.am.include b/libsecp256k1/src/modules/ecdh/Makefile.am.include new file mode 100644 index 0000000..e3088b4 --- /dev/null +++ b/libsecp256k1/src/modules/ecdh/Makefile.am.include @@ -0,0 +1,8 @@ +include_HEADERS += include/secp256k1_ecdh.h +noinst_HEADERS += src/modules/ecdh/main_impl.h +noinst_HEADERS += src/modules/ecdh/tests_impl.h +if USE_BENCHMARK +noinst_PROGRAMS += bench_ecdh +bench_ecdh_SOURCES = src/bench_ecdh.c +bench_ecdh_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB) +endif diff --git a/libsecp256k1/src/modules/ecdh/dummy.go b/libsecp256k1/src/modules/ecdh/dummy.go new file mode 100644 index 0000000..b6fc383 --- /dev/null +++ b/libsecp256k1/src/modules/ecdh/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package ecdh diff --git a/libsecp256k1/src/modules/ecdh/main_impl.h b/libsecp256k1/src/modules/ecdh/main_impl.h new file mode 100644 index 0000000..07a25b8 --- /dev/null +++ b/libsecp256k1/src/modules/ecdh/main_impl.h @@ -0,0 +1,71 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_MAIN_H +#define SECP256K1_MODULE_ECDH_MAIN_H + +#include "include/secp256k1_ecdh.h" +#include "ecmult_const_impl.h" + +static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) { + unsigned char version = (y32[31] & 0x01) | 0x02; + secp256k1_sha256 sha; + (void)data; + + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, &version, 1); + secp256k1_sha256_write(&sha, x32, 32); + secp256k1_sha256_finalize(&sha, output); + + return 1; +} + +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256 = ecdh_hash_function_sha256; +const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default = ecdh_hash_function_sha256; + +int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const secp256k1_pubkey *point, const unsigned char *scalar, secp256k1_ecdh_hash_function hashfp, void *data) { + int ret = 0; + int overflow = 0; + secp256k1_gej res; + secp256k1_ge pt; + secp256k1_scalar s; + unsigned char x[32]; + unsigned char y[32]; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(point != NULL); + ARG_CHECK(scalar != NULL); + + if (hashfp == NULL) { + hashfp = secp256k1_ecdh_hash_function_default; + } + + secp256k1_pubkey_load(ctx, &pt, point); + secp256k1_scalar_set_b32(&s, scalar, &overflow); + + overflow |= secp256k1_scalar_is_zero(&s); + secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow); + + secp256k1_ecmult_const(&res, &pt, &s, 256); + secp256k1_ge_set_gej(&pt, &res); + + /* Compute a hash of the point */ + secp256k1_fe_normalize(&pt.x); + secp256k1_fe_normalize(&pt.y); + secp256k1_fe_get_b32(x, &pt.x); + secp256k1_fe_get_b32(y, &pt.y); + + ret = hashfp(output, x, y, data); + + memset(x, 0, 32); + memset(y, 0, 32); + secp256k1_scalar_clear(&s); + + return !!ret & !overflow; +} + +#endif /* SECP256K1_MODULE_ECDH_MAIN_H */ diff --git a/libsecp256k1/src/modules/ecdh/tests_impl.h b/libsecp256k1/src/modules/ecdh/tests_impl.h new file mode 100644 index 0000000..fe26e8f --- /dev/null +++ b/libsecp256k1/src/modules/ecdh/tests_impl.h @@ -0,0 +1,132 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODULE_ECDH_TESTS_H +#define SECP256K1_MODULE_ECDH_TESTS_H + +int ecdh_hash_function_test_fail(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)output; + (void)x; + (void)y; + (void)data; + return 0; +} + +int ecdh_hash_function_custom(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) { + (void)data; + /* Save x and y as uncompressed public key */ + output[0] = 0x04; + memcpy(output + 1, x, 32); + memcpy(output + 33, y, 32); + return 1; +} + +void test_ecdh_api(void) { + /* Setup context that just counts errors */ + secp256k1_context *tctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); + secp256k1_pubkey point; + unsigned char res[32]; + unsigned char s_one[32] = { 0 }; + int32_t ecount = 0; + s_one[31] = 1; + + secp256k1_context_set_error_callback(tctx, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(tctx, counting_illegal_callback_fn, &ecount); + CHECK(secp256k1_ec_pubkey_create(tctx, &point, s_one) == 1); + + /* Check all NULLs are detected */ + CHECK(secp256k1_ecdh(tctx, res, &point, s_one, NULL, NULL) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdh(tctx, NULL, &point, s_one, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdh(tctx, res, NULL, s_one, NULL, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdh(tctx, res, &point, NULL, NULL, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdh(tctx, res, &point, s_one, NULL, NULL) == 1); + CHECK(ecount == 3); + + /* Cleanup */ + secp256k1_context_destroy(tctx); +} + +void test_ecdh_generator_basepoint(void) { + unsigned char s_one[32] = { 0 }; + secp256k1_pubkey point[2]; + int i; + + s_one[31] = 1; + /* Check against pubkey creation when the basepoint is the generator */ + for (i = 0; i < 100; ++i) { + secp256k1_sha256 sha; + unsigned char s_b32[32]; + unsigned char output_ecdh[65]; + unsigned char output_ser[32]; + unsigned char point_ser[65]; + size_t point_ser_len = sizeof(point_ser); + secp256k1_scalar s; + + random_scalar_order(&s); + secp256k1_scalar_get_b32(s_b32, &s); + + CHECK(secp256k1_ec_pubkey_create(ctx, &point[0], s_one) == 1); + CHECK(secp256k1_ec_pubkey_create(ctx, &point[1], s_b32) == 1); + + /* compute using ECDH function with custom hash function */ + CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32, ecdh_hash_function_custom, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_UNCOMPRESSED) == 1); + /* compare */ + CHECK(memcmp(output_ecdh, point_ser, 65) == 0); + + /* compute using ECDH function with default hash function */ + CHECK(secp256k1_ecdh(ctx, output_ecdh, &point[0], s_b32, NULL, NULL) == 1); + /* compute "explicitly" */ + CHECK(secp256k1_ec_pubkey_serialize(ctx, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1); + secp256k1_sha256_initialize(&sha); + secp256k1_sha256_write(&sha, point_ser, point_ser_len); + secp256k1_sha256_finalize(&sha, output_ser); + /* compare */ + CHECK(memcmp(output_ecdh, output_ser, 32) == 0); + } +} + +void test_bad_scalar(void) { + unsigned char s_zero[32] = { 0 }; + unsigned char s_overflow[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 + }; + unsigned char s_rand[32] = { 0 }; + unsigned char output[32]; + secp256k1_scalar rand; + secp256k1_pubkey point; + + /* Create random point */ + random_scalar_order(&rand); + secp256k1_scalar_get_b32(s_rand, &rand); + CHECK(secp256k1_ec_pubkey_create(ctx, &point, s_rand) == 1); + + /* Try to multiply it by bad values */ + CHECK(secp256k1_ecdh(ctx, output, &point, s_zero, NULL, NULL) == 0); + CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow, NULL, NULL) == 0); + /* ...and a good one */ + s_overflow[31] -= 1; + CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow, NULL, NULL) == 1); + + /* Hash function failure results in ecdh failure */ + CHECK(secp256k1_ecdh(ctx, output, &point, s_overflow, ecdh_hash_function_test_fail, NULL) == 0); +} + +void run_ecdh_tests(void) { + test_ecdh_api(); + test_ecdh_generator_basepoint(); + test_bad_scalar(); +} + +#endif /* SECP256K1_MODULE_ECDH_TESTS_H */ diff --git a/libsecp256k1/src/modules/recovery/Makefile.am.include b/libsecp256k1/src/modules/recovery/Makefile.am.include new file mode 100644 index 0000000..bf23c26 --- /dev/null +++ b/libsecp256k1/src/modules/recovery/Makefile.am.include @@ -0,0 +1,8 @@ +include_HEADERS += include/secp256k1_recovery.h +noinst_HEADERS += src/modules/recovery/main_impl.h +noinst_HEADERS += src/modules/recovery/tests_impl.h +if USE_BENCHMARK +noinst_PROGRAMS += bench_recover +bench_recover_SOURCES = src/bench_recover.c +bench_recover_LDADD = libsecp256k1.la $(SECP_LIBS) $(COMMON_LIB) +endif diff --git a/libsecp256k1/src/modules/recovery/dummy.go b/libsecp256k1/src/modules/recovery/dummy.go new file mode 100644 index 0000000..b9491f0 --- /dev/null +++ b/libsecp256k1/src/modules/recovery/dummy.go @@ -0,0 +1,7 @@ +// +build dummy + +// Package c contains only a C file. +// +// This Go file is part of a workaround for `go mod vendor`. +// Please see the file crypto/secp256k1/dummy.go for more information. +package recovery diff --git a/libsecp256k1/src/modules/recovery/main_impl.h b/libsecp256k1/src/modules/recovery/main_impl.h new file mode 100644 index 0000000..ed356e5 --- /dev/null +++ b/libsecp256k1/src/modules/recovery/main_impl.h @@ -0,0 +1,193 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_MAIN_H +#define SECP256K1_MODULE_RECOVERY_MAIN_H + +#include "include/secp256k1_recovery.h" + +static void secp256k1_ecdsa_recoverable_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, int* recid, const secp256k1_ecdsa_recoverable_signature* sig) { + (void)ctx; + if (sizeof(secp256k1_scalar) == 32) { + /* When the secp256k1_scalar type is exactly 32 byte, use its + * representation inside secp256k1_ecdsa_signature, as conversion is very fast. + * Note that secp256k1_ecdsa_signature_save must use the same representation. */ + memcpy(r, &sig->data[0], 32); + memcpy(s, &sig->data[32], 32); + } else { + secp256k1_scalar_set_b32(r, &sig->data[0], NULL); + secp256k1_scalar_set_b32(s, &sig->data[32], NULL); + } + *recid = sig->data[64]; +} + +static void secp256k1_ecdsa_recoverable_signature_save(secp256k1_ecdsa_recoverable_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s, int recid) { + if (sizeof(secp256k1_scalar) == 32) { + memcpy(&sig->data[0], r, 32); + memcpy(&sig->data[32], s, 32); + } else { + secp256k1_scalar_get_b32(&sig->data[0], r); + secp256k1_scalar_get_b32(&sig->data[32], s); + } + sig->data[64] = recid; +} + +int secp256k1_ecdsa_recoverable_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature* sig, const unsigned char *input64, int recid) { + secp256k1_scalar r, s; + int ret = 1; + int overflow = 0; + + (void)ctx; + ARG_CHECK(sig != NULL); + ARG_CHECK(input64 != NULL); + ARG_CHECK(recid >= 0 && recid <= 3); + + secp256k1_scalar_set_b32(&r, &input64[0], &overflow); + ret &= !overflow; + secp256k1_scalar_set_b32(&s, &input64[32], &overflow); + ret &= !overflow; + if (ret) { + secp256k1_ecdsa_recoverable_signature_save(sig, &r, &s, recid); + } else { + memset(sig, 0, sizeof(*sig)); + } + return ret; +} + +int secp256k1_ecdsa_recoverable_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, int *recid, const secp256k1_ecdsa_recoverable_signature* sig) { + secp256k1_scalar r, s; + + (void)ctx; + ARG_CHECK(output64 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(recid != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, recid, sig); + secp256k1_scalar_get_b32(&output64[0], &r); + secp256k1_scalar_get_b32(&output64[32], &s); + return 1; +} + +int secp256k1_ecdsa_recoverable_signature_convert(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const secp256k1_ecdsa_recoverable_signature* sigin) { + secp256k1_scalar r, s; + int recid; + + (void)ctx; + ARG_CHECK(sig != NULL); + ARG_CHECK(sigin != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, sigin); + secp256k1_ecdsa_signature_save(sig, &r, &s); + return 1; +} + +static int secp256k1_ecdsa_sig_recover(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar* sigs, secp256k1_ge *pubkey, const secp256k1_scalar *message, int recid) { + unsigned char brx[32]; + secp256k1_fe fx; + secp256k1_ge x; + secp256k1_gej xj; + secp256k1_scalar rn, u1, u2; + secp256k1_gej qj; + int r; + + if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) { + return 0; + } + + secp256k1_scalar_get_b32(brx, sigr); + r = secp256k1_fe_set_b32(&fx, brx); + (void)r; + VERIFY_CHECK(r); /* brx comes from a scalar, so is less than the order; certainly less than p */ + if (recid & 2) { + if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0) { + return 0; + } + secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe); + } + if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1)) { + return 0; + } + secp256k1_gej_set_ge(&xj, &x); + secp256k1_scalar_inverse_var(&rn, sigr); + secp256k1_scalar_mul(&u1, &rn, message); + secp256k1_scalar_negate(&u1, &u1); + secp256k1_scalar_mul(&u2, &rn, sigs); + secp256k1_ecmult(ctx, &qj, &xj, &u2, &u1); + secp256k1_ge_set_gej_var(pubkey, &qj); + return !secp256k1_gej_is_infinity(&qj); +} + +int secp256k1_ecdsa_sign_recoverable(const secp256k1_context* ctx, secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar r, s; + secp256k1_scalar sec, non, msg; + int recid; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(seckey != NULL); + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_default; + } + + secp256k1_scalar_set_b32(&sec, seckey, &overflow); + /* Fail if the secret key is invalid. */ + if (!overflow && !secp256k1_scalar_is_zero(&sec)) { + unsigned char nonce32[32]; + unsigned int count = 0; + secp256k1_scalar_set_b32(&msg, msg32, NULL); + while (1) { + ret = noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count); + if (!ret) { + break; + } + secp256k1_scalar_set_b32(&non, nonce32, &overflow); + if (!overflow && !secp256k1_scalar_is_zero(&non)) { + if (secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, &recid)) { + break; + } + } + count++; + } + memset(nonce32, 0, 32); + secp256k1_scalar_clear(&msg); + secp256k1_scalar_clear(&non); + secp256k1_scalar_clear(&sec); + } + if (ret) { + secp256k1_ecdsa_recoverable_signature_save(signature, &r, &s, recid); + } else { + memset(signature, 0, sizeof(*signature)); + } + return ret; +} + +int secp256k1_ecdsa_recover(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const secp256k1_ecdsa_recoverable_signature *signature, const unsigned char *msg32) { + secp256k1_ge q; + secp256k1_scalar r, s; + secp256k1_scalar m; + int recid; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(pubkey != NULL); + + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, signature); + VERIFY_CHECK(recid >= 0 && recid < 4); /* should have been caught in parse_compact */ + secp256k1_scalar_set_b32(&m, msg32, NULL); + if (secp256k1_ecdsa_sig_recover(&ctx->ecmult_ctx, &r, &s, &q, &m, recid)) { + secp256k1_pubkey_save(pubkey, &q); + return 1; + } else { + memset(pubkey, 0, sizeof(*pubkey)); + return 0; + } +} + +#endif /* SECP256K1_MODULE_RECOVERY_MAIN_H */ diff --git a/libsecp256k1/src/modules/recovery/tests_impl.h b/libsecp256k1/src/modules/recovery/tests_impl.h new file mode 100644 index 0000000..38a533a --- /dev/null +++ b/libsecp256k1/src/modules/recovery/tests_impl.h @@ -0,0 +1,393 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_MODULE_RECOVERY_TESTS_H +#define SECP256K1_MODULE_RECOVERY_TESTS_H + +static int recovery_test_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + (void) msg32; + (void) key32; + (void) algo16; + (void) data; + + /* On the first run, return 0 to force a second run */ + if (counter == 0) { + memset(nonce32, 0, 32); + return 1; + } + /* On the second run, return an overflow to force a third run */ + if (counter == 1) { + memset(nonce32, 0xff, 32); + return 1; + } + /* On the next run, return a valid nonce, but flip a coin as to whether or not to fail signing. */ + memset(nonce32, 1, 32); + return secp256k1_rand_bits(1); +} + +void test_ecdsa_recovery_api(void) { + /* Setup contexts that just count errors */ + secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + secp256k1_context *sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); + secp256k1_context *vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY); + secp256k1_context *both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + secp256k1_pubkey pubkey; + secp256k1_pubkey recpubkey; + secp256k1_ecdsa_signature normal_sig; + secp256k1_ecdsa_recoverable_signature recsig; + unsigned char privkey[32] = { 1 }; + unsigned char message[32] = { 2 }; + int32_t ecount = 0; + int recid = 0; + unsigned char sig[74]; + unsigned char zero_privkey[32] = { 0 }; + unsigned char over_privkey[32] = { 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff }; + + secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(vrfy, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(both, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(both, counting_illegal_callback_fn, &ecount); + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1); + + /* Check bad contexts and NULLs for signing */ + ecount = 0; + CHECK(secp256k1_ecdsa_sign_recoverable(none, &recsig, message, privkey, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(sign, &recsig, message, privkey, NULL, NULL) == 1); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(vrfy, &recsig, message, privkey, NULL, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_sign_recoverable(both, NULL, message, privkey, NULL, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, NULL, privkey, NULL, NULL) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, NULL, NULL, NULL) == 0); + CHECK(ecount == 5); + /* This will fail or succeed randomly, and in either case will not ARG_CHECK failure */ + secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, recovery_test_nonce_function, NULL); + CHECK(ecount == 5); + /* These will all fail, but not in ARG_CHECK way */ + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, zero_privkey, NULL, NULL) == 0); + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, over_privkey, NULL, NULL) == 0); + /* This one will succeed. */ + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1); + CHECK(ecount == 5); + + /* Check signing with a goofy nonce function */ + + /* Check bad contexts and NULLs for recovery */ + ecount = 0; + CHECK(secp256k1_ecdsa_recover(none, &recpubkey, &recsig, message) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recover(sign, &recpubkey, &recsig, message) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recover(vrfy, &recpubkey, &recsig, message) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, message) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recover(both, NULL, &recsig, message) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_recover(both, &recpubkey, NULL, message) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_recover(both, &recpubkey, &recsig, NULL) == 0); + CHECK(ecount == 5); + + /* Check NULLs for conversion */ + CHECK(secp256k1_ecdsa_sign(both, &normal_sig, message, privkey, NULL, NULL) == 1); + ecount = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, NULL, &recsig) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, NULL) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(both, &normal_sig, &recsig) == 1); + + /* Check NULLs for de/serialization */ + CHECK(secp256k1_ecdsa_sign_recoverable(both, &recsig, message, privkey, NULL, NULL) == 1); + ecount = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, NULL, &recid, &recsig) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, NULL, &recsig) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(both, sig, &recid, &recsig) == 1); + + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, NULL, sig, recid) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, NULL, recid) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, -1) == 0); + CHECK(ecount == 6); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, 5) == 0); + CHECK(ecount == 7); + /* overflow in signature will fail but not affect ecount */ + memcpy(sig, over_privkey, 32); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(both, &recsig, sig, recid) == 0); + CHECK(ecount == 7); + + /* cleanup */ + secp256k1_context_destroy(none); + secp256k1_context_destroy(sign); + secp256k1_context_destroy(vrfy); + secp256k1_context_destroy(both); +} + +void test_ecdsa_recovery_end_to_end(void) { + unsigned char extra[32] = {0x00}; + unsigned char privkey[32]; + unsigned char message[32]; + secp256k1_ecdsa_signature signature[5]; + secp256k1_ecdsa_recoverable_signature rsignature[5]; + unsigned char sig[74]; + secp256k1_pubkey pubkey; + secp256k1_pubkey recpubkey; + int recid = 0; + + /* Generate a random key and message. */ + { + secp256k1_scalar msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(privkey, &key); + secp256k1_scalar_get_b32(message, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1); + + /* Serialize/parse compact and verify/recover. */ + extra[0] = 0; + CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[4], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[1], message, privkey, NULL, extra) == 1); + extra[31] = 1; + CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[2], message, privkey, NULL, extra) == 1); + extra[31] = 0; + extra[0] = 1; + CHECK(secp256k1_ecdsa_sign_recoverable(ctx, &rsignature[3], message, privkey, NULL, extra) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1); + CHECK(memcmp(&signature[4], &signature[0], 64) == 0); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1); + memset(&rsignature[4], 0, sizeof(rsignature[4])); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 1); + /* Parse compact (with recovery id) and recover. */ + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 1); + CHECK(memcmp(&pubkey, &recpubkey, sizeof(pubkey)) == 0); + /* Serialize/destroy/parse signature and verify again. */ + CHECK(secp256k1_ecdsa_recoverable_signature_serialize_compact(ctx, sig, &recid, &rsignature[4]) == 1); + sig[secp256k1_rand_bits(6)] += 1 + secp256k1_rand_int(255); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsignature[4], sig, recid) == 1); + CHECK(secp256k1_ecdsa_recoverable_signature_convert(ctx, &signature[4], &rsignature[4]) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[4], message, &pubkey) == 0); + /* Recover again */ + CHECK(secp256k1_ecdsa_recover(ctx, &recpubkey, &rsignature[4], message) == 0 || + memcmp(&pubkey, &recpubkey, sizeof(pubkey)) != 0); +} + +/* Tests several edge cases. */ +void test_ecdsa_recovery_edge_cases(void) { + const unsigned char msg32[32] = { + 'T', 'h', 'i', 's', ' ', 'i', 's', ' ', + 'a', ' ', 'v', 'e', 'r', 'y', ' ', 's', + 'e', 'c', 'r', 'e', 't', ' ', 'm', 'e', + 's', 's', 'a', 'g', 'e', '.', '.', '.' + }; + const unsigned char sig64[64] = { + /* Generated by signing the above message with nonce 'This is the nonce we will use...' + * and secret key 0 (which is not valid), resulting in recid 1. */ + 0x67, 0xCB, 0x28, 0x5F, 0x9C, 0xD1, 0x94, 0xE8, + 0x40, 0xD6, 0x29, 0x39, 0x7A, 0xF5, 0x56, 0x96, + 0x62, 0xFD, 0xE4, 0x46, 0x49, 0x99, 0x59, 0x63, + 0x17, 0x9A, 0x7D, 0xD1, 0x7B, 0xD2, 0x35, 0x32, + 0x4B, 0x1B, 0x7D, 0xF3, 0x4C, 0xE1, 0xF6, 0x8E, + 0x69, 0x4F, 0xF6, 0xF1, 0x1A, 0xC7, 0x51, 0xDD, + 0x7D, 0xD7, 0x3E, 0x38, 0x7E, 0xE4, 0xFC, 0x86, + 0x6E, 0x1B, 0xE8, 0xEC, 0xC7, 0xDD, 0x95, 0x57 + }; + secp256k1_pubkey pubkey; + /* signature (r,s) = (4,4), which can be recovered with all 4 recids. */ + const unsigned char sigb64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + secp256k1_pubkey pubkeyb; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + int recid; + + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 0)); + CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 1)); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 2)); + CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32)); + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sig64, 3)); + CHECK(!secp256k1_ecdsa_recover(ctx, &pubkey, &rsig, msg32)); + + for (recid = 0; recid < 4; recid++) { + int i; + int recid2; + /* (4,4) encoded in DER. */ + unsigned char sigbder[8] = {0x30, 0x06, 0x02, 0x01, 0x04, 0x02, 0x01, 0x04}; + unsigned char sigcder_zr[7] = {0x30, 0x05, 0x02, 0x00, 0x02, 0x01, 0x01}; + unsigned char sigcder_zs[7] = {0x30, 0x05, 0x02, 0x01, 0x01, 0x02, 0x00}; + unsigned char sigbderalt1[39] = { + 0x30, 0x25, 0x02, 0x20, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt2[39] = { + 0x30, 0x25, 0x02, 0x01, 0x04, 0x02, 0x20, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + unsigned char sigbderalt3[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x04, 0x02, 0x01, 0x04, + }; + unsigned char sigbderalt4[40] = { + 0x30, 0x26, 0x02, 0x01, 0x04, 0x02, 0x21, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x04, + }; + /* (order + r,4) encoded in DER. */ + unsigned char sigbderlong[40] = { + 0x30, 0x26, 0x02, 0x21, 0x00, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xBA, 0xAE, 0xDC, + 0xE6, 0xAF, 0x48, 0xA0, 0x3B, 0xBF, 0xD2, 0x5E, + 0x8C, 0xD0, 0x36, 0x41, 0x45, 0x02, 0x01, 0x04 + }; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 1); + for (recid2 = 0; recid2 < 4; recid2++) { + secp256k1_pubkey pubkey2b; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigb64, recid2) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkey2b, &rsig, msg32) == 1); + /* Verifying with (order + r,4) should always fail. */ + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderlong, sizeof(sigbderlong)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0); + } + /* DER parsing tests. */ + /* Zero length r/s. */ + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zr, sizeof(sigcder_zr)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder_zs, sizeof(sigcder_zs)) == 0); + /* Leading zeros. */ + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt1, sizeof(sigbderalt1)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt2, sizeof(sigbderalt2)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 0); + sigbderalt3[4] = 1; + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt3, sizeof(sigbderalt3)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0); + sigbderalt4[7] = 1; + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbderalt4, sizeof(sigbderalt4)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0); + /* Damage signature. */ + sigbder[7]++; + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0); + sigbder[7]--; + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, 6) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder) - 1) == 0); + for(i = 0; i < 8; i++) { + int c; + unsigned char orig = sigbder[i]; + /*Try every single-byte change.*/ + for (c = 0; c < 256; c++) { + if (c == orig ) { + continue; + } + sigbder[i] = c; + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigbder, sizeof(sigbder)) == 0 || secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyb) == 0); + } + sigbder[i] = orig; + } + } + + /* Test r/s equal to zero */ + { + /* (1,1) encoded in DER. */ + unsigned char sigcder[8] = {0x30, 0x06, 0x02, 0x01, 0x01, 0x02, 0x01, 0x01}; + unsigned char sigc64[64] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + secp256k1_pubkey pubkeyc; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyc, &rsig, msg32) == 1); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 1); + sigcder[4] = 0; + sigc64[31] = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0); + sigcder[4] = 1; + sigcder[7] = 0; + sigc64[31] = 1; + sigc64[63] = 0; + CHECK(secp256k1_ecdsa_recoverable_signature_parse_compact(ctx, &rsig, sigc64, 0) == 1); + CHECK(secp256k1_ecdsa_recover(ctx, &pubkeyb, &rsig, msg32) == 0); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, sigcder, sizeof(sigcder)) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg32, &pubkeyc) == 0); + } +} + +void run_recovery_tests(void) { + int i; + for (i = 0; i < count; i++) { + test_ecdsa_recovery_api(); + } + for (i = 0; i < 64*count; i++) { + test_ecdsa_recovery_end_to_end(); + } + test_ecdsa_recovery_edge_cases(); +} + +#endif /* SECP256K1_MODULE_RECOVERY_TESTS_H */ diff --git a/libsecp256k1/src/num.h b/libsecp256k1/src/num.h new file mode 100644 index 0000000..49f2dd7 --- /dev/null +++ b/libsecp256k1/src/num.h @@ -0,0 +1,74 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_NUM_H +#define SECP256K1_NUM_H + +#ifndef USE_NUM_NONE + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(USE_NUM_GMP) +#include "num_gmp.h" +#else +#error "Please select num implementation" +#endif + +/** Copy a number. */ +static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a); + +/** Convert a number's absolute value to a binary big-endian string. + * There must be enough place. */ +static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a); + +/** Set a number to the value of a binary big-endian string. */ +static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen); + +/** Compute a modular inverse. The input must be less than the modulus. */ +static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m); + +/** Compute the jacobi symbol (a|b). b must be positive and odd. */ +static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b); + +/** Compare the absolute value of two numbers. */ +static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b); + +/** Test whether two number are equal (including sign). */ +static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b); + +/** Add two (signed) numbers. */ +static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Subtract two (signed) numbers. */ +static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Multiply two (signed) numbers. */ +static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b); + +/** Replace a number by its remainder modulo m. M's sign is ignored. The result is a number between 0 and m-1, + even if r was negative. */ +static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m); + +/** Right-shift the passed number by bits bits. */ +static void secp256k1_num_shift(secp256k1_num *r, int bits); + +/** Check whether a number is zero. */ +static int secp256k1_num_is_zero(const secp256k1_num *a); + +/** Check whether a number is one. */ +static int secp256k1_num_is_one(const secp256k1_num *a); + +/** Check whether a number is strictly negative. */ +static int secp256k1_num_is_neg(const secp256k1_num *a); + +/** Change a number's sign. */ +static void secp256k1_num_negate(secp256k1_num *r); + +#endif + +#endif /* SECP256K1_NUM_H */ diff --git a/libsecp256k1/src/num_gmp.h b/libsecp256k1/src/num_gmp.h new file mode 100644 index 0000000..3619844 --- /dev/null +++ b/libsecp256k1/src/num_gmp.h @@ -0,0 +1,20 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_NUM_REPR_H +#define SECP256K1_NUM_REPR_H + +#include + +#define NUM_LIMBS ((256+GMP_NUMB_BITS-1)/GMP_NUMB_BITS) + +typedef struct { + mp_limb_t data[2*NUM_LIMBS]; + int neg; + int limbs; +} secp256k1_num; + +#endif /* SECP256K1_NUM_REPR_H */ diff --git a/libsecp256k1/src/num_gmp_impl.h b/libsecp256k1/src/num_gmp_impl.h new file mode 100644 index 0000000..0ae2a8b --- /dev/null +++ b/libsecp256k1/src/num_gmp_impl.h @@ -0,0 +1,288 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_NUM_REPR_IMPL_H +#define SECP256K1_NUM_REPR_IMPL_H + +#include +#include +#include + +#include "util.h" +#include "num.h" + +#ifdef VERIFY +static void secp256k1_num_sanity(const secp256k1_num *a) { + VERIFY_CHECK(a->limbs == 1 || (a->limbs > 1 && a->data[a->limbs-1] != 0)); +} +#else +#define secp256k1_num_sanity(a) do { } while(0) +#endif + +static void secp256k1_num_copy(secp256k1_num *r, const secp256k1_num *a) { + *r = *a; +} + +static void secp256k1_num_get_bin(unsigned char *r, unsigned int rlen, const secp256k1_num *a) { + unsigned char tmp[65]; + int len = 0; + int shift = 0; + if (a->limbs>1 || a->data[0] != 0) { + len = mpn_get_str(tmp, 256, (mp_limb_t*)a->data, a->limbs); + } + while (shift < len && tmp[shift] == 0) shift++; + VERIFY_CHECK(len-shift <= (int)rlen); + memset(r, 0, rlen - len + shift); + if (len > shift) { + memcpy(r + rlen - len + shift, tmp + shift, len - shift); + } + memset(tmp, 0, sizeof(tmp)); +} + +static void secp256k1_num_set_bin(secp256k1_num *r, const unsigned char *a, unsigned int alen) { + int len; + VERIFY_CHECK(alen > 0); + VERIFY_CHECK(alen <= 64); + len = mpn_set_str(r->data, a, alen, 256); + if (len == 0) { + r->data[0] = 0; + len = 1; + } + VERIFY_CHECK(len <= NUM_LIMBS*2); + r->limbs = len; + r->neg = 0; + while (r->limbs > 1 && r->data[r->limbs-1]==0) { + r->limbs--; + } +} + +static void secp256k1_num_add_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { + mp_limb_t c = mpn_add(r->data, a->data, a->limbs, b->data, b->limbs); + r->limbs = a->limbs; + if (c != 0) { + VERIFY_CHECK(r->limbs < 2*NUM_LIMBS); + r->data[r->limbs++] = c; + } +} + +static void secp256k1_num_sub_abs(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { + mp_limb_t c = mpn_sub(r->data, a->data, a->limbs, b->data, b->limbs); + (void)c; + VERIFY_CHECK(c == 0); + r->limbs = a->limbs; + while (r->limbs > 1 && r->data[r->limbs-1]==0) { + r->limbs--; + } +} + +static void secp256k1_num_mod(secp256k1_num *r, const secp256k1_num *m) { + secp256k1_num_sanity(r); + secp256k1_num_sanity(m); + + if (r->limbs >= m->limbs) { + mp_limb_t t[2*NUM_LIMBS]; + mpn_tdiv_qr(t, r->data, 0, r->data, r->limbs, m->data, m->limbs); + memset(t, 0, sizeof(t)); + r->limbs = m->limbs; + while (r->limbs > 1 && r->data[r->limbs-1]==0) { + r->limbs--; + } + } + + if (r->neg && (r->limbs > 1 || r->data[0] != 0)) { + secp256k1_num_sub_abs(r, m, r); + r->neg = 0; + } +} + +static void secp256k1_num_mod_inverse(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *m) { + int i; + mp_limb_t g[NUM_LIMBS+1]; + mp_limb_t u[NUM_LIMBS+1]; + mp_limb_t v[NUM_LIMBS+1]; + mp_size_t sn; + mp_size_t gn; + secp256k1_num_sanity(a); + secp256k1_num_sanity(m); + + /** mpn_gcdext computes: (G,S) = gcdext(U,V), where + * * G = gcd(U,V) + * * G = U*S + V*T + * * U has equal or more limbs than V, and V has no padding + * If we set U to be (a padded version of) a, and V = m: + * G = a*S + m*T + * G = a*S mod m + * Assuming G=1: + * S = 1/a mod m + */ + VERIFY_CHECK(m->limbs <= NUM_LIMBS); + VERIFY_CHECK(m->data[m->limbs-1] != 0); + for (i = 0; i < m->limbs; i++) { + u[i] = (i < a->limbs) ? a->data[i] : 0; + v[i] = m->data[i]; + } + sn = NUM_LIMBS+1; + gn = mpn_gcdext(g, r->data, &sn, u, m->limbs, v, m->limbs); + (void)gn; + VERIFY_CHECK(gn == 1); + VERIFY_CHECK(g[0] == 1); + r->neg = a->neg ^ m->neg; + if (sn < 0) { + mpn_sub(r->data, m->data, m->limbs, r->data, -sn); + r->limbs = m->limbs; + while (r->limbs > 1 && r->data[r->limbs-1]==0) { + r->limbs--; + } + } else { + r->limbs = sn; + } + memset(g, 0, sizeof(g)); + memset(u, 0, sizeof(u)); + memset(v, 0, sizeof(v)); +} + +static int secp256k1_num_jacobi(const secp256k1_num *a, const secp256k1_num *b) { + int ret; + mpz_t ga, gb; + secp256k1_num_sanity(a); + secp256k1_num_sanity(b); + VERIFY_CHECK(!b->neg && (b->limbs > 0) && (b->data[0] & 1)); + + mpz_inits(ga, gb, NULL); + + mpz_import(gb, b->limbs, -1, sizeof(mp_limb_t), 0, 0, b->data); + mpz_import(ga, a->limbs, -1, sizeof(mp_limb_t), 0, 0, a->data); + if (a->neg) { + mpz_neg(ga, ga); + } + + ret = mpz_jacobi(ga, gb); + + mpz_clears(ga, gb, NULL); + + return ret; +} + +static int secp256k1_num_is_one(const secp256k1_num *a) { + return (a->limbs == 1 && a->data[0] == 1); +} + +static int secp256k1_num_is_zero(const secp256k1_num *a) { + return (a->limbs == 1 && a->data[0] == 0); +} + +static int secp256k1_num_is_neg(const secp256k1_num *a) { + return (a->limbs > 1 || a->data[0] != 0) && a->neg; +} + +static int secp256k1_num_cmp(const secp256k1_num *a, const secp256k1_num *b) { + if (a->limbs > b->limbs) { + return 1; + } + if (a->limbs < b->limbs) { + return -1; + } + return mpn_cmp(a->data, b->data, a->limbs); +} + +static int secp256k1_num_eq(const secp256k1_num *a, const secp256k1_num *b) { + if (a->limbs > b->limbs) { + return 0; + } + if (a->limbs < b->limbs) { + return 0; + } + if ((a->neg && !secp256k1_num_is_zero(a)) != (b->neg && !secp256k1_num_is_zero(b))) { + return 0; + } + return mpn_cmp(a->data, b->data, a->limbs) == 0; +} + +static void secp256k1_num_subadd(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b, int bneg) { + if (!(b->neg ^ bneg ^ a->neg)) { /* a and b have the same sign */ + r->neg = a->neg; + if (a->limbs >= b->limbs) { + secp256k1_num_add_abs(r, a, b); + } else { + secp256k1_num_add_abs(r, b, a); + } + } else { + if (secp256k1_num_cmp(a, b) > 0) { + r->neg = a->neg; + secp256k1_num_sub_abs(r, a, b); + } else { + r->neg = b->neg ^ bneg; + secp256k1_num_sub_abs(r, b, a); + } + } +} + +static void secp256k1_num_add(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { + secp256k1_num_sanity(a); + secp256k1_num_sanity(b); + secp256k1_num_subadd(r, a, b, 0); +} + +static void secp256k1_num_sub(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { + secp256k1_num_sanity(a); + secp256k1_num_sanity(b); + secp256k1_num_subadd(r, a, b, 1); +} + +static void secp256k1_num_mul(secp256k1_num *r, const secp256k1_num *a, const secp256k1_num *b) { + mp_limb_t tmp[2*NUM_LIMBS+1]; + secp256k1_num_sanity(a); + secp256k1_num_sanity(b); + + VERIFY_CHECK(a->limbs + b->limbs <= 2*NUM_LIMBS+1); + if ((a->limbs==1 && a->data[0]==0) || (b->limbs==1 && b->data[0]==0)) { + r->limbs = 1; + r->neg = 0; + r->data[0] = 0; + return; + } + if (a->limbs >= b->limbs) { + mpn_mul(tmp, a->data, a->limbs, b->data, b->limbs); + } else { + mpn_mul(tmp, b->data, b->limbs, a->data, a->limbs); + } + r->limbs = a->limbs + b->limbs; + if (r->limbs > 1 && tmp[r->limbs - 1]==0) { + r->limbs--; + } + VERIFY_CHECK(r->limbs <= 2*NUM_LIMBS); + mpn_copyi(r->data, tmp, r->limbs); + r->neg = a->neg ^ b->neg; + memset(tmp, 0, sizeof(tmp)); +} + +static void secp256k1_num_shift(secp256k1_num *r, int bits) { + if (bits % GMP_NUMB_BITS) { + /* Shift within limbs. */ + mpn_rshift(r->data, r->data, r->limbs, bits % GMP_NUMB_BITS); + } + if (bits >= GMP_NUMB_BITS) { + int i; + /* Shift full limbs. */ + for (i = 0; i < r->limbs; i++) { + int index = i + (bits / GMP_NUMB_BITS); + if (index < r->limbs && index < 2*NUM_LIMBS) { + r->data[i] = r->data[index]; + } else { + r->data[i] = 0; + } + } + } + while (r->limbs>1 && r->data[r->limbs-1]==0) { + r->limbs--; + } +} + +static void secp256k1_num_negate(secp256k1_num *r) { + r->neg ^= 1; +} + +#endif /* SECP256K1_NUM_REPR_IMPL_H */ diff --git a/libsecp256k1/src/num_impl.h b/libsecp256k1/src/num_impl.h new file mode 100644 index 0000000..c45193b --- /dev/null +++ b/libsecp256k1/src/num_impl.h @@ -0,0 +1,24 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_NUM_IMPL_H +#define SECP256K1_NUM_IMPL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include "num.h" + +#if defined(USE_NUM_GMP) +#include "num_gmp_impl.h" +#elif defined(USE_NUM_NONE) +/* Nothing. */ +#else +#error "Please select num implementation" +#endif + +#endif /* SECP256K1_NUM_IMPL_H */ diff --git a/libsecp256k1/src/scalar.h b/libsecp256k1/src/scalar.h new file mode 100644 index 0000000..6dc7574 --- /dev/null +++ b/libsecp256k1/src/scalar.h @@ -0,0 +1,117 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_H +#define SECP256K1_SCALAR_H + +#include "num.h" + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low.h" +#elif defined(USE_SCALAR_4X64) +#include "scalar_4x64.h" +#elif defined(USE_SCALAR_8X32) +#include "scalar_8x32.h" +#else +#error "Please select scalar implementation" +#endif + +/** Clear a scalar to prevent the leak of sensitive data. */ +static void secp256k1_scalar_clear(secp256k1_scalar *r); + +/** Access bits from a scalar. All requested bits must belong to the same 32-bit limb. */ +static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Access bits from a scalar. Not constant time. */ +static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count); + +/** Set a scalar from a big endian byte array. The scalar will be reduced modulo group order `n`. + * In: bin: pointer to a 32-byte array. + * Out: r: scalar to be set. + * overflow: non-zero if the scalar was bigger or equal to `n` before reduction, zero otherwise (can be NULL). + */ +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *bin, int *overflow); + +/** Set a scalar from a big endian byte array and returns 1 if it is a valid + * seckey and 0 otherwise. */ +static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin); + +/** Set a scalar to an unsigned integer. */ +static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v); + +/** Convert a scalar to a byte array. */ +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a); + +/** Add two scalars together (modulo the group order). Returns whether it overflowed. */ +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Conditionally add a power of two to a scalar. The result is not allowed to overflow. */ +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag); + +/** Multiply two scalars (modulo the group order). */ +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b); + +/** Shift a scalar right by some amount strictly between 0 and 16, returning + * the low bits that were shifted off */ +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n); + +/** Compute the square of a scalar (modulo the group order). */ +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the inverse of a scalar (modulo the group order). */ +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the inverse of a scalar (modulo the group order), without constant-time guarantee. */ +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Compute the complement of a scalar (modulo the group order). */ +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a); + +/** Check whether a scalar equals zero. */ +static int secp256k1_scalar_is_zero(const secp256k1_scalar *a); + +/** Check whether a scalar equals one. */ +static int secp256k1_scalar_is_one(const secp256k1_scalar *a); + +/** Check whether a scalar, considered as an nonnegative integer, is even. */ +static int secp256k1_scalar_is_even(const secp256k1_scalar *a); + +/** Check whether a scalar is higher than the group order divided by 2. */ +static int secp256k1_scalar_is_high(const secp256k1_scalar *a); + +/** Conditionally negate a number, in constant time. + * Returns -1 if the number was negated, 1 otherwise */ +static int secp256k1_scalar_cond_negate(secp256k1_scalar *a, int flag); + +#ifndef USE_NUM_NONE +/** Convert a scalar to a number. */ +static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a); + +/** Get the order of the group as a number. */ +static void secp256k1_scalar_order_get_num(secp256k1_num *r); +#endif + +/** Compare two scalars. */ +static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b); + +#ifdef USE_ENDOMORPHISM +/** Find r1 and r2 such that r1+r2*2^128 = a. */ +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); +/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (see secp256k1_gej_mul_lambda). */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a); +#endif + +/** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */ +static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift); + +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */ +static void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag); + +#endif /* SECP256K1_SCALAR_H */ diff --git a/libsecp256k1/src/scalar_4x64.h b/libsecp256k1/src/scalar_4x64.h new file mode 100644 index 0000000..19c7495 --- /dev/null +++ b/libsecp256k1/src/scalar_4x64.h @@ -0,0 +1,19 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef struct { + uint64_t d[4]; +} secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}} + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/libsecp256k1/src/scalar_4x64_impl.h b/libsecp256k1/src/scalar_4x64_impl.h new file mode 100644 index 0000000..2d81006 --- /dev/null +++ b/libsecp256k1/src/scalar_4x64_impl.h @@ -0,0 +1,959 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +/* Limbs of the secp256k1 order. */ +#define SECP256K1_N_0 ((uint64_t)0xBFD25E8CD0364141ULL) +#define SECP256K1_N_1 ((uint64_t)0xBAAEDCE6AF48A03BULL) +#define SECP256K1_N_2 ((uint64_t)0xFFFFFFFFFFFFFFFEULL) +#define SECP256K1_N_3 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) + +/* Limbs of 2^256 minus the secp256k1 order. */ +#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) +#define SECP256K1_N_C_1 (~SECP256K1_N_1) +#define SECP256K1_N_C_2 (1) + +/* Limbs of half the secp256k1 order. */ +#define SECP256K1_N_H_0 ((uint64_t)0xDFE92F46681B20A0ULL) +#define SECP256K1_N_H_1 ((uint64_t)0x5D576E7357A4501DULL) +#define SECP256K1_N_H_2 ((uint64_t)0xFFFFFFFFFFFFFFFFULL) +#define SECP256K1_N_H_3 ((uint64_t)0x7FFFFFFFFFFFFFFFULL) + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { + r->d[0] = 0; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { + r->d[0] = v; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK((offset + count - 1) >> 6 == offset >> 6); + return (a->d[offset >> 6] >> (offset & 0x3F)) & ((((uint64_t)1) << count) - 1); +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK(count < 32); + VERIFY_CHECK(offset + count <= 256); + if ((offset + count - 1) >> 6 == offset >> 6) { + return secp256k1_scalar_get_bits(a, offset, count); + } else { + VERIFY_CHECK((offset >> 6) + 1 < 4); + return ((a->d[offset >> 6] >> (offset & 0x3F)) | (a->d[(offset >> 6) + 1] << (64 - (offset & 0x3F)))) & ((((uint64_t)1) << count) - 1); + } +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_3); /* No need for a > check. */ + no |= (a->d[2] < SECP256K1_N_2); + yes |= (a->d[2] > SECP256K1_N_2) & ~no; + no |= (a->d[1] < SECP256K1_N_1); + yes |= (a->d[1] > SECP256K1_N_1) & ~no; + yes |= (a->d[0] >= SECP256K1_N_0) & ~no; + return yes; +} + +SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, unsigned int overflow) { + uint128_t t; + VERIFY_CHECK(overflow <= 1); + t = (uint128_t)r->d[0] + overflow * SECP256K1_N_C_0; + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[1] + overflow * SECP256K1_N_C_1; + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[2] + overflow * SECP256K1_N_C_2; + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint64_t)r->d[3]; + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; + return overflow; +} + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + int overflow; + uint128_t t = (uint128_t)a->d[0] + b->d[0]; + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[1] + b->d[1]; + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[2] + b->d[2]; + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)a->d[3] + b->d[3]; + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + overflow = t + secp256k1_scalar_check_overflow(r); + VERIFY_CHECK(overflow == 0 || overflow == 1); + secp256k1_scalar_reduce(r, overflow); + return overflow; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + uint128_t t; + VERIFY_CHECK(bit < 256); + bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 6) > 3 makes this a noop */ + t = (uint128_t)r->d[0] + (((uint64_t)((bit >> 6) == 0)) << (bit & 0x3F)); + r->d[0] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[1] + (((uint64_t)((bit >> 6) == 1)) << (bit & 0x3F)); + r->d[1] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[2] + (((uint64_t)((bit >> 6) == 2)) << (bit & 0x3F)); + r->d[2] = t & 0xFFFFFFFFFFFFFFFFULL; t >>= 64; + t += (uint128_t)r->d[3] + (((uint64_t)((bit >> 6) == 3)) << (bit & 0x3F)); + r->d[3] = t & 0xFFFFFFFFFFFFFFFFULL; +#ifdef VERIFY + VERIFY_CHECK((t >> 64) == 0); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int over; + r->d[0] = (uint64_t)b32[31] | (uint64_t)b32[30] << 8 | (uint64_t)b32[29] << 16 | (uint64_t)b32[28] << 24 | (uint64_t)b32[27] << 32 | (uint64_t)b32[26] << 40 | (uint64_t)b32[25] << 48 | (uint64_t)b32[24] << 56; + r->d[1] = (uint64_t)b32[23] | (uint64_t)b32[22] << 8 | (uint64_t)b32[21] << 16 | (uint64_t)b32[20] << 24 | (uint64_t)b32[19] << 32 | (uint64_t)b32[18] << 40 | (uint64_t)b32[17] << 48 | (uint64_t)b32[16] << 56; + r->d[2] = (uint64_t)b32[15] | (uint64_t)b32[14] << 8 | (uint64_t)b32[13] << 16 | (uint64_t)b32[12] << 24 | (uint64_t)b32[11] << 32 | (uint64_t)b32[10] << 40 | (uint64_t)b32[9] << 48 | (uint64_t)b32[8] << 56; + r->d[3] = (uint64_t)b32[7] | (uint64_t)b32[6] << 8 | (uint64_t)b32[5] << 16 | (uint64_t)b32[4] << 24 | (uint64_t)b32[3] << 32 | (uint64_t)b32[2] << 40 | (uint64_t)b32[1] << 48 | (uint64_t)b32[0] << 56; + over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); + if (overflow) { + *overflow = over; + } +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + bin[0] = a->d[3] >> 56; bin[1] = a->d[3] >> 48; bin[2] = a->d[3] >> 40; bin[3] = a->d[3] >> 32; bin[4] = a->d[3] >> 24; bin[5] = a->d[3] >> 16; bin[6] = a->d[3] >> 8; bin[7] = a->d[3]; + bin[8] = a->d[2] >> 56; bin[9] = a->d[2] >> 48; bin[10] = a->d[2] >> 40; bin[11] = a->d[2] >> 32; bin[12] = a->d[2] >> 24; bin[13] = a->d[2] >> 16; bin[14] = a->d[2] >> 8; bin[15] = a->d[2]; + bin[16] = a->d[1] >> 56; bin[17] = a->d[1] >> 48; bin[18] = a->d[1] >> 40; bin[19] = a->d[1] >> 32; bin[20] = a->d[1] >> 24; bin[21] = a->d[1] >> 16; bin[22] = a->d[1] >> 8; bin[23] = a->d[1]; + bin[24] = a->d[0] >> 56; bin[25] = a->d[0] >> 48; bin[26] = a->d[0] >> 40; bin[27] = a->d[0] >> 32; bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return (a->d[0] | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint64_t nonzero = 0xFFFFFFFFFFFFFFFFULL * (secp256k1_scalar_is_zero(a) == 0); + uint128_t t = (uint128_t)(~a->d[0]) + SECP256K1_N_0 + 1; + r->d[0] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[1]) + SECP256K1_N_1; + r->d[1] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[2]) + SECP256K1_N_2; + r->d[2] = t & nonzero; t >>= 64; + t += (uint128_t)(~a->d[3]) + SECP256K1_N_3; + r->d[3] = t & nonzero; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3]) == 0; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[3] < SECP256K1_N_H_3); + yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; + no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; /* No need for a > check. */ + no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; + yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; + return yes; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + /* If we are flag = 0, mask = 00...00 and this is a no-op; + * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ + uint64_t mask = !flag - 1; + uint64_t nonzero = (secp256k1_scalar_is_zero(r) != 0) - 1; + uint128_t t = (uint128_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask); + r->d[0] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask); + r->d[1] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask); + r->d[2] = t & nonzero; t >>= 64; + t += (uint128_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask); + r->d[3] = t & nonzero; + return 2 * (mask == 0) - 1; +} + +/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ + +/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd(a,b) { \ + uint64_t tl, th; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* overflow is handled on the next line */ \ + c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ +} + +/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ +#define muladd_fast(a,b) { \ + uint64_t tl, th; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c1 += th; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK(c1 >= th); \ +} + +/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd2(a,b) { \ + uint64_t tl, th, th2, tl2; \ + { \ + uint128_t t = (uint128_t)a * b; \ + th = t >> 64; /* at most 0xFFFFFFFFFFFFFFFE */ \ + tl = t; \ + } \ + th2 = th + th; /* at most 0xFFFFFFFFFFFFFFFE (in case th was 0x7FFFFFFFFFFFFFFF) */ \ + c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((th2 >= th) || (c2 != 0)); \ + tl2 = tl + tl; /* at most 0xFFFFFFFFFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFFFFFFFFFF) */ \ + th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFFFFFFFFFF */ \ + c0 += tl2; /* overflow is handled on the next line */ \ + th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \ + c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \ + c1 += th2; /* overflow is handled on the next line */ \ + c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \ +} + +/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define sumadd(a) { \ + unsigned int over; \ + c0 += (a); /* overflow is handled on the next line */ \ + over = (c0 < (a)) ? 1 : 0; \ + c1 += over; /* overflow is handled on the next line */ \ + c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \ +} + +/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ +#define sumadd_fast(a) { \ + c0 += (a); /* overflow is handled on the next line */ \ + c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ + VERIFY_CHECK(c2 == 0); \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. */ +#define extract(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = c2; \ + c2 = 0; \ +} + +/** Extract the lowest 64 bits of (c0,c1,c2) into n, and left shift the number 64 bits. c2 is required to be zero. */ +#define extract_fast(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = 0; \ + VERIFY_CHECK(c2 == 0); \ +} + +static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint64_t *l) { +#ifdef USE_ASM_X86_64 + /* Reduce 512 bits into 385. */ + uint64_t m0, m1, m2, m3, m4, m5, m6; + uint64_t p0, p1, p2, p3, p4; + uint64_t c; + + __asm__ __volatile__( + /* Preload. */ + "movq 32(%%rsi), %%r11\n" + "movq 40(%%rsi), %%r12\n" + "movq 48(%%rsi), %%r13\n" + "movq 56(%%rsi), %%r14\n" + /* Initialize r8,r9,r10 */ + "movq 0(%%rsi), %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += n0 * c0 */ + "movq %8, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract m0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += l1 */ + "addq 8(%%rsi), %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += n1 * c0 */ + "movq %8, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n0 * c1 */ + "movq %9, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract m1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += l2 */ + "addq 16(%%rsi), %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n2 * c0 */ + "movq %8, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n1 * c1 */ + "movq %9, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += n0 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract m2 */ + "movq %%r10, %q2\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += l3 */ + "addq 24(%%rsi), %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n3 * c0 */ + "movq %8, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n2 * c1 */ + "movq %9, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += n1 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + "adcq $0, %%r10\n" + /* extract m3 */ + "movq %%r8, %q3\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += n3 * c1 */ + "movq %9, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += n2 */ + "addq %%r13, %%r9\n" + "adcq $0, %%r10\n" + "adcq $0, %%r8\n" + /* extract m4 */ + "movq %%r9, %q4\n" + /* (r10,r8) += n3 */ + "addq %%r14, %%r10\n" + "adcq $0, %%r8\n" + /* extract m5 */ + "movq %%r10, %q5\n" + /* extract m6 */ + "movq %%r8, %q6\n" + : "=g"(m0), "=g"(m1), "=g"(m2), "=g"(m3), "=g"(m4), "=g"(m5), "=g"(m6) + : "S"(l), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc"); + + /* Reduce 385 bits into 258. */ + __asm__ __volatile__( + /* Preload */ + "movq %q9, %%r11\n" + "movq %q10, %%r12\n" + "movq %q11, %%r13\n" + /* Initialize (r8,r9,r10) */ + "movq %q5, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9) += m4 * c0 */ + "movq %12, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* extract p0 */ + "movq %%r8, %q0\n" + "xorq %%r8, %%r8\n" + /* (r9,r10) += m1 */ + "addq %q6, %%r9\n" + "adcq $0, %%r10\n" + /* (r9,r10,r8) += m5 * c0 */ + "movq %12, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += m4 * c1 */ + "movq %13, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* extract p1 */ + "movq %%r9, %q1\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += m2 */ + "addq %q7, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m6 * c0 */ + "movq %12, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m5 * c1 */ + "movq %13, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += m4 */ + "addq %%r11, %%r10\n" + "adcq $0, %%r8\n" + "adcq $0, %%r9\n" + /* extract p2 */ + "movq %%r10, %q2\n" + /* (r8,r9) += m3 */ + "addq %q8, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += m6 * c1 */ + "movq %13, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* (r8,r9) += m5 */ + "addq %%r12, %%r8\n" + "adcq $0, %%r9\n" + /* extract p3 */ + "movq %%r8, %q3\n" + /* (r9) += m6 */ + "addq %%r13, %%r9\n" + /* extract p4 */ + "movq %%r9, %q4\n" + : "=&g"(p0), "=&g"(p1), "=&g"(p2), "=g"(p3), "=g"(p4) + : "g"(m0), "g"(m1), "g"(m2), "g"(m3), "g"(m4), "g"(m5), "g"(m6), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "cc"); + + /* Reduce 258 bits into 256. */ + __asm__ __volatile__( + /* Preload */ + "movq %q5, %%r10\n" + /* (rax,rdx) = p4 * c0 */ + "movq %7, %%rax\n" + "mulq %%r10\n" + /* (rax,rdx) += p0 */ + "addq %q1, %%rax\n" + "adcq $0, %%rdx\n" + /* extract r0 */ + "movq %%rax, 0(%q6)\n" + /* Move to (r8,r9) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p1 */ + "addq %q2, %%r8\n" + "adcq $0, %%r9\n" + /* (r8,r9) += p4 * c1 */ + "movq %8, %%rax\n" + "mulq %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + /* Extract r1 */ + "movq %%r8, 8(%q6)\n" + "xorq %%r8, %%r8\n" + /* (r9,r8) += p4 */ + "addq %%r10, %%r9\n" + "adcq $0, %%r8\n" + /* (r9,r8) += p2 */ + "addq %q3, %%r9\n" + "adcq $0, %%r8\n" + /* Extract r2 */ + "movq %%r9, 16(%q6)\n" + "xorq %%r9, %%r9\n" + /* (r8,r9) += p3 */ + "addq %q4, %%r8\n" + "adcq $0, %%r9\n" + /* Extract r3 */ + "movq %%r8, 24(%q6)\n" + /* Extract c */ + "movq %%r9, %q0\n" + : "=g"(c) + : "g"(p0), "g"(p1), "g"(p2), "g"(p3), "g"(p4), "D"(r), "i"(SECP256K1_N_C_0), "i"(SECP256K1_N_C_1) + : "rax", "rdx", "r8", "r9", "r10", "cc", "memory"); +#else + uint128_t c; + uint64_t c0, c1, c2; + uint64_t n0 = l[4], n1 = l[5], n2 = l[6], n3 = l[7]; + uint64_t m0, m1, m2, m3, m4, m5; + uint32_t m6; + uint64_t p0, p1, p2, p3; + uint32_t p4; + + /* Reduce 512 bits into 385. */ + /* m[0..6] = l[0..3] + n[0..3] * SECP256K1_N_C. */ + c0 = l[0]; c1 = 0; c2 = 0; + muladd_fast(n0, SECP256K1_N_C_0); + extract_fast(m0); + sumadd_fast(l[1]); + muladd(n1, SECP256K1_N_C_0); + muladd(n0, SECP256K1_N_C_1); + extract(m1); + sumadd(l[2]); + muladd(n2, SECP256K1_N_C_0); + muladd(n1, SECP256K1_N_C_1); + sumadd(n0); + extract(m2); + sumadd(l[3]); + muladd(n3, SECP256K1_N_C_0); + muladd(n2, SECP256K1_N_C_1); + sumadd(n1); + extract(m3); + muladd(n3, SECP256K1_N_C_1); + sumadd(n2); + extract(m4); + sumadd_fast(n3); + extract_fast(m5); + VERIFY_CHECK(c0 <= 1); + m6 = c0; + + /* Reduce 385 bits into 258. */ + /* p[0..4] = m[0..3] + m[4..6] * SECP256K1_N_C. */ + c0 = m0; c1 = 0; c2 = 0; + muladd_fast(m4, SECP256K1_N_C_0); + extract_fast(p0); + sumadd_fast(m1); + muladd(m5, SECP256K1_N_C_0); + muladd(m4, SECP256K1_N_C_1); + extract(p1); + sumadd(m2); + muladd(m6, SECP256K1_N_C_0); + muladd(m5, SECP256K1_N_C_1); + sumadd(m4); + extract(p2); + sumadd_fast(m3); + muladd_fast(m6, SECP256K1_N_C_1); + sumadd_fast(m5); + extract_fast(p3); + p4 = c0 + m6; + VERIFY_CHECK(p4 <= 2); + + /* Reduce 258 bits into 256. */ + /* r[0..3] = p[0..3] + p[4] * SECP256K1_N_C. */ + c = p0 + (uint128_t)SECP256K1_N_C_0 * p4; + r->d[0] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p1 + (uint128_t)SECP256K1_N_C_1 * p4; + r->d[1] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p2 + (uint128_t)p4; + r->d[2] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; + c += p3; + r->d[3] = c & 0xFFFFFFFFFFFFFFFFULL; c >>= 64; +#endif + + /* Final reduction of r. */ + secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); +} + +static void secp256k1_scalar_mul_512(uint64_t l[8], const secp256k1_scalar *a, const secp256k1_scalar *b) { +#ifdef USE_ASM_X86_64 + const uint64_t *pb = b->d; + __asm__ __volatile__( + /* Preload */ + "movq 0(%%rdi), %%r15\n" + "movq 8(%%rdi), %%rbx\n" + "movq 16(%%rdi), %%rcx\n" + "movq 0(%%rdx), %%r11\n" + "movq 8(%%rdx), %%r12\n" + "movq 16(%%rdx), %%r13\n" + "movq 24(%%rdx), %%r14\n" + /* (rax,rdx) = a0 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + /* Extract l0 */ + "movq %%rax, 0(%%rsi)\n" + /* (r8,r9,r10) = (rdx) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a0 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a1 * b0 */ + "movq %%rbx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l1 */ + "movq %%r8, 8(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a0 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a1 * b1 */ + "movq %%rbx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a2 * b0 */ + "movq %%rcx, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l2 */ + "movq %%r9, 16(%%rsi)\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += a0 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Preload a3 */ + "movq 24(%%rdi), %%r15\n" + /* (r10,r8,r9) += a1 * b2 */ + "movq %%rbx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a2 * b1 */ + "movq %%rcx, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += a3 * b0 */ + "movq %%r15, %%rax\n" + "mulq %%r11\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Extract l3 */ + "movq %%r10, 24(%%rsi)\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += a1 * b3 */ + "movq %%rbx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a2 * b2 */ + "movq %%rcx, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a3 * b1 */ + "movq %%r15, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l4 */ + "movq %%r8, 32(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += a2 * b3 */ + "movq %%rcx, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a3 * b2 */ + "movq %%r15, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l5 */ + "movq %%r9, 40(%%rsi)\n" + /* (r10,r8) += a3 * b3 */ + "movq %%r15, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + /* Extract l6 */ + "movq %%r10, 48(%%rsi)\n" + /* Extract l7 */ + "movq %%r8, 56(%%rsi)\n" + : "+d"(pb) + : "S"(l), "D"(a->d) + : "rax", "rbx", "rcx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "r15", "cc", "memory"); +#else + /* 160 bit accumulator. */ + uint64_t c0 = 0, c1 = 0; + uint32_t c2 = 0; + + /* l[0..7] = a[0..3] * b[0..3]. */ + muladd_fast(a->d[0], b->d[0]); + extract_fast(l[0]); + muladd(a->d[0], b->d[1]); + muladd(a->d[1], b->d[0]); + extract(l[1]); + muladd(a->d[0], b->d[2]); + muladd(a->d[1], b->d[1]); + muladd(a->d[2], b->d[0]); + extract(l[2]); + muladd(a->d[0], b->d[3]); + muladd(a->d[1], b->d[2]); + muladd(a->d[2], b->d[1]); + muladd(a->d[3], b->d[0]); + extract(l[3]); + muladd(a->d[1], b->d[3]); + muladd(a->d[2], b->d[2]); + muladd(a->d[3], b->d[1]); + extract(l[4]); + muladd(a->d[2], b->d[3]); + muladd(a->d[3], b->d[2]); + extract(l[5]); + muladd_fast(a->d[3], b->d[3]); + extract_fast(l[6]); + VERIFY_CHECK(c1 == 0); + l[7] = c0; +#endif +} + +static void secp256k1_scalar_sqr_512(uint64_t l[8], const secp256k1_scalar *a) { +#ifdef USE_ASM_X86_64 + __asm__ __volatile__( + /* Preload */ + "movq 0(%%rdi), %%r11\n" + "movq 8(%%rdi), %%r12\n" + "movq 16(%%rdi), %%r13\n" + "movq 24(%%rdi), %%r14\n" + /* (rax,rdx) = a0 * a0 */ + "movq %%r11, %%rax\n" + "mulq %%r11\n" + /* Extract l0 */ + "movq %%rax, 0(%%rsi)\n" + /* (r8,r9,r10) = (rdx,0) */ + "movq %%rdx, %%r8\n" + "xorq %%r9, %%r9\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += 2 * a0 * a1 */ + "movq %%r11, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l1 */ + "movq %%r8, 8(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += 2 * a0 * a2 */ + "movq %%r11, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* (r9,r10,r8) += a1 * a1 */ + "movq %%r12, %%rax\n" + "mulq %%r12\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l2 */ + "movq %%r9, 16(%%rsi)\n" + "xorq %%r9, %%r9\n" + /* (r10,r8,r9) += 2 * a0 * a3 */ + "movq %%r11, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* (r10,r8,r9) += 2 * a1 * a2 */ + "movq %%r12, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + "adcq $0, %%r9\n" + /* Extract l3 */ + "movq %%r10, 24(%%rsi)\n" + "xorq %%r10, %%r10\n" + /* (r8,r9,r10) += 2 * a1 * a3 */ + "movq %%r12, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* (r8,r9,r10) += a2 * a2 */ + "movq %%r13, %%rax\n" + "mulq %%r13\n" + "addq %%rax, %%r8\n" + "adcq %%rdx, %%r9\n" + "adcq $0, %%r10\n" + /* Extract l4 */ + "movq %%r8, 32(%%rsi)\n" + "xorq %%r8, %%r8\n" + /* (r9,r10,r8) += 2 * a2 * a3 */ + "movq %%r13, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + "addq %%rax, %%r9\n" + "adcq %%rdx, %%r10\n" + "adcq $0, %%r8\n" + /* Extract l5 */ + "movq %%r9, 40(%%rsi)\n" + /* (r10,r8) += a3 * a3 */ + "movq %%r14, %%rax\n" + "mulq %%r14\n" + "addq %%rax, %%r10\n" + "adcq %%rdx, %%r8\n" + /* Extract l6 */ + "movq %%r10, 48(%%rsi)\n" + /* Extract l7 */ + "movq %%r8, 56(%%rsi)\n" + : + : "S"(l), "D"(a->d) + : "rax", "rdx", "r8", "r9", "r10", "r11", "r12", "r13", "r14", "cc", "memory"); +#else + /* 160 bit accumulator. */ + uint64_t c0 = 0, c1 = 0; + uint32_t c2 = 0; + + /* l[0..7] = a[0..3] * b[0..3]. */ + muladd_fast(a->d[0], a->d[0]); + extract_fast(l[0]); + muladd2(a->d[0], a->d[1]); + extract(l[1]); + muladd2(a->d[0], a->d[2]); + muladd(a->d[1], a->d[1]); + extract(l[2]); + muladd2(a->d[0], a->d[3]); + muladd2(a->d[1], a->d[2]); + extract(l[3]); + muladd2(a->d[1], a->d[3]); + muladd(a->d[2], a->d[2]); + extract(l[4]); + muladd2(a->d[2], a->d[3]); + extract(l[5]); + muladd_fast(a->d[3], a->d[3]); + extract_fast(l[6]); + VERIFY_CHECK(c1 == 0); + l[7] = c0; +#endif +} + +#undef sumadd +#undef sumadd_fast +#undef muladd +#undef muladd_fast +#undef muladd2 +#undef extract +#undef extract_fast + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + uint64_t l[8]; + secp256k1_scalar_mul_512(l, a, b); + secp256k1_scalar_reduce_512(r, l); +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = r->d[0] & ((1 << n) - 1); + r->d[0] = (r->d[0] >> n) + (r->d[1] << (64 - n)); + r->d[1] = (r->d[1] >> n) + (r->d[2] << (64 - n)); + r->d[2] = (r->d[2] >> n) + (r->d[3] << (64 - n)); + r->d[3] = (r->d[3] >> n); + return ret; +} + +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint64_t l[8]; + secp256k1_scalar_sqr_512(l, a); + secp256k1_scalar_reduce_512(r, l); +} + +#ifdef USE_ENDOMORPHISM +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + r1->d[0] = a->d[0]; + r1->d[1] = a->d[1]; + r1->d[2] = 0; + r1->d[3] = 0; + r2->d[0] = a->d[2]; + r2->d[1] = a->d[3]; + r2->d[2] = 0; + r2->d[3] = 0; +} +#endif + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3])) == 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { + uint64_t l[8]; + unsigned int shiftlimbs; + unsigned int shiftlow; + unsigned int shifthigh; + VERIFY_CHECK(shift >= 256); + secp256k1_scalar_mul_512(l, a, b); + shiftlimbs = shift >> 6; + shiftlow = shift & 0x3F; + shifthigh = 64 - shiftlow; + r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[1] = shift < 448 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[2] = shift < 384 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[3] = shift < 320 ? (l[3 + shiftlimbs] >> shiftlow) : 0; + secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 6] >> ((shift - 1) & 0x3f)) & 1); +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint64_t mask0, mask1; + mask0 = flag + ~((uint64_t)0); + mask1 = ~mask0; + r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1); + r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1); + r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1); + r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/libsecp256k1/src/scalar_8x32.h b/libsecp256k1/src/scalar_8x32.h new file mode 100644 index 0000000..2c9a348 --- /dev/null +++ b/libsecp256k1/src/scalar_8x32.h @@ -0,0 +1,19 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef struct { + uint32_t d[8]; +} secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}} + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/libsecp256k1/src/scalar_8x32_impl.h b/libsecp256k1/src/scalar_8x32_impl.h new file mode 100644 index 0000000..f504289 --- /dev/null +++ b/libsecp256k1/src/scalar_8x32_impl.h @@ -0,0 +1,735 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +/* Limbs of the secp256k1 order. */ +#define SECP256K1_N_0 ((uint32_t)0xD0364141UL) +#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL) +#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL) +#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL) +#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL) +#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL) + +/* Limbs of 2^256 minus the secp256k1 order. */ +#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1) +#define SECP256K1_N_C_1 (~SECP256K1_N_1) +#define SECP256K1_N_C_2 (~SECP256K1_N_2) +#define SECP256K1_N_C_3 (~SECP256K1_N_3) +#define SECP256K1_N_C_4 (1) + +/* Limbs of half the secp256k1 order. */ +#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL) +#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL) +#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL) +#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL) +#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL) +#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL) + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { + r->d[0] = 0; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; + r->d[4] = 0; + r->d[5] = 0; + r->d[6] = 0; + r->d[7] = 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { + r->d[0] = v; + r->d[1] = 0; + r->d[2] = 0; + r->d[3] = 0; + r->d[4] = 0; + r->d[5] = 0; + r->d[6] = 0; + r->d[7] = 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5); + return (a->d[offset >> 5] >> (offset & 0x1F)) & ((1 << count) - 1); +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + VERIFY_CHECK(count < 32); + VERIFY_CHECK(offset + count <= 256); + if ((offset + count - 1) >> 5 == offset >> 5) { + return secp256k1_scalar_get_bits(a, offset, count); + } else { + VERIFY_CHECK((offset >> 5) + 1 < 8); + return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & ((((uint32_t)1) << count) - 1); + } +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */ + no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */ + no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */ + no |= (a->d[4] < SECP256K1_N_4); + yes |= (a->d[4] > SECP256K1_N_4) & ~no; + no |= (a->d[3] < SECP256K1_N_3) & ~yes; + yes |= (a->d[3] > SECP256K1_N_3) & ~no; + no |= (a->d[2] < SECP256K1_N_2) & ~yes; + yes |= (a->d[2] > SECP256K1_N_2) & ~no; + no |= (a->d[1] < SECP256K1_N_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_1) & ~no; + yes |= (a->d[0] >= SECP256K1_N_0) & ~no; + return yes; +} + +SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) { + uint64_t t; + VERIFY_CHECK(overflow <= 1); + t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0; + r->d[0] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1; + r->d[1] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2; + r->d[2] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3; + r->d[3] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4; + r->d[4] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[5]; + r->d[5] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[6]; + r->d[6] = t & 0xFFFFFFFFUL; t >>= 32; + t += (uint64_t)r->d[7]; + r->d[7] = t & 0xFFFFFFFFUL; + return overflow; +} + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + int overflow; + uint64_t t = (uint64_t)a->d[0] + b->d[0]; + r->d[0] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[1] + b->d[1]; + r->d[1] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[2] + b->d[2]; + r->d[2] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[3] + b->d[3]; + r->d[3] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[4] + b->d[4]; + r->d[4] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[5] + b->d[5]; + r->d[5] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[6] + b->d[6]; + r->d[6] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)a->d[7] + b->d[7]; + r->d[7] = t & 0xFFFFFFFFULL; t >>= 32; + overflow = t + secp256k1_scalar_check_overflow(r); + VERIFY_CHECK(overflow == 0 || overflow == 1); + secp256k1_scalar_reduce(r, overflow); + return overflow; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + uint64_t t; + VERIFY_CHECK(bit < 256); + bit += ((uint32_t) flag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */ + t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F)); + r->d[0] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F)); + r->d[1] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F)); + r->d[2] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F)); + r->d[3] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F)); + r->d[4] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F)); + r->d[5] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F)); + r->d[6] = t & 0xFFFFFFFFULL; t >>= 32; + t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F)); + r->d[7] = t & 0xFFFFFFFFULL; +#ifdef VERIFY + VERIFY_CHECK((t >> 32) == 0); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + int over; + r->d[0] = (uint32_t)b32[31] | (uint32_t)b32[30] << 8 | (uint32_t)b32[29] << 16 | (uint32_t)b32[28] << 24; + r->d[1] = (uint32_t)b32[27] | (uint32_t)b32[26] << 8 | (uint32_t)b32[25] << 16 | (uint32_t)b32[24] << 24; + r->d[2] = (uint32_t)b32[23] | (uint32_t)b32[22] << 8 | (uint32_t)b32[21] << 16 | (uint32_t)b32[20] << 24; + r->d[3] = (uint32_t)b32[19] | (uint32_t)b32[18] << 8 | (uint32_t)b32[17] << 16 | (uint32_t)b32[16] << 24; + r->d[4] = (uint32_t)b32[15] | (uint32_t)b32[14] << 8 | (uint32_t)b32[13] << 16 | (uint32_t)b32[12] << 24; + r->d[5] = (uint32_t)b32[11] | (uint32_t)b32[10] << 8 | (uint32_t)b32[9] << 16 | (uint32_t)b32[8] << 24; + r->d[6] = (uint32_t)b32[7] | (uint32_t)b32[6] << 8 | (uint32_t)b32[5] << 16 | (uint32_t)b32[4] << 24; + r->d[7] = (uint32_t)b32[3] | (uint32_t)b32[2] << 8 | (uint32_t)b32[1] << 16 | (uint32_t)b32[0] << 24; + over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r)); + if (overflow) { + *overflow = over; + } +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + bin[0] = a->d[7] >> 24; bin[1] = a->d[7] >> 16; bin[2] = a->d[7] >> 8; bin[3] = a->d[7]; + bin[4] = a->d[6] >> 24; bin[5] = a->d[6] >> 16; bin[6] = a->d[6] >> 8; bin[7] = a->d[6]; + bin[8] = a->d[5] >> 24; bin[9] = a->d[5] >> 16; bin[10] = a->d[5] >> 8; bin[11] = a->d[5]; + bin[12] = a->d[4] >> 24; bin[13] = a->d[4] >> 16; bin[14] = a->d[4] >> 8; bin[15] = a->d[4]; + bin[16] = a->d[3] >> 24; bin[17] = a->d[3] >> 16; bin[18] = a->d[3] >> 8; bin[19] = a->d[3]; + bin[20] = a->d[2] >> 24; bin[21] = a->d[2] >> 16; bin[22] = a->d[2] >> 8; bin[23] = a->d[2]; + bin[24] = a->d[1] >> 24; bin[25] = a->d[1] >> 16; bin[26] = a->d[1] >> 8; bin[27] = a->d[1]; + bin[28] = a->d[0] >> 24; bin[29] = a->d[0] >> 16; bin[30] = a->d[0] >> 8; bin[31] = a->d[0]; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0); + uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1; + r->d[0] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[1]) + SECP256K1_N_1; + r->d[1] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[2]) + SECP256K1_N_2; + r->d[2] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[3]) + SECP256K1_N_3; + r->d[3] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[4]) + SECP256K1_N_4; + r->d[4] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[5]) + SECP256K1_N_5; + r->d[5] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[6]) + SECP256K1_N_6; + r->d[6] = t & nonzero; t >>= 32; + t += (uint64_t)(~a->d[7]) + SECP256K1_N_7; + r->d[7] = t & nonzero; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + int yes = 0; + int no = 0; + no |= (a->d[7] < SECP256K1_N_H_7); + yes |= (a->d[7] > SECP256K1_N_H_7) & ~no; + no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */ + no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */ + no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */ + no |= (a->d[3] < SECP256K1_N_H_3) & ~yes; + yes |= (a->d[3] > SECP256K1_N_H_3) & ~no; + no |= (a->d[2] < SECP256K1_N_H_2) & ~yes; + yes |= (a->d[2] > SECP256K1_N_H_2) & ~no; + no |= (a->d[1] < SECP256K1_N_H_1) & ~yes; + yes |= (a->d[1] > SECP256K1_N_H_1) & ~no; + yes |= (a->d[0] > SECP256K1_N_H_0) & ~no; + return yes; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + /* If we are flag = 0, mask = 00...00 and this is a no-op; + * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */ + uint32_t mask = !flag - 1; + uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0); + uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask); + r->d[0] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask); + r->d[1] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask); + r->d[2] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask); + r->d[3] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask); + r->d[4] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask); + r->d[5] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask); + r->d[6] = t & nonzero; t >>= 32; + t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask); + r->d[7] = t & nonzero; + return 2 * (mask == 0) - 1; +} + + +/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */ + +/** Add a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd(a,b) { \ + uint32_t tl, th; \ + { \ + uint64_t t = (uint64_t)a * b; \ + th = t >> 32; /* at most 0xFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \ + c1 += th; /* overflow is handled on the next line */ \ + c2 += (c1 < th) ? 1 : 0; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK((c1 >= th) || (c2 != 0)); \ +} + +/** Add a*b to the number defined by (c0,c1). c1 must never overflow. */ +#define muladd_fast(a,b) { \ + uint32_t tl, th; \ + { \ + uint64_t t = (uint64_t)a * b; \ + th = t >> 32; /* at most 0xFFFFFFFE */ \ + tl = t; \ + } \ + c0 += tl; /* overflow is handled on the next line */ \ + th += (c0 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \ + c1 += th; /* never overflows by contract (verified in the next line) */ \ + VERIFY_CHECK(c1 >= th); \ +} + +/** Add 2*a*b to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define muladd2(a,b) { \ + uint32_t tl, th, th2, tl2; \ + { \ + uint64_t t = (uint64_t)a * b; \ + th = t >> 32; /* at most 0xFFFFFFFE */ \ + tl = t; \ + } \ + th2 = th + th; /* at most 0xFFFFFFFE (in case th was 0x7FFFFFFF) */ \ + c2 += (th2 < th) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((th2 >= th) || (c2 != 0)); \ + tl2 = tl + tl; /* at most 0xFFFFFFFE (in case the lowest 63 bits of tl were 0x7FFFFFFF) */ \ + th2 += (tl2 < tl) ? 1 : 0; /* at most 0xFFFFFFFF */ \ + c0 += tl2; /* overflow is handled on the next line */ \ + th2 += (c0 < tl2) ? 1 : 0; /* second overflow is handled on the next line */ \ + c2 += (c0 < tl2) & (th2 == 0); /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c0 >= tl2) || (th2 != 0) || (c2 != 0)); \ + c1 += th2; /* overflow is handled on the next line */ \ + c2 += (c1 < th2) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 >= th2) || (c2 != 0)); \ +} + +/** Add a to the number defined by (c0,c1,c2). c2 must never overflow. */ +#define sumadd(a) { \ + unsigned int over; \ + c0 += (a); /* overflow is handled on the next line */ \ + over = (c0 < (a)) ? 1 : 0; \ + c1 += over; /* overflow is handled on the next line */ \ + c2 += (c1 < over) ? 1 : 0; /* never overflows by contract */ \ +} + +/** Add a to the number defined by (c0,c1). c1 must never overflow, c2 must be zero. */ +#define sumadd_fast(a) { \ + c0 += (a); /* overflow is handled on the next line */ \ + c1 += (c0 < (a)) ? 1 : 0; /* never overflows by contract (verified the next line) */ \ + VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \ + VERIFY_CHECK(c2 == 0); \ +} + +/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. */ +#define extract(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = c2; \ + c2 = 0; \ +} + +/** Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits. c2 is required to be zero. */ +#define extract_fast(n) { \ + (n) = c0; \ + c0 = c1; \ + c1 = 0; \ + VERIFY_CHECK(c2 == 0); \ +} + +static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) { + uint64_t c; + uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15]; + uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12; + uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8; + + /* 96 bit accumulator. */ + uint32_t c0, c1, c2; + + /* Reduce 512 bits into 385. */ + /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */ + c0 = l[0]; c1 = 0; c2 = 0; + muladd_fast(n0, SECP256K1_N_C_0); + extract_fast(m0); + sumadd_fast(l[1]); + muladd(n1, SECP256K1_N_C_0); + muladd(n0, SECP256K1_N_C_1); + extract(m1); + sumadd(l[2]); + muladd(n2, SECP256K1_N_C_0); + muladd(n1, SECP256K1_N_C_1); + muladd(n0, SECP256K1_N_C_2); + extract(m2); + sumadd(l[3]); + muladd(n3, SECP256K1_N_C_0); + muladd(n2, SECP256K1_N_C_1); + muladd(n1, SECP256K1_N_C_2); + muladd(n0, SECP256K1_N_C_3); + extract(m3); + sumadd(l[4]); + muladd(n4, SECP256K1_N_C_0); + muladd(n3, SECP256K1_N_C_1); + muladd(n2, SECP256K1_N_C_2); + muladd(n1, SECP256K1_N_C_3); + sumadd(n0); + extract(m4); + sumadd(l[5]); + muladd(n5, SECP256K1_N_C_0); + muladd(n4, SECP256K1_N_C_1); + muladd(n3, SECP256K1_N_C_2); + muladd(n2, SECP256K1_N_C_3); + sumadd(n1); + extract(m5); + sumadd(l[6]); + muladd(n6, SECP256K1_N_C_0); + muladd(n5, SECP256K1_N_C_1); + muladd(n4, SECP256K1_N_C_2); + muladd(n3, SECP256K1_N_C_3); + sumadd(n2); + extract(m6); + sumadd(l[7]); + muladd(n7, SECP256K1_N_C_0); + muladd(n6, SECP256K1_N_C_1); + muladd(n5, SECP256K1_N_C_2); + muladd(n4, SECP256K1_N_C_3); + sumadd(n3); + extract(m7); + muladd(n7, SECP256K1_N_C_1); + muladd(n6, SECP256K1_N_C_2); + muladd(n5, SECP256K1_N_C_3); + sumadd(n4); + extract(m8); + muladd(n7, SECP256K1_N_C_2); + muladd(n6, SECP256K1_N_C_3); + sumadd(n5); + extract(m9); + muladd(n7, SECP256K1_N_C_3); + sumadd(n6); + extract(m10); + sumadd_fast(n7); + extract_fast(m11); + VERIFY_CHECK(c0 <= 1); + m12 = c0; + + /* Reduce 385 bits into 258. */ + /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */ + c0 = m0; c1 = 0; c2 = 0; + muladd_fast(m8, SECP256K1_N_C_0); + extract_fast(p0); + sumadd_fast(m1); + muladd(m9, SECP256K1_N_C_0); + muladd(m8, SECP256K1_N_C_1); + extract(p1); + sumadd(m2); + muladd(m10, SECP256K1_N_C_0); + muladd(m9, SECP256K1_N_C_1); + muladd(m8, SECP256K1_N_C_2); + extract(p2); + sumadd(m3); + muladd(m11, SECP256K1_N_C_0); + muladd(m10, SECP256K1_N_C_1); + muladd(m9, SECP256K1_N_C_2); + muladd(m8, SECP256K1_N_C_3); + extract(p3); + sumadd(m4); + muladd(m12, SECP256K1_N_C_0); + muladd(m11, SECP256K1_N_C_1); + muladd(m10, SECP256K1_N_C_2); + muladd(m9, SECP256K1_N_C_3); + sumadd(m8); + extract(p4); + sumadd(m5); + muladd(m12, SECP256K1_N_C_1); + muladd(m11, SECP256K1_N_C_2); + muladd(m10, SECP256K1_N_C_3); + sumadd(m9); + extract(p5); + sumadd(m6); + muladd(m12, SECP256K1_N_C_2); + muladd(m11, SECP256K1_N_C_3); + sumadd(m10); + extract(p6); + sumadd_fast(m7); + muladd_fast(m12, SECP256K1_N_C_3); + sumadd_fast(m11); + extract_fast(p7); + p8 = c0 + m12; + VERIFY_CHECK(p8 <= 2); + + /* Reduce 258 bits into 256. */ + /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */ + c = p0 + (uint64_t)SECP256K1_N_C_0 * p8; + r->d[0] = c & 0xFFFFFFFFUL; c >>= 32; + c += p1 + (uint64_t)SECP256K1_N_C_1 * p8; + r->d[1] = c & 0xFFFFFFFFUL; c >>= 32; + c += p2 + (uint64_t)SECP256K1_N_C_2 * p8; + r->d[2] = c & 0xFFFFFFFFUL; c >>= 32; + c += p3 + (uint64_t)SECP256K1_N_C_3 * p8; + r->d[3] = c & 0xFFFFFFFFUL; c >>= 32; + c += p4 + (uint64_t)p8; + r->d[4] = c & 0xFFFFFFFFUL; c >>= 32; + c += p5; + r->d[5] = c & 0xFFFFFFFFUL; c >>= 32; + c += p6; + r->d[6] = c & 0xFFFFFFFFUL; c >>= 32; + c += p7; + r->d[7] = c & 0xFFFFFFFFUL; c >>= 32; + + /* Final reduction of r. */ + secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r)); +} + +static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) { + /* 96 bit accumulator. */ + uint32_t c0 = 0, c1 = 0, c2 = 0; + + /* l[0..15] = a[0..7] * b[0..7]. */ + muladd_fast(a->d[0], b->d[0]); + extract_fast(l[0]); + muladd(a->d[0], b->d[1]); + muladd(a->d[1], b->d[0]); + extract(l[1]); + muladd(a->d[0], b->d[2]); + muladd(a->d[1], b->d[1]); + muladd(a->d[2], b->d[0]); + extract(l[2]); + muladd(a->d[0], b->d[3]); + muladd(a->d[1], b->d[2]); + muladd(a->d[2], b->d[1]); + muladd(a->d[3], b->d[0]); + extract(l[3]); + muladd(a->d[0], b->d[4]); + muladd(a->d[1], b->d[3]); + muladd(a->d[2], b->d[2]); + muladd(a->d[3], b->d[1]); + muladd(a->d[4], b->d[0]); + extract(l[4]); + muladd(a->d[0], b->d[5]); + muladd(a->d[1], b->d[4]); + muladd(a->d[2], b->d[3]); + muladd(a->d[3], b->d[2]); + muladd(a->d[4], b->d[1]); + muladd(a->d[5], b->d[0]); + extract(l[5]); + muladd(a->d[0], b->d[6]); + muladd(a->d[1], b->d[5]); + muladd(a->d[2], b->d[4]); + muladd(a->d[3], b->d[3]); + muladd(a->d[4], b->d[2]); + muladd(a->d[5], b->d[1]); + muladd(a->d[6], b->d[0]); + extract(l[6]); + muladd(a->d[0], b->d[7]); + muladd(a->d[1], b->d[6]); + muladd(a->d[2], b->d[5]); + muladd(a->d[3], b->d[4]); + muladd(a->d[4], b->d[3]); + muladd(a->d[5], b->d[2]); + muladd(a->d[6], b->d[1]); + muladd(a->d[7], b->d[0]); + extract(l[7]); + muladd(a->d[1], b->d[7]); + muladd(a->d[2], b->d[6]); + muladd(a->d[3], b->d[5]); + muladd(a->d[4], b->d[4]); + muladd(a->d[5], b->d[3]); + muladd(a->d[6], b->d[2]); + muladd(a->d[7], b->d[1]); + extract(l[8]); + muladd(a->d[2], b->d[7]); + muladd(a->d[3], b->d[6]); + muladd(a->d[4], b->d[5]); + muladd(a->d[5], b->d[4]); + muladd(a->d[6], b->d[3]); + muladd(a->d[7], b->d[2]); + extract(l[9]); + muladd(a->d[3], b->d[7]); + muladd(a->d[4], b->d[6]); + muladd(a->d[5], b->d[5]); + muladd(a->d[6], b->d[4]); + muladd(a->d[7], b->d[3]); + extract(l[10]); + muladd(a->d[4], b->d[7]); + muladd(a->d[5], b->d[6]); + muladd(a->d[6], b->d[5]); + muladd(a->d[7], b->d[4]); + extract(l[11]); + muladd(a->d[5], b->d[7]); + muladd(a->d[6], b->d[6]); + muladd(a->d[7], b->d[5]); + extract(l[12]); + muladd(a->d[6], b->d[7]); + muladd(a->d[7], b->d[6]); + extract(l[13]); + muladd_fast(a->d[7], b->d[7]); + extract_fast(l[14]); + VERIFY_CHECK(c1 == 0); + l[15] = c0; +} + +static void secp256k1_scalar_sqr_512(uint32_t *l, const secp256k1_scalar *a) { + /* 96 bit accumulator. */ + uint32_t c0 = 0, c1 = 0, c2 = 0; + + /* l[0..15] = a[0..7]^2. */ + muladd_fast(a->d[0], a->d[0]); + extract_fast(l[0]); + muladd2(a->d[0], a->d[1]); + extract(l[1]); + muladd2(a->d[0], a->d[2]); + muladd(a->d[1], a->d[1]); + extract(l[2]); + muladd2(a->d[0], a->d[3]); + muladd2(a->d[1], a->d[2]); + extract(l[3]); + muladd2(a->d[0], a->d[4]); + muladd2(a->d[1], a->d[3]); + muladd(a->d[2], a->d[2]); + extract(l[4]); + muladd2(a->d[0], a->d[5]); + muladd2(a->d[1], a->d[4]); + muladd2(a->d[2], a->d[3]); + extract(l[5]); + muladd2(a->d[0], a->d[6]); + muladd2(a->d[1], a->d[5]); + muladd2(a->d[2], a->d[4]); + muladd(a->d[3], a->d[3]); + extract(l[6]); + muladd2(a->d[0], a->d[7]); + muladd2(a->d[1], a->d[6]); + muladd2(a->d[2], a->d[5]); + muladd2(a->d[3], a->d[4]); + extract(l[7]); + muladd2(a->d[1], a->d[7]); + muladd2(a->d[2], a->d[6]); + muladd2(a->d[3], a->d[5]); + muladd(a->d[4], a->d[4]); + extract(l[8]); + muladd2(a->d[2], a->d[7]); + muladd2(a->d[3], a->d[6]); + muladd2(a->d[4], a->d[5]); + extract(l[9]); + muladd2(a->d[3], a->d[7]); + muladd2(a->d[4], a->d[6]); + muladd(a->d[5], a->d[5]); + extract(l[10]); + muladd2(a->d[4], a->d[7]); + muladd2(a->d[5], a->d[6]); + extract(l[11]); + muladd2(a->d[5], a->d[7]); + muladd(a->d[6], a->d[6]); + extract(l[12]); + muladd2(a->d[6], a->d[7]); + extract(l[13]); + muladd_fast(a->d[7], a->d[7]); + extract_fast(l[14]); + VERIFY_CHECK(c1 == 0); + l[15] = c0; +} + +#undef sumadd +#undef sumadd_fast +#undef muladd +#undef muladd_fast +#undef muladd2 +#undef extract +#undef extract_fast + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + uint32_t l[16]; + secp256k1_scalar_mul_512(l, a, b); + secp256k1_scalar_reduce_512(r, l); +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = r->d[0] & ((1 << n) - 1); + r->d[0] = (r->d[0] >> n) + (r->d[1] << (32 - n)); + r->d[1] = (r->d[1] >> n) + (r->d[2] << (32 - n)); + r->d[2] = (r->d[2] >> n) + (r->d[3] << (32 - n)); + r->d[3] = (r->d[3] >> n) + (r->d[4] << (32 - n)); + r->d[4] = (r->d[4] >> n) + (r->d[5] << (32 - n)); + r->d[5] = (r->d[5] >> n) + (r->d[6] << (32 - n)); + r->d[6] = (r->d[6] >> n) + (r->d[7] << (32 - n)); + r->d[7] = (r->d[7] >> n); + return ret; +} + +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { + uint32_t l[16]; + secp256k1_scalar_sqr_512(l, a); + secp256k1_scalar_reduce_512(r, l); +} + +#ifdef USE_ENDOMORPHISM +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + r1->d[0] = a->d[0]; + r1->d[1] = a->d[1]; + r1->d[2] = a->d[2]; + r1->d[3] = a->d[3]; + r1->d[4] = 0; + r1->d[5] = 0; + r1->d[6] = 0; + r1->d[7] = 0; + r2->d[0] = a->d[4]; + r2->d[1] = a->d[5]; + r2->d[2] = a->d[6]; + r2->d[3] = a->d[7]; + r2->d[4] = 0; + r2->d[5] = 0; + r2->d[6] = 0; + r2->d[7] = 0; +} +#endif + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0; +} + +SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) { + uint32_t l[16]; + unsigned int shiftlimbs; + unsigned int shiftlow; + unsigned int shifthigh; + VERIFY_CHECK(shift >= 256); + secp256k1_scalar_mul_512(l, a, b); + shiftlimbs = shift >> 5; + shiftlow = shift & 0x1F; + shifthigh = 32 - shiftlow; + r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0; + r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0; + secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1); +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint32_t mask0, mask1; + mask0 = flag + ~((uint32_t)0); + mask1 = ~mask0; + r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1); + r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1); + r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1); + r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1); + r->d[4] = (r->d[4] & mask0) | (a->d[4] & mask1); + r->d[5] = (r->d[5] & mask0) | (a->d[5] & mask1); + r->d[6] = (r->d[6] & mask0) | (a->d[6] & mask1); + r->d[7] = (r->d[7] & mask0) | (a->d[7] & mask1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/libsecp256k1/src/scalar_impl.h b/libsecp256k1/src/scalar_impl.h new file mode 100644 index 0000000..70cd73d --- /dev/null +++ b/libsecp256k1/src/scalar_impl.h @@ -0,0 +1,342 @@ +/********************************************************************** + * Copyright (c) 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_IMPL_H +#define SECP256K1_SCALAR_IMPL_H + +#include "scalar.h" +#include "util.h" + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#if defined(EXHAUSTIVE_TEST_ORDER) +#include "scalar_low_impl.h" +#elif defined(USE_SCALAR_4X64) +#include "scalar_4x64_impl.h" +#elif defined(USE_SCALAR_8X32) +#include "scalar_8x32_impl.h" +#else +#error "Please select scalar implementation" +#endif + +static const secp256k1_scalar secp256k1_scalar_one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); +static const secp256k1_scalar secp256k1_scalar_zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + +#ifndef USE_NUM_NONE +static void secp256k1_scalar_get_num(secp256k1_num *r, const secp256k1_scalar *a) { + unsigned char c[32]; + secp256k1_scalar_get_b32(c, a); + secp256k1_num_set_bin(r, c, 32); +} + +/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */ +static void secp256k1_scalar_order_get_num(secp256k1_num *r) { +#if defined(EXHAUSTIVE_TEST_ORDER) + static const unsigned char order[32] = { + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,0, + 0,0,0,0,0,0,0,EXHAUSTIVE_TEST_ORDER + }; +#else + static const unsigned char order[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41 + }; +#endif + secp256k1_num_set_bin(r, order, 32); +} +#endif + +static int secp256k1_scalar_set_b32_seckey(secp256k1_scalar *r, const unsigned char *bin) { + int overflow; + secp256k1_scalar_set_b32(r, bin, &overflow); + return (!overflow) & (!secp256k1_scalar_is_zero(r)); +} + +static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) { +#if defined(EXHAUSTIVE_TEST_ORDER) + int i; + *r = 0; + for (i = 0; i < EXHAUSTIVE_TEST_ORDER; i++) + if ((i * *x) % EXHAUSTIVE_TEST_ORDER == 1) + *r = i; + /* If this VERIFY_CHECK triggers we were given a noninvertible scalar (and thus + * have a composite group order; fix it in exhaustive_tests.c). */ + VERIFY_CHECK(*r != 0); +} +#else + secp256k1_scalar *t; + int i; + /* First compute xN as x ^ (2^N - 1) for some values of N, + * and uM as x ^ M for some values of M. */ + secp256k1_scalar x2, x3, x6, x8, x14, x28, x56, x112, x126; + secp256k1_scalar u2, u5, u9, u11, u13; + + secp256k1_scalar_sqr(&u2, x); + secp256k1_scalar_mul(&x2, &u2, x); + secp256k1_scalar_mul(&u5, &u2, &x2); + secp256k1_scalar_mul(&x3, &u5, &u2); + secp256k1_scalar_mul(&u9, &x3, &u2); + secp256k1_scalar_mul(&u11, &u9, &u2); + secp256k1_scalar_mul(&u13, &u11, &u2); + + secp256k1_scalar_sqr(&x6, &u13); + secp256k1_scalar_sqr(&x6, &x6); + secp256k1_scalar_mul(&x6, &x6, &u11); + + secp256k1_scalar_sqr(&x8, &x6); + secp256k1_scalar_sqr(&x8, &x8); + secp256k1_scalar_mul(&x8, &x8, &x2); + + secp256k1_scalar_sqr(&x14, &x8); + for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(&x14, &x14); + } + secp256k1_scalar_mul(&x14, &x14, &x6); + + secp256k1_scalar_sqr(&x28, &x14); + for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x28, &x28); + } + secp256k1_scalar_mul(&x28, &x28, &x14); + + secp256k1_scalar_sqr(&x56, &x28); + for (i = 0; i < 27; i++) { + secp256k1_scalar_sqr(&x56, &x56); + } + secp256k1_scalar_mul(&x56, &x56, &x28); + + secp256k1_scalar_sqr(&x112, &x56); + for (i = 0; i < 55; i++) { + secp256k1_scalar_sqr(&x112, &x112); + } + secp256k1_scalar_mul(&x112, &x112, &x56); + + secp256k1_scalar_sqr(&x126, &x112); + for (i = 0; i < 13; i++) { + secp256k1_scalar_sqr(&x126, &x126); + } + secp256k1_scalar_mul(&x126, &x126, &x14); + + /* Then accumulate the final result (t starts at x126). */ + t = &x126; + for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 5; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 3; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u5); /* 101 */ + for (i = 0; i < 10; i++) { /* 0000000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 4; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x3); /* 111 */ + for (i = 0; i < 9; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x8); /* 11111111 */ + for (i = 0; i < 5; i++) { /* 0 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u11); /* 1011 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 5; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &x2); /* 11 */ + for (i = 0; i < 6; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 10; i++) { /* 000000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u13); /* 1101 */ + for (i = 0; i < 4; i++) { + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, &u9); /* 1001 */ + for (i = 0; i < 6; i++) { /* 00000 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(t, t, x); /* 1 */ + for (i = 0; i < 8; i++) { /* 00 */ + secp256k1_scalar_sqr(t, t); + } + secp256k1_scalar_mul(r, t, &x6); /* 111111 */ +} + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(a->d[0] & 1); +} +#endif + +static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) { +#if defined(USE_SCALAR_INV_BUILTIN) + secp256k1_scalar_inverse(r, x); +#elif defined(USE_SCALAR_INV_NUM) + unsigned char b[32]; + secp256k1_num n, m; + secp256k1_scalar t = *x; + secp256k1_scalar_get_b32(b, &t); + secp256k1_num_set_bin(&n, b, 32); + secp256k1_scalar_order_get_num(&m); + secp256k1_num_mod_inverse(&n, &n, &m); + secp256k1_num_get_bin(b, 32, &n); + secp256k1_scalar_set_b32(r, b, NULL); + /* Verify that the inverse was computed correctly, without GMP code. */ + secp256k1_scalar_mul(&t, &t, r); + CHECK(secp256k1_scalar_is_one(&t)); +#else +#error "Please select scalar inverse implementation" +#endif +} + +#ifdef USE_ENDOMORPHISM +#if defined(EXHAUSTIVE_TEST_ORDER) +/** + * Find k1 and k2 given k, such that k1 + k2 * lambda == k mod n; unlike in the + * full case we don't bother making k1 and k2 be small, we just want them to be + * nontrivial to get full test coverage for the exhaustive tests. We therefore + * (arbitrarily) set k2 = k + 5 and k1 = k - k2 * lambda. + */ +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r2 = (*a + 5) % EXHAUSTIVE_TEST_ORDER; + *r1 = (*a + (EXHAUSTIVE_TEST_ORDER - *r2) * EXHAUSTIVE_TEST_LAMBDA) % EXHAUSTIVE_TEST_ORDER; +} +#else +/** + * The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where + * lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a, + * 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72} + * + * "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm + * (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1 + * and k2 have a small size. + * It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are: + * + * - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3} + * - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8} + * - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15} + * + * The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives + * k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and + * compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2. + * + * g1, g2 are precomputed constants used to replace division with a rounded multiplication + * when decomposing the scalar for an endomorphism-based point multiplication. + * + * The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve + * Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5. + * + * The derivation is described in the paper "Efficient Software Implementation of Public-Key + * Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez), + * Section 4.3 (here we use a somewhat higher-precision estimate): + * d = a1*b2 - b1*a2 + * g1 = round((2^272)*b2/d) + * g2 = round((2^272)*b1/d) + * + * (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found + * as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda'). + * + * The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order). + */ + +static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + secp256k1_scalar c1, c2; + static const secp256k1_scalar minus_lambda = SECP256K1_SCALAR_CONST( + 0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL, + 0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL + ); + static const secp256k1_scalar minus_b1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, + 0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL + ); + static const secp256k1_scalar minus_b2 = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, + 0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL + ); + static const secp256k1_scalar g1 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL, + 0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL + ); + static const secp256k1_scalar g2 = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL, + 0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL + ); + VERIFY_CHECK(r1 != a); + VERIFY_CHECK(r2 != a); + /* these _var calls are constant time since the shift amount is constant */ + secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272); + secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272); + secp256k1_scalar_mul(&c1, &c1, &minus_b1); + secp256k1_scalar_mul(&c2, &c2, &minus_b2); + secp256k1_scalar_add(r2, &c1, &c2); + secp256k1_scalar_mul(r1, r2, &minus_lambda); + secp256k1_scalar_add(r1, r1, a); +} +#endif +#endif + +#endif /* SECP256K1_SCALAR_IMPL_H */ diff --git a/libsecp256k1/src/scalar_low.h b/libsecp256k1/src/scalar_low.h new file mode 100644 index 0000000..2794a7f --- /dev/null +++ b/libsecp256k1/src/scalar_low.h @@ -0,0 +1,17 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_H +#define SECP256K1_SCALAR_REPR_H + +#include + +/** A scalar modulo the group order of the secp256k1 curve. */ +typedef uint32_t secp256k1_scalar; + +#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) (d0) + +#endif /* SECP256K1_SCALAR_REPR_H */ diff --git a/libsecp256k1/src/scalar_low_impl.h b/libsecp256k1/src/scalar_low_impl.h new file mode 100644 index 0000000..ad81f37 --- /dev/null +++ b/libsecp256k1/src/scalar_low_impl.h @@ -0,0 +1,124 @@ +/********************************************************************** + * Copyright (c) 2015 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_SCALAR_REPR_IMPL_H +#define SECP256K1_SCALAR_REPR_IMPL_H + +#include "scalar.h" + +#include + +SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) { + return !(*a & 1); +} + +SECP256K1_INLINE static void secp256k1_scalar_clear(secp256k1_scalar *r) { *r = 0; } +SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) { *r = v; } + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + if (offset < 32) + return ((*a >> offset) & ((((uint32_t)1) << count) - 1)); + else + return 0; +} + +SECP256K1_INLINE static unsigned int secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) { + return secp256k1_scalar_get_bits(a, offset, count); +} + +SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) { return *a >= EXHAUSTIVE_TEST_ORDER; } + +static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a + *b) % EXHAUSTIVE_TEST_ORDER; + return *r < *b; +} + +static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) { + if (flag && bit < 32) + *r += ((uint32_t)1 << bit); +#ifdef VERIFY + VERIFY_CHECK(bit < 32); + /* Verify that adding (1 << bit) will not overflow any in-range scalar *r by overflowing the underlying uint32_t. */ + VERIFY_CHECK(((uint32_t)1 << bit) - 1 <= UINT32_MAX - EXHAUSTIVE_TEST_ORDER); + VERIFY_CHECK(secp256k1_scalar_check_overflow(r) == 0); +#endif +} + +static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) { + const int base = 0x100 % EXHAUSTIVE_TEST_ORDER; + int i; + *r = 0; + for (i = 0; i < 32; i++) { + *r = ((*r * base) + b32[i]) % EXHAUSTIVE_TEST_ORDER; + } + /* just deny overflow, it basically always happens */ + if (overflow) *overflow = 0; +} + +static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) { + memset(bin, 0, 32); + bin[28] = *a >> 24; bin[29] = *a >> 16; bin[30] = *a >> 8; bin[31] = *a; +} + +SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) { + return *a == 0; +} + +static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) { + if (*a == 0) { + *r = 0; + } else { + *r = EXHAUSTIVE_TEST_ORDER - *a; + } +} + +SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) { + return *a == 1; +} + +static int secp256k1_scalar_is_high(const secp256k1_scalar *a) { + return *a > EXHAUSTIVE_TEST_ORDER / 2; +} + +static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) { + if (flag) secp256k1_scalar_negate(r, r); + return flag ? -1 : 1; +} + +static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) { + *r = (*a * *b) % EXHAUSTIVE_TEST_ORDER; +} + +static int secp256k1_scalar_shr_int(secp256k1_scalar *r, int n) { + int ret; + VERIFY_CHECK(n > 0); + VERIFY_CHECK(n < 16); + ret = *r & ((1 << n) - 1); + *r >>= n; + return ret; +} + +static void secp256k1_scalar_sqr(secp256k1_scalar *r, const secp256k1_scalar *a) { + *r = (*a * *a) % EXHAUSTIVE_TEST_ORDER; +} + +static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *a) { + *r1 = *a; + *r2 = 0; +} + +SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) { + return *a == *b; +} + +static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) { + uint32_t mask0, mask1; + mask0 = flag + ~((uint32_t)0); + mask1 = ~mask0; + *r = (*r & mask0) | (*a & mask1); +} + +#endif /* SECP256K1_SCALAR_REPR_IMPL_H */ diff --git a/libsecp256k1/src/scratch.h b/libsecp256k1/src/scratch.h new file mode 100644 index 0000000..77b35d1 --- /dev/null +++ b/libsecp256k1/src/scratch.h @@ -0,0 +1,42 @@ +/********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCRATCH_ +#define _SECP256K1_SCRATCH_ + +/* The typedef is used internally; the struct name is used in the public API + * (where it is exposed as a different typedef) */ +typedef struct secp256k1_scratch_space_struct { + /** guard against interpreting this object as other types */ + unsigned char magic[8]; + /** actual allocated data */ + void *data; + /** amount that has been allocated (i.e. `data + offset` is the next + * available pointer) */ + size_t alloc_size; + /** maximum size available to allocate */ + size_t max_size; +} secp256k1_scratch; + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t max_size); + +static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch); + +/** Returns an opaque object used to "checkpoint" a scratch space. Used + * with `secp256k1_scratch_apply_checkpoint` to undo allocations. */ +static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch); + +/** Applies a check point received from `secp256k1_scratch_checkpoint`, + * undoing all allocations since that point. */ +static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t checkpoint); + +/** Returns the maximum allocation the scratch space will allow */ +static size_t secp256k1_scratch_max_allocation(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch, size_t n_objects); + +/** Returns a pointer into the most recently allocated frame, or NULL if there is insufficient available space */ +static void *secp256k1_scratch_alloc(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t n); + +#endif diff --git a/libsecp256k1/src/scratch_impl.h b/libsecp256k1/src/scratch_impl.h new file mode 100644 index 0000000..4cee700 --- /dev/null +++ b/libsecp256k1/src/scratch_impl.h @@ -0,0 +1,88 @@ +/********************************************************************** + * Copyright (c) 2017 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_SCRATCH_IMPL_H_ +#define _SECP256K1_SCRATCH_IMPL_H_ + +#include "util.h" +#include "scratch.h" + +static secp256k1_scratch* secp256k1_scratch_create(const secp256k1_callback* error_callback, size_t size) { + const size_t base_alloc = ((sizeof(secp256k1_scratch) + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT; + void *alloc = checked_malloc(error_callback, base_alloc + size); + secp256k1_scratch* ret = (secp256k1_scratch *)alloc; + if (ret != NULL) { + memset(ret, 0, sizeof(*ret)); + memcpy(ret->magic, "scratch", 8); + ret->data = (void *) ((char *) alloc + base_alloc); + ret->max_size = size; + } + return ret; +} + +static void secp256k1_scratch_destroy(const secp256k1_callback* error_callback, secp256k1_scratch* scratch) { + if (scratch != NULL) { + VERIFY_CHECK(scratch->alloc_size == 0); /* all checkpoints should be applied */ + if (memcmp(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return; + } + memset(scratch->magic, 0, sizeof(scratch->magic)); + free(scratch); + } +} + +static size_t secp256k1_scratch_checkpoint(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch) { + if (memcmp(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return 0; + } + return scratch->alloc_size; +} + +static void secp256k1_scratch_apply_checkpoint(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t checkpoint) { + if (memcmp(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return; + } + if (checkpoint > scratch->alloc_size) { + secp256k1_callback_call(error_callback, "invalid checkpoint"); + return; + } + scratch->alloc_size = checkpoint; +} + +static size_t secp256k1_scratch_max_allocation(const secp256k1_callback* error_callback, const secp256k1_scratch* scratch, size_t objects) { + if (memcmp(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return 0; + } + if (scratch->max_size - scratch->alloc_size <= objects * (ALIGNMENT - 1)) { + return 0; + } + return scratch->max_size - scratch->alloc_size - objects * (ALIGNMENT - 1); +} + +static void *secp256k1_scratch_alloc(const secp256k1_callback* error_callback, secp256k1_scratch* scratch, size_t size) { + void *ret; + size = ROUND_TO_ALIGN(size); + + if (memcmp(scratch->magic, "scratch", 8) != 0) { + secp256k1_callback_call(error_callback, "invalid scratch space"); + return NULL; + } + + if (size > scratch->max_size - scratch->alloc_size) { + return NULL; + } + ret = (void *) ((char *) scratch->data + scratch->alloc_size); + memset(ret, 0, size); + scratch->alloc_size += size; + + return ret; +} + +#endif diff --git a/libsecp256k1/src/secp256k1.c b/libsecp256k1/src/secp256k1.c new file mode 100644 index 0000000..de66be5 --- /dev/null +++ b/libsecp256k1/src/secp256k1.c @@ -0,0 +1,726 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include "include/secp256k1.h" +#include "include/secp256k1_preallocated.h" + +#include "util.h" +#include "num_impl.h" +#include "field_impl.h" +#include "scalar_impl.h" +#include "group_impl.h" +#include "ecmult_impl.h" +#include "ecmult_const_impl.h" +#include "ecmult_gen_impl.h" +#include "ecdsa_impl.h" +#include "eckey_impl.h" +#include "hash_impl.h" +#include "scratch_impl.h" + +#if defined(VALGRIND) +# include +#endif + +#define ARG_CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + secp256k1_callback_call(&ctx->illegal_callback, #cond); \ + return 0; \ + } \ +} while(0) + +#define ARG_CHECK_NO_RETURN(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + secp256k1_callback_call(&ctx->illegal_callback, #cond); \ + } \ +} while(0) + +#ifndef USE_EXTERNAL_DEFAULT_CALLBACKS +#include +#include +static void secp256k1_default_illegal_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] illegal argument: %s\n", str); + abort(); +} +static void secp256k1_default_error_callback_fn(const char* str, void* data) { + (void)data; + fprintf(stderr, "[libsecp256k1] internal consistency check failed: %s\n", str); + abort(); +} +#else +void secp256k1_default_illegal_callback_fn(const char* str, void* data); +void secp256k1_default_error_callback_fn(const char* str, void* data); +#endif + +static const secp256k1_callback default_illegal_callback = { + secp256k1_default_illegal_callback_fn, + NULL +}; + +static const secp256k1_callback default_error_callback = { + secp256k1_default_error_callback_fn, + NULL +}; + +struct secp256k1_context_struct { + secp256k1_ecmult_context ecmult_ctx; + secp256k1_ecmult_gen_context ecmult_gen_ctx; + secp256k1_callback illegal_callback; + secp256k1_callback error_callback; + int declassify; +}; + +static const secp256k1_context secp256k1_context_no_precomp_ = { + { 0 }, + { 0 }, + { secp256k1_default_illegal_callback_fn, 0 }, + { secp256k1_default_error_callback_fn, 0 }, + 0 +}; +const secp256k1_context *secp256k1_context_no_precomp = &secp256k1_context_no_precomp_; + +size_t secp256k1_context_preallocated_size(unsigned int flags) { + size_t ret = ROUND_TO_ALIGN(sizeof(secp256k1_context)); + + if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) { + secp256k1_callback_call(&default_illegal_callback, + "Invalid flags"); + return 0; + } + + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) { + ret += SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE; + } + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) { + ret += SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE; + } + return ret; +} + +size_t secp256k1_context_preallocated_clone_size(const secp256k1_context* ctx) { + size_t ret = ROUND_TO_ALIGN(sizeof(secp256k1_context)); + VERIFY_CHECK(ctx != NULL); + if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) { + ret += SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE; + } + if (secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)) { + ret += SECP256K1_ECMULT_CONTEXT_PREALLOCATED_SIZE; + } + return ret; +} + +secp256k1_context* secp256k1_context_preallocated_create(void* prealloc, unsigned int flags) { + void* const base = prealloc; + size_t prealloc_size; + secp256k1_context* ret; + + VERIFY_CHECK(prealloc != NULL); + prealloc_size = secp256k1_context_preallocated_size(flags); + ret = (secp256k1_context*)manual_alloc(&prealloc, sizeof(secp256k1_context), base, prealloc_size); + ret->illegal_callback = default_illegal_callback; + ret->error_callback = default_error_callback; + + if (EXPECT((flags & SECP256K1_FLAGS_TYPE_MASK) != SECP256K1_FLAGS_TYPE_CONTEXT, 0)) { + secp256k1_callback_call(&ret->illegal_callback, + "Invalid flags"); + return NULL; + } + + secp256k1_ecmult_context_init(&ret->ecmult_ctx); + secp256k1_ecmult_gen_context_init(&ret->ecmult_gen_ctx); + + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_SIGN) { + secp256k1_ecmult_gen_context_build(&ret->ecmult_gen_ctx, &prealloc); + } + if (flags & SECP256K1_FLAGS_BIT_CONTEXT_VERIFY) { + secp256k1_ecmult_context_build(&ret->ecmult_ctx, &prealloc); + } + ret->declassify = !!(flags & SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY); + + return (secp256k1_context*) ret; +} + +secp256k1_context* secp256k1_context_create(unsigned int flags) { + size_t const prealloc_size = secp256k1_context_preallocated_size(flags); + secp256k1_context* ctx = (secp256k1_context*)checked_malloc(&default_error_callback, prealloc_size); + if (EXPECT(secp256k1_context_preallocated_create(ctx, flags) == NULL, 0)) { + free(ctx); + return NULL; + } + + return ctx; +} + +secp256k1_context* secp256k1_context_preallocated_clone(const secp256k1_context* ctx, void* prealloc) { + size_t prealloc_size; + secp256k1_context* ret; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(prealloc != NULL); + + prealloc_size = secp256k1_context_preallocated_clone_size(ctx); + ret = (secp256k1_context*)prealloc; + memcpy(ret, ctx, prealloc_size); + secp256k1_ecmult_gen_context_finalize_memcpy(&ret->ecmult_gen_ctx, &ctx->ecmult_gen_ctx); + secp256k1_ecmult_context_finalize_memcpy(&ret->ecmult_ctx, &ctx->ecmult_ctx); + return ret; +} + +secp256k1_context* secp256k1_context_clone(const secp256k1_context* ctx) { + secp256k1_context* ret; + size_t prealloc_size; + + VERIFY_CHECK(ctx != NULL); + prealloc_size = secp256k1_context_preallocated_clone_size(ctx); + ret = (secp256k1_context*)checked_malloc(&ctx->error_callback, prealloc_size); + ret = secp256k1_context_preallocated_clone(ctx, ret); + return ret; +} + +void secp256k1_context_preallocated_destroy(secp256k1_context* ctx) { + ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp); + if (ctx != NULL) { + secp256k1_ecmult_context_clear(&ctx->ecmult_ctx); + secp256k1_ecmult_gen_context_clear(&ctx->ecmult_gen_ctx); + } +} + +void secp256k1_context_destroy(secp256k1_context* ctx) { + if (ctx != NULL) { + secp256k1_context_preallocated_destroy(ctx); + free(ctx); + } +} + +void secp256k1_context_set_illegal_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp); + if (fun == NULL) { + fun = secp256k1_default_illegal_callback_fn; + } + ctx->illegal_callback.fn = fun; + ctx->illegal_callback.data = data; +} + +void secp256k1_context_set_error_callback(secp256k1_context* ctx, void (*fun)(const char* message, void* data), const void* data) { + ARG_CHECK_NO_RETURN(ctx != secp256k1_context_no_precomp); + if (fun == NULL) { + fun = secp256k1_default_error_callback_fn; + } + ctx->error_callback.fn = fun; + ctx->error_callback.data = data; +} + +secp256k1_scratch_space* secp256k1_scratch_space_create(const secp256k1_context* ctx, size_t max_size) { + VERIFY_CHECK(ctx != NULL); + return secp256k1_scratch_create(&ctx->error_callback, max_size); +} + +void secp256k1_scratch_space_destroy(const secp256k1_context *ctx, secp256k1_scratch_space* scratch) { + VERIFY_CHECK(ctx != NULL); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); +} + +/* Mark memory as no-longer-secret for the purpose of analysing constant-time behaviour + * of the software. This is setup for use with valgrind but could be substituted with + * the appropriate instrumentation for other analysis tools. + */ +static SECP256K1_INLINE void secp256k1_declassify(const secp256k1_context* ctx, void *p, size_t len) { +#if defined(VALGRIND) + if (EXPECT(ctx->declassify,0)) VALGRIND_MAKE_MEM_DEFINED(p, len); +#else + (void)ctx; + (void)p; + (void)len; +#endif +} + +static int secp256k1_pubkey_load(const secp256k1_context* ctx, secp256k1_ge* ge, const secp256k1_pubkey* pubkey) { + if (sizeof(secp256k1_ge_storage) == 64) { + /* When the secp256k1_ge_storage type is exactly 64 byte, use its + * representation inside secp256k1_pubkey, as conversion is very fast. + * Note that secp256k1_pubkey_save must use the same representation. */ + secp256k1_ge_storage s; + memcpy(&s, &pubkey->data[0], sizeof(s)); + secp256k1_ge_from_storage(ge, &s); + } else { + /* Otherwise, fall back to 32-byte big endian for X and Y. */ + secp256k1_fe x, y; + secp256k1_fe_set_b32(&x, pubkey->data); + secp256k1_fe_set_b32(&y, pubkey->data + 32); + secp256k1_ge_set_xy(ge, &x, &y); + } + ARG_CHECK(!secp256k1_fe_is_zero(&ge->x)); + return 1; +} + +static void secp256k1_pubkey_save(secp256k1_pubkey* pubkey, secp256k1_ge* ge) { + if (sizeof(secp256k1_ge_storage) == 64) { + secp256k1_ge_storage s; + secp256k1_ge_to_storage(&s, ge); + memcpy(&pubkey->data[0], &s, sizeof(s)); + } else { + VERIFY_CHECK(!secp256k1_ge_is_infinity(ge)); + secp256k1_fe_normalize_var(&ge->x); + secp256k1_fe_normalize_var(&ge->y); + secp256k1_fe_get_b32(pubkey->data, &ge->x); + secp256k1_fe_get_b32(pubkey->data + 32, &ge->y); + } +} + +int secp256k1_ec_pubkey_parse(const secp256k1_context* ctx, secp256k1_pubkey* pubkey, const unsigned char *input, size_t inputlen) { + secp256k1_ge Q; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(input != NULL); + if (!secp256k1_eckey_pubkey_parse(&Q, input, inputlen)) { + return 0; + } + secp256k1_pubkey_save(pubkey, &Q); + secp256k1_ge_clear(&Q); + return 1; +} + +int secp256k1_ec_pubkey_serialize(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_pubkey* pubkey, unsigned int flags) { + secp256k1_ge Q; + size_t len; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(*outputlen >= ((flags & SECP256K1_FLAGS_BIT_COMPRESSION) ? 33 : 65)); + len = *outputlen; + *outputlen = 0; + ARG_CHECK(output != NULL); + memset(output, 0, len); + ARG_CHECK(pubkey != NULL); + ARG_CHECK((flags & SECP256K1_FLAGS_TYPE_MASK) == SECP256K1_FLAGS_TYPE_COMPRESSION); + if (secp256k1_pubkey_load(ctx, &Q, pubkey)) { + ret = secp256k1_eckey_pubkey_serialize(&Q, output, &len, flags & SECP256K1_FLAGS_BIT_COMPRESSION); + if (ret) { + *outputlen = len; + } + } + return ret; +} + +static void secp256k1_ecdsa_signature_load(const secp256k1_context* ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_ecdsa_signature* sig) { + (void)ctx; + if (sizeof(secp256k1_scalar) == 32) { + /* When the secp256k1_scalar type is exactly 32 byte, use its + * representation inside secp256k1_ecdsa_signature, as conversion is very fast. + * Note that secp256k1_ecdsa_signature_save must use the same representation. */ + memcpy(r, &sig->data[0], 32); + memcpy(s, &sig->data[32], 32); + } else { + secp256k1_scalar_set_b32(r, &sig->data[0], NULL); + secp256k1_scalar_set_b32(s, &sig->data[32], NULL); + } +} + +static void secp256k1_ecdsa_signature_save(secp256k1_ecdsa_signature* sig, const secp256k1_scalar* r, const secp256k1_scalar* s) { + if (sizeof(secp256k1_scalar) == 32) { + memcpy(&sig->data[0], r, 32); + memcpy(&sig->data[32], s, 32); + } else { + secp256k1_scalar_get_b32(&sig->data[0], r); + secp256k1_scalar_get_b32(&sig->data[32], s); + } +} + +int secp256k1_ecdsa_signature_parse_der(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input, size_t inputlen) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input != NULL); + + if (secp256k1_ecdsa_sig_parse(&r, &s, input, inputlen)) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + return 1; + } else { + memset(sig, 0, sizeof(*sig)); + return 0; + } +} + +int secp256k1_ecdsa_signature_parse_compact(const secp256k1_context* ctx, secp256k1_ecdsa_signature* sig, const unsigned char *input64) { + secp256k1_scalar r, s; + int ret = 1; + int overflow = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(input64 != NULL); + + secp256k1_scalar_set_b32(&r, &input64[0], &overflow); + ret &= !overflow; + secp256k1_scalar_set_b32(&s, &input64[32], &overflow); + ret &= !overflow; + if (ret) { + secp256k1_ecdsa_signature_save(sig, &r, &s); + } else { + memset(sig, 0, sizeof(*sig)); + } + return ret; +} + +int secp256k1_ecdsa_signature_serialize_der(const secp256k1_context* ctx, unsigned char *output, size_t *outputlen, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output != NULL); + ARG_CHECK(outputlen != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return secp256k1_ecdsa_sig_serialize(output, outputlen, &r, &s); +} + +int secp256k1_ecdsa_signature_serialize_compact(const secp256k1_context* ctx, unsigned char *output64, const secp256k1_ecdsa_signature* sig) { + secp256k1_scalar r, s; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(output64 != NULL); + ARG_CHECK(sig != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + secp256k1_scalar_get_b32(&output64[0], &r); + secp256k1_scalar_get_b32(&output64[32], &s); + return 1; +} + +int secp256k1_ecdsa_signature_normalize(const secp256k1_context* ctx, secp256k1_ecdsa_signature *sigout, const secp256k1_ecdsa_signature *sigin) { + secp256k1_scalar r, s; + int ret = 0; + + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(sigin != NULL); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, sigin); + ret = secp256k1_scalar_is_high(&s); + if (sigout != NULL) { + if (ret) { + secp256k1_scalar_negate(&s, &s); + } + secp256k1_ecdsa_signature_save(sigout, &r, &s); + } + + return ret; +} + +int secp256k1_ecdsa_verify(const secp256k1_context* ctx, const secp256k1_ecdsa_signature *sig, const unsigned char *msg32, const secp256k1_pubkey *pubkey) { + secp256k1_ge q; + secp256k1_scalar r, s; + secp256k1_scalar m; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(sig != NULL); + ARG_CHECK(pubkey != NULL); + + secp256k1_scalar_set_b32(&m, msg32, NULL); + secp256k1_ecdsa_signature_load(ctx, &r, &s, sig); + return (!secp256k1_scalar_is_high(&s) && + secp256k1_pubkey_load(ctx, &q, pubkey) && + secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &r, &s, &q, &m)); +} + +static SECP256K1_INLINE void buffer_append(unsigned char *buf, unsigned int *offset, const void *data, unsigned int len) { + memcpy(buf + *offset, data, len); + *offset += len; +} + +static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + unsigned char keydata[112]; + unsigned int offset = 0; + secp256k1_rfc6979_hmac_sha256 rng; + unsigned int i; + /* We feed a byte array to the PRNG as input, consisting of: + * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d. + * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data. + * - optionally 16 extra bytes with the algorithm name. + * Because the arguments have distinct fixed lengths it is not possible for + * different argument mixtures to emulate each other and result in the same + * nonces. + */ + buffer_append(keydata, &offset, key32, 32); + buffer_append(keydata, &offset, msg32, 32); + if (data != NULL) { + buffer_append(keydata, &offset, data, 32); + } + if (algo16 != NULL) { + buffer_append(keydata, &offset, algo16, 16); + } + secp256k1_rfc6979_hmac_sha256_initialize(&rng, keydata, offset); + memset(keydata, 0, sizeof(keydata)); + for (i = 0; i <= counter; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, nonce32, 32); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + return 1; +} + +const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function_rfc6979; +const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979; + +int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) { + secp256k1_scalar r, s; + secp256k1_scalar sec, non, msg; + int ret = 0; + int is_sec_valid; + unsigned char nonce32[32]; + unsigned int count = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(msg32 != NULL); + ARG_CHECK(signature != NULL); + ARG_CHECK(seckey != NULL); + if (noncefp == NULL) { + noncefp = secp256k1_nonce_function_default; + } + + /* Fail if the secret key is invalid. */ + is_sec_valid = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_one, !is_sec_valid); + secp256k1_scalar_set_b32(&msg, msg32, NULL); + while (1) { + int is_nonce_valid; + ret = !!noncefp(nonce32, msg32, seckey, NULL, (void*)noncedata, count); + if (!ret) { + break; + } + is_nonce_valid = secp256k1_scalar_set_b32_seckey(&non, nonce32); + /* The nonce is still secret here, but it being invalid is is less likely than 1:2^255. */ + secp256k1_declassify(ctx, &is_nonce_valid, sizeof(is_nonce_valid)); + if (is_nonce_valid) { + ret = secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, &r, &s, &sec, &msg, &non, NULL); + /* The final signature is no longer a secret, nor is the fact that we were successful or not. */ + secp256k1_declassify(ctx, &ret, sizeof(ret)); + if (ret) { + break; + } + } + count++; + } + /* We don't want to declassify is_sec_valid and therefore the range of + * seckey. As a result is_sec_valid is included in ret only after ret was + * used as a branching variable. */ + ret &= is_sec_valid; + memset(nonce32, 0, 32); + secp256k1_scalar_clear(&msg); + secp256k1_scalar_clear(&non); + secp256k1_scalar_clear(&sec); + secp256k1_scalar_cmov(&r, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_cmov(&s, &secp256k1_scalar_zero, !ret); + secp256k1_ecdsa_signature_save(signature, &r, &s); + return ret; +} + +int secp256k1_ec_seckey_verify(const secp256k1_context* ctx, const unsigned char *seckey) { + secp256k1_scalar sec; + int ret; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_pubkey_create(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *seckey) { + secp256k1_gej pj; + secp256k1_ge p; + secp256k1_scalar sec; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + memset(pubkey, 0, sizeof(*pubkey)); + ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_one, !ret); + + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pj, &sec); + secp256k1_ge_set_gej(&p, &pj); + secp256k1_pubkey_save(pubkey, &p); + memczero(pubkey, sizeof(*pubkey), !ret); + + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_seckey_negate(const secp256k1_context* ctx, unsigned char *seckey) { + secp256k1_scalar sec; + int ret = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_negate(&sec, &sec); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + return ret; +} + +int secp256k1_ec_privkey_negate(const secp256k1_context* ctx, unsigned char *seckey) { + return secp256k1_ec_seckey_negate(ctx, seckey); +} + +int secp256k1_ec_pubkey_negate(const secp256k1_context* ctx, secp256k1_pubkey *pubkey) { + int ret = 0; + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + + ret = secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + secp256k1_ge_neg(&p, &p); + secp256k1_pubkey_save(pubkey, &p); + } + return ret; +} + +int secp256k1_ec_seckey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + secp256k1_scalar term; + secp256k1_scalar sec; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&term, tweak, &overflow); + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + + ret &= (!overflow) & secp256k1_eckey_privkey_tweak_add(&sec, &term); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&term); + return ret; +} + +int secp256k1_ec_privkey_tweak_add(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + return secp256k1_ec_seckey_tweak_add(ctx, seckey, tweak); +} + +int secp256k1_ec_pubkey_tweak_add(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) { + secp256k1_ge p; + secp256k1_scalar term; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&term, tweak, &overflow); + ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + if (secp256k1_eckey_pubkey_tweak_add(&ctx->ecmult_ctx, &p, &term)) { + secp256k1_pubkey_save(pubkey, &p); + } else { + ret = 0; + } + } + + return ret; +} + +int secp256k1_ec_seckey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + secp256k1_scalar factor; + secp256k1_scalar sec; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(seckey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&factor, tweak, &overflow); + ret = secp256k1_scalar_set_b32_seckey(&sec, seckey); + ret &= (!overflow) & secp256k1_eckey_privkey_tweak_mul(&sec, &factor); + secp256k1_scalar_cmov(&sec, &secp256k1_scalar_zero, !ret); + secp256k1_scalar_get_b32(seckey, &sec); + + secp256k1_scalar_clear(&sec); + secp256k1_scalar_clear(&factor); + return ret; +} + +int secp256k1_ec_privkey_tweak_mul(const secp256k1_context* ctx, unsigned char *seckey, const unsigned char *tweak) { + return secp256k1_ec_seckey_tweak_mul(ctx, seckey, tweak); +} + +int secp256k1_ec_pubkey_tweak_mul(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *tweak) { + secp256k1_ge p; + secp256k1_scalar factor; + int ret = 0; + int overflow = 0; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(secp256k1_ecmult_context_is_built(&ctx->ecmult_ctx)); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(tweak != NULL); + + secp256k1_scalar_set_b32(&factor, tweak, &overflow); + ret = !overflow && secp256k1_pubkey_load(ctx, &p, pubkey); + memset(pubkey, 0, sizeof(*pubkey)); + if (ret) { + if (secp256k1_eckey_pubkey_tweak_mul(&ctx->ecmult_ctx, &p, &factor)) { + secp256k1_pubkey_save(pubkey, &p); + } else { + ret = 0; + } + } + + return ret; +} + +int secp256k1_context_randomize(secp256k1_context* ctx, const unsigned char *seed32) { + VERIFY_CHECK(ctx != NULL); + if (secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx)) { + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32); + } + return 1; +} + +int secp256k1_ec_pubkey_combine(const secp256k1_context* ctx, secp256k1_pubkey *pubnonce, const secp256k1_pubkey * const *pubnonces, size_t n) { + size_t i; + secp256k1_gej Qj; + secp256k1_ge Q; + + ARG_CHECK(pubnonce != NULL); + memset(pubnonce, 0, sizeof(*pubnonce)); + ARG_CHECK(n >= 1); + ARG_CHECK(pubnonces != NULL); + + secp256k1_gej_set_infinity(&Qj); + + for (i = 0; i < n; i++) { + secp256k1_pubkey_load(ctx, &Q, pubnonces[i]); + secp256k1_gej_add_ge(&Qj, &Qj, &Q); + } + if (secp256k1_gej_is_infinity(&Qj)) { + return 0; + } + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(pubnonce, &Q); + return 1; +} + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/main_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/main_impl.h" +#endif diff --git a/libsecp256k1/src/testrand.h b/libsecp256k1/src/testrand.h new file mode 100644 index 0000000..f1f9be0 --- /dev/null +++ b/libsecp256k1/src/testrand.h @@ -0,0 +1,38 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_TESTRAND_H +#define SECP256K1_TESTRAND_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +/* A non-cryptographic RNG used only for test infrastructure. */ + +/** Seed the pseudorandom number generator for testing. */ +SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16); + +/** Generate a pseudorandom number in the range [0..2**32-1]. */ +static uint32_t secp256k1_rand32(void); + +/** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or + * more. */ +static uint32_t secp256k1_rand_bits(int bits); + +/** Generate a pseudorandom number in the range [0..range-1]. */ +static uint32_t secp256k1_rand_int(uint32_t range); + +/** Generate a pseudorandom 32-byte array. */ +static void secp256k1_rand256(unsigned char *b32); + +/** Generate a pseudorandom 32-byte array with long sequences of zero and one bits. */ +static void secp256k1_rand256_test(unsigned char *b32); + +/** Generate pseudorandom bytes with long sequences of zero and one bits. */ +static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len); + +#endif /* SECP256K1_TESTRAND_H */ diff --git a/libsecp256k1/src/testrand_impl.h b/libsecp256k1/src/testrand_impl.h new file mode 100644 index 0000000..30a91e5 --- /dev/null +++ b/libsecp256k1/src/testrand_impl.h @@ -0,0 +1,110 @@ +/********************************************************************** + * Copyright (c) 2013-2015 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_TESTRAND_IMPL_H +#define SECP256K1_TESTRAND_IMPL_H + +#include +#include + +#include "testrand.h" +#include "hash.h" + +static secp256k1_rfc6979_hmac_sha256 secp256k1_test_rng; +static uint32_t secp256k1_test_rng_precomputed[8]; +static int secp256k1_test_rng_precomputed_used = 8; +static uint64_t secp256k1_test_rng_integer; +static int secp256k1_test_rng_integer_bits_left = 0; + +SECP256K1_INLINE static void secp256k1_rand_seed(const unsigned char *seed16) { + secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16); +} + +SECP256K1_INLINE static uint32_t secp256k1_rand32(void) { + if (secp256k1_test_rng_precomputed_used == 8) { + secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed)); + secp256k1_test_rng_precomputed_used = 0; + } + return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++]; +} + +static uint32_t secp256k1_rand_bits(int bits) { + uint32_t ret; + if (secp256k1_test_rng_integer_bits_left < bits) { + secp256k1_test_rng_integer |= (((uint64_t)secp256k1_rand32()) << secp256k1_test_rng_integer_bits_left); + secp256k1_test_rng_integer_bits_left += 32; + } + ret = secp256k1_test_rng_integer; + secp256k1_test_rng_integer >>= bits; + secp256k1_test_rng_integer_bits_left -= bits; + ret &= ((~((uint32_t)0)) >> (32 - bits)); + return ret; +} + +static uint32_t secp256k1_rand_int(uint32_t range) { + /* We want a uniform integer between 0 and range-1, inclusive. + * B is the smallest number such that range <= 2**B. + * two mechanisms implemented here: + * - generate B bits numbers until one below range is found, and return it + * - find the largest multiple M of range that is <= 2**(B+A), generate B+A + * bits numbers until one below M is found, and return it modulo range + * The second mechanism consumes A more bits of entropy in every iteration, + * but may need fewer iterations due to M being closer to 2**(B+A) then + * range is to 2**B. The array below (indexed by B) contains a 0 when the + * first mechanism is to be used, and the number A otherwise. + */ + static const int addbits[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0}; + uint32_t trange, mult; + int bits = 0; + if (range <= 1) { + return 0; + } + trange = range - 1; + while (trange > 0) { + trange >>= 1; + bits++; + } + if (addbits[bits]) { + bits = bits + addbits[bits]; + mult = ((~((uint32_t)0)) >> (32 - bits)) / range; + trange = range * mult; + } else { + trange = range; + mult = 1; + } + while(1) { + uint32_t x = secp256k1_rand_bits(bits); + if (x < trange) { + return (mult == 1) ? x : (x % range); + } + } +} + +static void secp256k1_rand256(unsigned char *b32) { + secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32); +} + +static void secp256k1_rand_bytes_test(unsigned char *bytes, size_t len) { + size_t bits = 0; + memset(bytes, 0, len); + while (bits < len * 8) { + int now; + uint32_t val; + now = 1 + (secp256k1_rand_bits(6) * secp256k1_rand_bits(5) + 16) / 31; + val = secp256k1_rand_bits(1); + while (now > 0 && bits < len * 8) { + bytes[bits / 8] |= val << (bits % 8); + now--; + bits++; + } + } +} + +static void secp256k1_rand256_test(unsigned char *b32) { + secp256k1_rand_bytes_test(b32, 32); +} + +#endif /* SECP256K1_TESTRAND_IMPL_H */ diff --git a/libsecp256k1/src/tests.c b/libsecp256k1/src/tests.c new file mode 100644 index 0000000..324b60c --- /dev/null +++ b/libsecp256k1/src/tests.c @@ -0,0 +1,5453 @@ +/********************************************************************** + * Copyright (c) 2013, 2014, 2015 Pieter Wuille, Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include +#include + +#include + +#include "secp256k1.c" +#include "include/secp256k1.h" +#include "include/secp256k1_preallocated.h" +#include "testrand_impl.h" + +#ifdef ENABLE_OPENSSL_TESTS +#include "openssl/bn.h" +#include "openssl/ec.h" +#include "openssl/ecdsa.h" +#include "openssl/obj_mac.h" +# if OPENSSL_VERSION_NUMBER < 0x10100000L +void ECDSA_SIG_get0(const ECDSA_SIG *sig, const BIGNUM **pr, const BIGNUM **ps) {*pr = sig->r; *ps = sig->s;} +# endif +#endif + +#include "contrib/lax_der_parsing.c" +#include "contrib/lax_der_privatekey_parsing.c" + +#if !defined(VG_CHECK) +# if defined(VALGRIND) +# include +# define VG_UNDEF(x,y) VALGRIND_MAKE_MEM_UNDEFINED((x),(y)) +# define VG_CHECK(x,y) VALGRIND_CHECK_MEM_IS_DEFINED((x),(y)) +# else +# define VG_UNDEF(x,y) +# define VG_CHECK(x,y) +# endif +#endif + +static int count = 64; +static secp256k1_context *ctx = NULL; + +static void counting_illegal_callback_fn(const char* str, void* data) { + /* Dummy callback function that just counts. */ + int32_t *p; + (void)str; + p = data; + (*p)++; +} + +static void uncounting_illegal_callback_fn(const char* str, void* data) { + /* Dummy callback function that just counts (backwards). */ + int32_t *p; + (void)str; + p = data; + (*p)--; +} + +void random_field_element_test(secp256k1_fe *fe) { + do { + unsigned char b32[32]; + secp256k1_rand256_test(b32); + if (secp256k1_fe_set_b32(fe, b32)) { + break; + } + } while(1); +} + +void random_field_element_magnitude(secp256k1_fe *fe) { + secp256k1_fe zero; + int n = secp256k1_rand_int(9); + secp256k1_fe_normalize(fe); + if (n == 0) { + return; + } + secp256k1_fe_clear(&zero); + secp256k1_fe_negate(&zero, &zero, 0); + secp256k1_fe_mul_int(&zero, n - 1); + secp256k1_fe_add(fe, &zero); +#ifdef VERIFY + CHECK(fe->magnitude == n); +#endif +} + +void random_group_element_test(secp256k1_ge *ge) { + secp256k1_fe fe; + do { + random_field_element_test(&fe); + if (secp256k1_ge_set_xo_var(ge, &fe, secp256k1_rand_bits(1))) { + secp256k1_fe_normalize(&ge->y); + break; + } + } while(1); +} + +void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge *ge) { + secp256k1_fe z2, z3; + do { + random_field_element_test(&gej->z); + if (!secp256k1_fe_is_zero(&gej->z)) { + break; + } + } while(1); + secp256k1_fe_sqr(&z2, &gej->z); + secp256k1_fe_mul(&z3, &z2, &gej->z); + secp256k1_fe_mul(&gej->x, &ge->x, &z2); + secp256k1_fe_mul(&gej->y, &ge->y, &z3); + gej->infinity = ge->infinity; +} + +void random_scalar_order_test(secp256k1_scalar *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_rand256_test(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) { + continue; + } + break; + } while(1); +} + +void random_scalar_order(secp256k1_scalar *num) { + do { + unsigned char b32[32]; + int overflow = 0; + secp256k1_rand256(b32); + secp256k1_scalar_set_b32(num, b32, &overflow); + if (overflow || secp256k1_scalar_is_zero(num)) { + continue; + } + break; + } while(1); +} + +void random_scalar_order_b32(unsigned char *b32) { + secp256k1_scalar num; + random_scalar_order(&num); + secp256k1_scalar_get_b32(b32, &num); +} + +void run_context_tests(int use_prealloc) { + secp256k1_pubkey pubkey; + secp256k1_pubkey zero_pubkey; + secp256k1_ecdsa_signature sig; + unsigned char ctmp[32]; + int32_t ecount; + int32_t ecount2; + secp256k1_context *none; + secp256k1_context *sign; + secp256k1_context *vrfy; + secp256k1_context *both; + void *none_prealloc = NULL; + void *sign_prealloc = NULL; + void *vrfy_prealloc = NULL; + void *both_prealloc = NULL; + + secp256k1_gej pubj; + secp256k1_ge pub; + secp256k1_scalar msg, key, nonce; + secp256k1_scalar sigr, sigs; + + if (use_prealloc) { + none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); + vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); + both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); + CHECK(none_prealloc != NULL); + CHECK(sign_prealloc != NULL); + CHECK(vrfy_prealloc != NULL); + CHECK(both_prealloc != NULL); + none = secp256k1_context_preallocated_create(none_prealloc, SECP256K1_CONTEXT_NONE); + sign = secp256k1_context_preallocated_create(sign_prealloc, SECP256K1_CONTEXT_SIGN); + vrfy = secp256k1_context_preallocated_create(vrfy_prealloc, SECP256K1_CONTEXT_VERIFY); + both = secp256k1_context_preallocated_create(both_prealloc, SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + } else { + none = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + sign = secp256k1_context_create(SECP256K1_CONTEXT_SIGN); + vrfy = secp256k1_context_create(SECP256K1_CONTEXT_VERIFY); + both = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + } + + memset(&zero_pubkey, 0, sizeof(zero_pubkey)); + + ecount = 0; + ecount2 = 10; + secp256k1_context_set_illegal_callback(vrfy, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_illegal_callback(sign, counting_illegal_callback_fn, &ecount2); + secp256k1_context_set_error_callback(sign, counting_illegal_callback_fn, NULL); + CHECK(vrfy->error_callback.fn != sign->error_callback.fn); + + /* check if sizes for cloning are consistent */ + CHECK(secp256k1_context_preallocated_clone_size(none) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); + CHECK(secp256k1_context_preallocated_clone_size(sign) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); + CHECK(secp256k1_context_preallocated_clone_size(vrfy) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); + CHECK(secp256k1_context_preallocated_clone_size(both) == secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); + + /*** clone and destroy all of them to make sure cloning was complete ***/ + { + secp256k1_context *ctx_tmp; + + if (use_prealloc) { + /* clone into a non-preallocated context and then again into a new preallocated one. */ + ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp); + free(none_prealloc); none_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(none_prealloc != NULL); + ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, none_prealloc); secp256k1_context_destroy(ctx_tmp); + + ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp); + free(sign_prealloc); sign_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(sign_prealloc != NULL); + ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, sign_prealloc); secp256k1_context_destroy(ctx_tmp); + + ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp); + free(vrfy_prealloc); vrfy_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(vrfy_prealloc != NULL); + ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, vrfy_prealloc); secp256k1_context_destroy(ctx_tmp); + + ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp); + free(both_prealloc); both_prealloc = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(both_prealloc != NULL); + ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, both_prealloc); secp256k1_context_destroy(ctx_tmp); + } else { + /* clone into a preallocated context and then again into a new non-preallocated one. */ + void *prealloc_tmp; + + prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_NONE)); CHECK(prealloc_tmp != NULL); + ctx_tmp = none; none = secp256k1_context_preallocated_clone(none, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); + ctx_tmp = none; none = secp256k1_context_clone(none); secp256k1_context_preallocated_destroy(ctx_tmp); + free(prealloc_tmp); + + prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN)); CHECK(prealloc_tmp != NULL); + ctx_tmp = sign; sign = secp256k1_context_preallocated_clone(sign, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); + ctx_tmp = sign; sign = secp256k1_context_clone(sign); secp256k1_context_preallocated_destroy(ctx_tmp); + free(prealloc_tmp); + + prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); + ctx_tmp = vrfy; vrfy = secp256k1_context_preallocated_clone(vrfy, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); + ctx_tmp = vrfy; vrfy = secp256k1_context_clone(vrfy); secp256k1_context_preallocated_destroy(ctx_tmp); + free(prealloc_tmp); + + prealloc_tmp = malloc(secp256k1_context_preallocated_size(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY)); CHECK(prealloc_tmp != NULL); + ctx_tmp = both; both = secp256k1_context_preallocated_clone(both, prealloc_tmp); secp256k1_context_destroy(ctx_tmp); + ctx_tmp = both; both = secp256k1_context_clone(both); secp256k1_context_preallocated_destroy(ctx_tmp); + free(prealloc_tmp); + } + } + + /* Verify that the error callback makes it across the clone. */ + CHECK(vrfy->error_callback.fn != sign->error_callback.fn); + /* And that it resets back to default. */ + secp256k1_context_set_error_callback(sign, NULL, NULL); + CHECK(vrfy->error_callback.fn == sign->error_callback.fn); + + /*** attempt to use them ***/ + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&both->ecmult_gen_ctx, &pubj, &key); + secp256k1_ge_set_gej(&pub, &pubj); + + /* Verify context-type checking illegal-argument errors. */ + memset(ctmp, 1, 32); + CHECK(secp256k1_ec_pubkey_create(vrfy, &pubkey, ctmp) == 0); + CHECK(ecount == 1); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(sign, &pubkey, ctmp) == 1); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ecdsa_sign(vrfy, &sig, ctmp, ctmp, NULL, NULL) == 0); + CHECK(ecount == 2); + VG_UNDEF(&sig, sizeof(sig)); + CHECK(secp256k1_ecdsa_sign(sign, &sig, ctmp, ctmp, NULL, NULL) == 1); + VG_CHECK(&sig, sizeof(sig)); + CHECK(ecount2 == 10); + CHECK(secp256k1_ecdsa_verify(sign, &sig, ctmp, &pubkey) == 0); + CHECK(ecount2 == 11); + CHECK(secp256k1_ecdsa_verify(vrfy, &sig, ctmp, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_tweak_add(sign, &pubkey, ctmp) == 0); + CHECK(ecount2 == 12); + CHECK(secp256k1_ec_pubkey_tweak_add(vrfy, &pubkey, ctmp) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_tweak_mul(sign, &pubkey, ctmp) == 0); + CHECK(ecount2 == 13); + CHECK(secp256k1_ec_pubkey_negate(vrfy, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_negate(sign, &pubkey) == 1); + CHECK(ecount == 2); + CHECK(secp256k1_ec_pubkey_negate(sign, NULL) == 0); + CHECK(ecount2 == 14); + CHECK(secp256k1_ec_pubkey_negate(vrfy, &zero_pubkey) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ec_pubkey_tweak_mul(vrfy, &pubkey, ctmp) == 1); + CHECK(ecount == 3); + CHECK(secp256k1_context_randomize(vrfy, ctmp) == 1); + CHECK(ecount == 3); + CHECK(secp256k1_context_randomize(vrfy, NULL) == 1); + CHECK(ecount == 3); + CHECK(secp256k1_context_randomize(sign, ctmp) == 1); + CHECK(ecount2 == 14); + CHECK(secp256k1_context_randomize(sign, NULL) == 1); + CHECK(ecount2 == 14); + secp256k1_context_set_illegal_callback(vrfy, NULL, NULL); + secp256k1_context_set_illegal_callback(sign, NULL, NULL); + + /* obtain a working nonce */ + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); + + /* try signing */ + CHECK(secp256k1_ecdsa_sig_sign(&sign->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); + CHECK(secp256k1_ecdsa_sig_sign(&both->ecmult_gen_ctx, &sigr, &sigs, &key, &msg, &nonce, NULL)); + + /* try verifying */ + CHECK(secp256k1_ecdsa_sig_verify(&vrfy->ecmult_ctx, &sigr, &sigs, &pub, &msg)); + CHECK(secp256k1_ecdsa_sig_verify(&both->ecmult_ctx, &sigr, &sigs, &pub, &msg)); + + /* cleanup */ + if (use_prealloc) { + secp256k1_context_preallocated_destroy(none); + secp256k1_context_preallocated_destroy(sign); + secp256k1_context_preallocated_destroy(vrfy); + secp256k1_context_preallocated_destroy(both); + free(none_prealloc); + free(sign_prealloc); + free(vrfy_prealloc); + free(both_prealloc); + } else { + secp256k1_context_destroy(none); + secp256k1_context_destroy(sign); + secp256k1_context_destroy(vrfy); + secp256k1_context_destroy(both); + } + /* Defined as no-op. */ + secp256k1_context_destroy(NULL); + secp256k1_context_preallocated_destroy(NULL); + +} + +void run_scratch_tests(void) { + const size_t adj_alloc = ((500 + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT; + + int32_t ecount = 0; + size_t checkpoint; + size_t checkpoint_2; + secp256k1_context *none = secp256k1_context_create(SECP256K1_CONTEXT_NONE); + secp256k1_scratch_space *scratch; + secp256k1_scratch_space local_scratch; + + /* Test public API */ + secp256k1_context_set_illegal_callback(none, counting_illegal_callback_fn, &ecount); + secp256k1_context_set_error_callback(none, counting_illegal_callback_fn, &ecount); + + scratch = secp256k1_scratch_space_create(none, 1000); + CHECK(scratch != NULL); + CHECK(ecount == 0); + + /* Test internal API */ + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size == 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* Allocating 500 bytes succeeds */ + checkpoint = secp256k1_scratch_checkpoint(&none->error_callback, scratch); + CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size != 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* Allocating another 500 bytes fails */ + CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) == NULL); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000 - adj_alloc); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 1) == 1000 - adj_alloc - (ALIGNMENT - 1)); + CHECK(scratch->alloc_size != 0); + CHECK(scratch->alloc_size % ALIGNMENT == 0); + + /* ...but it succeeds once we apply the checkpoint to undo it */ + secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); + CHECK(scratch->alloc_size == 0); + CHECK(secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0) == 1000); + CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) != NULL); + CHECK(scratch->alloc_size != 0); + + /* try to apply a bad checkpoint */ + checkpoint_2 = secp256k1_scratch_checkpoint(&none->error_callback, scratch); + secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint); + CHECK(ecount == 0); + secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, checkpoint_2); /* checkpoint_2 is after checkpoint */ + CHECK(ecount == 1); + secp256k1_scratch_apply_checkpoint(&none->error_callback, scratch, (size_t) -1); /* this is just wildly invalid */ + CHECK(ecount == 2); + + /* try to use badly initialized scratch space */ + secp256k1_scratch_space_destroy(none, scratch); + memset(&local_scratch, 0, sizeof(local_scratch)); + scratch = &local_scratch; + CHECK(!secp256k1_scratch_max_allocation(&none->error_callback, scratch, 0)); + CHECK(ecount == 3); + CHECK(secp256k1_scratch_alloc(&none->error_callback, scratch, 500) == NULL); + CHECK(ecount == 4); + secp256k1_scratch_space_destroy(none, scratch); + CHECK(ecount == 5); + + /* cleanup */ + secp256k1_scratch_space_destroy(none, NULL); /* no-op */ + secp256k1_context_destroy(none); +} + +/***** HASH TESTS *****/ + +void run_sha256_tests(void) { + static const char *inputs[8] = { + "", "abc", "message digest", "secure hash algorithm", "SHA256 is considered to be safe", + "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq", + "For this sample, this 63-byte string will be used as input data", + "This is exactly 64 bytes long, not counting the terminating byte" + }; + static const unsigned char outputs[8][32] = { + {0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}, + {0xba, 0x78, 0x16, 0xbf, 0x8f, 0x01, 0xcf, 0xea, 0x41, 0x41, 0x40, 0xde, 0x5d, 0xae, 0x22, 0x23, 0xb0, 0x03, 0x61, 0xa3, 0x96, 0x17, 0x7a, 0x9c, 0xb4, 0x10, 0xff, 0x61, 0xf2, 0x00, 0x15, 0xad}, + {0xf7, 0x84, 0x6f, 0x55, 0xcf, 0x23, 0xe1, 0x4e, 0xeb, 0xea, 0xb5, 0xb4, 0xe1, 0x55, 0x0c, 0xad, 0x5b, 0x50, 0x9e, 0x33, 0x48, 0xfb, 0xc4, 0xef, 0xa3, 0xa1, 0x41, 0x3d, 0x39, 0x3c, 0xb6, 0x50}, + {0xf3, 0x0c, 0xeb, 0x2b, 0xb2, 0x82, 0x9e, 0x79, 0xe4, 0xca, 0x97, 0x53, 0xd3, 0x5a, 0x8e, 0xcc, 0x00, 0x26, 0x2d, 0x16, 0x4c, 0xc0, 0x77, 0x08, 0x02, 0x95, 0x38, 0x1c, 0xbd, 0x64, 0x3f, 0x0d}, + {0x68, 0x19, 0xd9, 0x15, 0xc7, 0x3f, 0x4d, 0x1e, 0x77, 0xe4, 0xe1, 0xb5, 0x2d, 0x1f, 0xa0, 0xf9, 0xcf, 0x9b, 0xea, 0xea, 0xd3, 0x93, 0x9f, 0x15, 0x87, 0x4b, 0xd9, 0x88, 0xe2, 0xa2, 0x36, 0x30}, + {0x24, 0x8d, 0x6a, 0x61, 0xd2, 0x06, 0x38, 0xb8, 0xe5, 0xc0, 0x26, 0x93, 0x0c, 0x3e, 0x60, 0x39, 0xa3, 0x3c, 0xe4, 0x59, 0x64, 0xff, 0x21, 0x67, 0xf6, 0xec, 0xed, 0xd4, 0x19, 0xdb, 0x06, 0xc1}, + {0xf0, 0x8a, 0x78, 0xcb, 0xba, 0xee, 0x08, 0x2b, 0x05, 0x2a, 0xe0, 0x70, 0x8f, 0x32, 0xfa, 0x1e, 0x50, 0xc5, 0xc4, 0x21, 0xaa, 0x77, 0x2b, 0xa5, 0xdb, 0xb4, 0x06, 0xa2, 0xea, 0x6b, 0xe3, 0x42}, + {0xab, 0x64, 0xef, 0xf7, 0xe8, 0x8e, 0x2e, 0x46, 0x16, 0x5e, 0x29, 0xf2, 0xbc, 0xe4, 0x18, 0x26, 0xbd, 0x4c, 0x7b, 0x35, 0x52, 0xf6, 0xb3, 0x82, 0xa9, 0xe7, 0xd3, 0xaf, 0x47, 0xc2, 0x45, 0xf8} + }; + int i; + for (i = 0; i < 8; i++) { + unsigned char out[32]; + secp256k1_sha256 hasher; + secp256k1_sha256_initialize(&hasher); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + secp256k1_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + if (strlen(inputs[i]) > 0) { + int split = secp256k1_rand_int(strlen(inputs[i])); + secp256k1_sha256_initialize(&hasher); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + secp256k1_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + } + } +} + +void run_hmac_sha256_tests(void) { + static const char *keys[6] = { + "\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b\x0b", + "\x4a\x65\x66\x65", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa", + "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa" + }; + static const char *inputs[6] = { + "\x48\x69\x20\x54\x68\x65\x72\x65", + "\x77\x68\x61\x74\x20\x64\x6f\x20\x79\x61\x20\x77\x61\x6e\x74\x20\x66\x6f\x72\x20\x6e\x6f\x74\x68\x69\x6e\x67\x3f", + "\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd\xdd", + "\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd\xcd", + "\x54\x65\x73\x74\x20\x55\x73\x69\x6e\x67\x20\x4c\x61\x72\x67\x65\x72\x20\x54\x68\x61\x6e\x20\x42\x6c\x6f\x63\x6b\x2d\x53\x69\x7a\x65\x20\x4b\x65\x79\x20\x2d\x20\x48\x61\x73\x68\x20\x4b\x65\x79\x20\x46\x69\x72\x73\x74", + "\x54\x68\x69\x73\x20\x69\x73\x20\x61\x20\x74\x65\x73\x74\x20\x75\x73\x69\x6e\x67\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x6b\x65\x79\x20\x61\x6e\x64\x20\x61\x20\x6c\x61\x72\x67\x65\x72\x20\x74\x68\x61\x6e\x20\x62\x6c\x6f\x63\x6b\x2d\x73\x69\x7a\x65\x20\x64\x61\x74\x61\x2e\x20\x54\x68\x65\x20\x6b\x65\x79\x20\x6e\x65\x65\x64\x73\x20\x74\x6f\x20\x62\x65\x20\x68\x61\x73\x68\x65\x64\x20\x62\x65\x66\x6f\x72\x65\x20\x62\x65\x69\x6e\x67\x20\x75\x73\x65\x64\x20\x62\x79\x20\x74\x68\x65\x20\x48\x4d\x41\x43\x20\x61\x6c\x67\x6f\x72\x69\x74\x68\x6d\x2e" + }; + static const unsigned char outputs[6][32] = { + {0xb0, 0x34, 0x4c, 0x61, 0xd8, 0xdb, 0x38, 0x53, 0x5c, 0xa8, 0xaf, 0xce, 0xaf, 0x0b, 0xf1, 0x2b, 0x88, 0x1d, 0xc2, 0x00, 0xc9, 0x83, 0x3d, 0xa7, 0x26, 0xe9, 0x37, 0x6c, 0x2e, 0x32, 0xcf, 0xf7}, + {0x5b, 0xdc, 0xc1, 0x46, 0xbf, 0x60, 0x75, 0x4e, 0x6a, 0x04, 0x24, 0x26, 0x08, 0x95, 0x75, 0xc7, 0x5a, 0x00, 0x3f, 0x08, 0x9d, 0x27, 0x39, 0x83, 0x9d, 0xec, 0x58, 0xb9, 0x64, 0xec, 0x38, 0x43}, + {0x77, 0x3e, 0xa9, 0x1e, 0x36, 0x80, 0x0e, 0x46, 0x85, 0x4d, 0xb8, 0xeb, 0xd0, 0x91, 0x81, 0xa7, 0x29, 0x59, 0x09, 0x8b, 0x3e, 0xf8, 0xc1, 0x22, 0xd9, 0x63, 0x55, 0x14, 0xce, 0xd5, 0x65, 0xfe}, + {0x82, 0x55, 0x8a, 0x38, 0x9a, 0x44, 0x3c, 0x0e, 0xa4, 0xcc, 0x81, 0x98, 0x99, 0xf2, 0x08, 0x3a, 0x85, 0xf0, 0xfa, 0xa3, 0xe5, 0x78, 0xf8, 0x07, 0x7a, 0x2e, 0x3f, 0xf4, 0x67, 0x29, 0x66, 0x5b}, + {0x60, 0xe4, 0x31, 0x59, 0x1e, 0xe0, 0xb6, 0x7f, 0x0d, 0x8a, 0x26, 0xaa, 0xcb, 0xf5, 0xb7, 0x7f, 0x8e, 0x0b, 0xc6, 0x21, 0x37, 0x28, 0xc5, 0x14, 0x05, 0x46, 0x04, 0x0f, 0x0e, 0xe3, 0x7f, 0x54}, + {0x9b, 0x09, 0xff, 0xa7, 0x1b, 0x94, 0x2f, 0xcb, 0x27, 0x63, 0x5f, 0xbc, 0xd5, 0xb0, 0xe9, 0x44, 0xbf, 0xdc, 0x63, 0x64, 0x4f, 0x07, 0x13, 0x93, 0x8a, 0x7f, 0x51, 0x53, 0x5c, 0x3a, 0x35, 0xe2} + }; + int i; + for (i = 0; i < 6; i++) { + secp256k1_hmac_sha256 hasher; + unsigned char out[32]; + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), strlen(inputs[i])); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + if (strlen(inputs[i]) > 0) { + int split = secp256k1_rand_int(strlen(inputs[i])); + secp256k1_hmac_sha256_initialize(&hasher, (const unsigned char*)(keys[i]), strlen(keys[i])); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i]), split); + secp256k1_hmac_sha256_write(&hasher, (const unsigned char*)(inputs[i] + split), strlen(inputs[i]) - split); + secp256k1_hmac_sha256_finalize(&hasher, out); + CHECK(memcmp(out, outputs[i], 32) == 0); + } + } +} + +void run_rfc6979_hmac_sha256_tests(void) { + static const unsigned char key1[65] = {0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x4b, 0xf5, 0x12, 0x2f, 0x34, 0x45, 0x54, 0xc5, 0x3b, 0xde, 0x2e, 0xbb, 0x8c, 0xd2, 0xb7, 0xe3, 0xd1, 0x60, 0x0a, 0xd6, 0x31, 0xc3, 0x85, 0xa5, 0xd7, 0xcc, 0xe2, 0x3c, 0x77, 0x85, 0x45, 0x9a, 0}; + static const unsigned char out1[3][32] = { + {0x4f, 0xe2, 0x95, 0x25, 0xb2, 0x08, 0x68, 0x09, 0x15, 0x9a, 0xcd, 0xf0, 0x50, 0x6e, 0xfb, 0x86, 0xb0, 0xec, 0x93, 0x2c, 0x7b, 0xa4, 0x42, 0x56, 0xab, 0x32, 0x1e, 0x42, 0x1e, 0x67, 0xe9, 0xfb}, + {0x2b, 0xf0, 0xff, 0xf1, 0xd3, 0xc3, 0x78, 0xa2, 0x2d, 0xc5, 0xde, 0x1d, 0x85, 0x65, 0x22, 0x32, 0x5c, 0x65, 0xb5, 0x04, 0x49, 0x1a, 0x0c, 0xbd, 0x01, 0xcb, 0x8f, 0x3a, 0xa6, 0x7f, 0xfd, 0x4a}, + {0xf5, 0x28, 0xb4, 0x10, 0xcb, 0x54, 0x1f, 0x77, 0x00, 0x0d, 0x7a, 0xfb, 0x6c, 0x5b, 0x53, 0xc5, 0xc4, 0x71, 0xea, 0xb4, 0x3e, 0x46, 0x6d, 0x9a, 0xc5, 0x19, 0x0c, 0x39, 0xc8, 0x2f, 0xd8, 0x2e} + }; + + static const unsigned char key2[64] = {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xb0, 0xc4, 0x42, 0x98, 0xfc, 0x1c, 0x14, 0x9a, 0xfb, 0xf4, 0xc8, 0x99, 0x6f, 0xb9, 0x24, 0x27, 0xae, 0x41, 0xe4, 0x64, 0x9b, 0x93, 0x4c, 0xa4, 0x95, 0x99, 0x1b, 0x78, 0x52, 0xb8, 0x55}; + static const unsigned char out2[3][32] = { + {0x9c, 0x23, 0x6c, 0x16, 0x5b, 0x82, 0xae, 0x0c, 0xd5, 0x90, 0x65, 0x9e, 0x10, 0x0b, 0x6b, 0xab, 0x30, 0x36, 0xe7, 0xba, 0x8b, 0x06, 0x74, 0x9b, 0xaf, 0x69, 0x81, 0xe1, 0x6f, 0x1a, 0x2b, 0x95}, + {0xdf, 0x47, 0x10, 0x61, 0x62, 0x5b, 0xc0, 0xea, 0x14, 0xb6, 0x82, 0xfe, 0xee, 0x2c, 0x9c, 0x02, 0xf2, 0x35, 0xda, 0x04, 0x20, 0x4c, 0x1d, 0x62, 0xa1, 0x53, 0x6c, 0x6e, 0x17, 0xae, 0xd7, 0xa9}, + {0x75, 0x97, 0x88, 0x7c, 0xbd, 0x76, 0x32, 0x1f, 0x32, 0xe3, 0x04, 0x40, 0x67, 0x9a, 0x22, 0xcf, 0x7f, 0x8d, 0x9d, 0x2e, 0xac, 0x39, 0x0e, 0x58, 0x1f, 0xea, 0x09, 0x1c, 0xe2, 0x02, 0xba, 0x94} + }; + + secp256k1_rfc6979_hmac_sha256 rng; + unsigned char out[32]; + int i; + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 64); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out1[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key1, 65); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out1[i], 32) != 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); + + secp256k1_rfc6979_hmac_sha256_initialize(&rng, key2, 64); + for (i = 0; i < 3; i++) { + secp256k1_rfc6979_hmac_sha256_generate(&rng, out, 32); + CHECK(memcmp(out, out2[i], 32) == 0); + } + secp256k1_rfc6979_hmac_sha256_finalize(&rng); +} + +/***** RANDOM TESTS *****/ + +void test_rand_bits(int rand32, int bits) { + /* (1-1/2^B)^rounds[B] < 1/10^9, so rounds is the number of iterations to + * get a false negative chance below once in a billion */ + static const unsigned int rounds[7] = {1, 30, 73, 156, 322, 653, 1316}; + /* We try multiplying the results with various odd numbers, which shouldn't + * influence the uniform distribution modulo a power of 2. */ + static const uint32_t mults[6] = {1, 3, 21, 289, 0x9999, 0x80402011}; + /* We only select up to 6 bits from the output to analyse */ + unsigned int usebits = bits > 6 ? 6 : bits; + unsigned int maxshift = bits - usebits; + /* For each of the maxshift+1 usebits-bit sequences inside a bits-bit + number, track all observed outcomes, one per bit in a uint64_t. */ + uint64_t x[6][27] = {{0}}; + unsigned int i, shift, m; + /* Multiply the output of all rand calls with the odd number m, which + should not change the uniformity of its distribution. */ + for (i = 0; i < rounds[usebits]; i++) { + uint32_t r = (rand32 ? secp256k1_rand32() : secp256k1_rand_bits(bits)); + CHECK((((uint64_t)r) >> bits) == 0); + for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) { + uint32_t rm = r * mults[m]; + for (shift = 0; shift <= maxshift; shift++) { + x[m][shift] |= (((uint64_t)1) << ((rm >> shift) & ((1 << usebits) - 1))); + } + } + } + for (m = 0; m < sizeof(mults) / sizeof(mults[0]); m++) { + for (shift = 0; shift <= maxshift; shift++) { + /* Test that the lower usebits bits of x[shift] are 1 */ + CHECK(((~x[m][shift]) << (64 - (1 << usebits))) == 0); + } + } +} + +/* Subrange must be a whole divisor of range, and at most 64 */ +void test_rand_int(uint32_t range, uint32_t subrange) { + /* (1-1/subrange)^rounds < 1/10^9 */ + int rounds = (subrange * 2073) / 100; + int i; + uint64_t x = 0; + CHECK((range % subrange) == 0); + for (i = 0; i < rounds; i++) { + uint32_t r = secp256k1_rand_int(range); + CHECK(r < range); + r = r % subrange; + x |= (((uint64_t)1) << r); + } + /* Test that the lower subrange bits of x are 1. */ + CHECK(((~x) << (64 - subrange)) == 0); +} + +void run_rand_bits(void) { + size_t b; + test_rand_bits(1, 32); + for (b = 1; b <= 32; b++) { + test_rand_bits(0, b); + } +} + +void run_rand_int(void) { + static const uint32_t ms[] = {1, 3, 17, 1000, 13771, 999999, 33554432}; + static const uint32_t ss[] = {1, 3, 6, 9, 13, 31, 64}; + unsigned int m, s; + for (m = 0; m < sizeof(ms) / sizeof(ms[0]); m++) { + for (s = 0; s < sizeof(ss) / sizeof(ss[0]); s++) { + test_rand_int(ms[m] * ss[s], ss[s]); + } + } +} + +/***** NUM TESTS *****/ + +#ifndef USE_NUM_NONE +void random_num_negate(secp256k1_num *num) { + if (secp256k1_rand_bits(1)) { + secp256k1_num_negate(num); + } +} + +void random_num_order_test(secp256k1_num *num) { + secp256k1_scalar sc; + random_scalar_order_test(&sc); + secp256k1_scalar_get_num(num, &sc); +} + +void random_num_order(secp256k1_num *num) { + secp256k1_scalar sc; + random_scalar_order(&sc); + secp256k1_scalar_get_num(num, &sc); +} + +void test_num_negate(void) { + secp256k1_num n1; + secp256k1_num n2; + random_num_order_test(&n1); /* n1 = R */ + random_num_negate(&n1); + secp256k1_num_copy(&n2, &n1); /* n2 = R */ + secp256k1_num_sub(&n1, &n2, &n1); /* n1 = n2-n1 = 0 */ + CHECK(secp256k1_num_is_zero(&n1)); + secp256k1_num_copy(&n1, &n2); /* n1 = R */ + secp256k1_num_negate(&n1); /* n1 = -R */ + CHECK(!secp256k1_num_is_zero(&n1)); + secp256k1_num_add(&n1, &n2, &n1); /* n1 = n2+n1 = 0 */ + CHECK(secp256k1_num_is_zero(&n1)); + secp256k1_num_copy(&n1, &n2); /* n1 = R */ + secp256k1_num_negate(&n1); /* n1 = -R */ + CHECK(secp256k1_num_is_neg(&n1) != secp256k1_num_is_neg(&n2)); + secp256k1_num_negate(&n1); /* n1 = R */ + CHECK(secp256k1_num_eq(&n1, &n2)); +} + +void test_num_add_sub(void) { + int i; + secp256k1_scalar s; + secp256k1_num n1; + secp256k1_num n2; + secp256k1_num n1p2, n2p1, n1m2, n2m1; + random_num_order_test(&n1); /* n1 = R1 */ + if (secp256k1_rand_bits(1)) { + random_num_negate(&n1); + } + random_num_order_test(&n2); /* n2 = R2 */ + if (secp256k1_rand_bits(1)) { + random_num_negate(&n2); + } + secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = R1 + R2 */ + secp256k1_num_add(&n2p1, &n2, &n1); /* n2p1 = R2 + R1 */ + secp256k1_num_sub(&n1m2, &n1, &n2); /* n1m2 = R1 - R2 */ + secp256k1_num_sub(&n2m1, &n2, &n1); /* n2m1 = R2 - R1 */ + CHECK(secp256k1_num_eq(&n1p2, &n2p1)); + CHECK(!secp256k1_num_eq(&n1p2, &n1m2)); + secp256k1_num_negate(&n2m1); /* n2m1 = -R2 + R1 */ + CHECK(secp256k1_num_eq(&n2m1, &n1m2)); + CHECK(!secp256k1_num_eq(&n2m1, &n1)); + secp256k1_num_add(&n2m1, &n2m1, &n2); /* n2m1 = -R2 + R1 + R2 = R1 */ + CHECK(secp256k1_num_eq(&n2m1, &n1)); + CHECK(!secp256k1_num_eq(&n2p1, &n1)); + secp256k1_num_sub(&n2p1, &n2p1, &n2); /* n2p1 = R2 + R1 - R2 = R1 */ + CHECK(secp256k1_num_eq(&n2p1, &n1)); + + /* check is_one */ + secp256k1_scalar_set_int(&s, 1); + secp256k1_scalar_get_num(&n1, &s); + CHECK(secp256k1_num_is_one(&n1)); + /* check that 2^n + 1 is never 1 */ + secp256k1_scalar_get_num(&n2, &s); + for (i = 0; i < 250; ++i) { + secp256k1_num_add(&n1, &n1, &n1); /* n1 *= 2 */ + secp256k1_num_add(&n1p2, &n1, &n2); /* n1p2 = n1 + 1 */ + CHECK(!secp256k1_num_is_one(&n1p2)); + } +} + +void test_num_mod(void) { + int i; + secp256k1_scalar s; + secp256k1_num order, n; + + /* check that 0 mod anything is 0 */ + random_scalar_order_test(&s); + secp256k1_scalar_get_num(&order, &s); + secp256k1_scalar_set_int(&s, 0); + secp256k1_scalar_get_num(&n, &s); + secp256k1_num_mod(&n, &order); + CHECK(secp256k1_num_is_zero(&n)); + + /* check that anything mod 1 is 0 */ + secp256k1_scalar_set_int(&s, 1); + secp256k1_scalar_get_num(&order, &s); + secp256k1_scalar_get_num(&n, &s); + secp256k1_num_mod(&n, &order); + CHECK(secp256k1_num_is_zero(&n)); + + /* check that increasing the number past 2^256 does not break this */ + random_scalar_order_test(&s); + secp256k1_scalar_get_num(&n, &s); + /* multiply by 2^8, which'll test this case with high probability */ + for (i = 0; i < 8; ++i) { + secp256k1_num_add(&n, &n, &n); + } + secp256k1_num_mod(&n, &order); + CHECK(secp256k1_num_is_zero(&n)); +} + +void test_num_jacobi(void) { + secp256k1_scalar sqr; + secp256k1_scalar small; + secp256k1_scalar five; /* five is not a quadratic residue */ + secp256k1_num order, n; + int i; + /* squares mod 5 are 1, 4 */ + const int jacobi5[10] = { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1 }; + + /* check some small values with 5 as the order */ + secp256k1_scalar_set_int(&five, 5); + secp256k1_scalar_get_num(&order, &five); + for (i = 0; i < 10; ++i) { + secp256k1_scalar_set_int(&small, i); + secp256k1_scalar_get_num(&n, &small); + CHECK(secp256k1_num_jacobi(&n, &order) == jacobi5[i]); + } + + /** test large values with 5 as group order */ + secp256k1_scalar_get_num(&order, &five); + /* we first need a scalar which is not a multiple of 5 */ + do { + secp256k1_num fiven; + random_scalar_order_test(&sqr); + secp256k1_scalar_get_num(&fiven, &five); + secp256k1_scalar_get_num(&n, &sqr); + secp256k1_num_mod(&n, &fiven); + } while (secp256k1_num_is_zero(&n)); + /* next force it to be a residue. 2 is a nonresidue mod 5 so we can + * just multiply by two, i.e. add the number to itself */ + if (secp256k1_num_jacobi(&n, &order) == -1) { + secp256k1_num_add(&n, &n, &n); + } + + /* test residue */ + CHECK(secp256k1_num_jacobi(&n, &order) == 1); + /* test nonresidue */ + secp256k1_num_add(&n, &n, &n); + CHECK(secp256k1_num_jacobi(&n, &order) == -1); + + /** test with secp group order as order */ + secp256k1_scalar_order_get_num(&order); + random_scalar_order_test(&sqr); + secp256k1_scalar_sqr(&sqr, &sqr); + /* test residue */ + secp256k1_scalar_get_num(&n, &sqr); + CHECK(secp256k1_num_jacobi(&n, &order) == 1); + /* test nonresidue */ + secp256k1_scalar_mul(&sqr, &sqr, &five); + secp256k1_scalar_get_num(&n, &sqr); + CHECK(secp256k1_num_jacobi(&n, &order) == -1); + /* test multiple of the order*/ + CHECK(secp256k1_num_jacobi(&order, &order) == 0); + + /* check one less than the order */ + secp256k1_scalar_set_int(&small, 1); + secp256k1_scalar_get_num(&n, &small); + secp256k1_num_sub(&n, &order, &n); + CHECK(secp256k1_num_jacobi(&n, &order) == 1); /* sage confirms this is 1 */ +} + +void run_num_smalltests(void) { + int i; + for (i = 0; i < 100*count; i++) { + test_num_negate(); + test_num_add_sub(); + test_num_mod(); + test_num_jacobi(); + } +} +#endif + +/***** SCALAR TESTS *****/ + +void scalar_test(void) { + secp256k1_scalar s; + secp256k1_scalar s1; + secp256k1_scalar s2; +#ifndef USE_NUM_NONE + secp256k1_num snum, s1num, s2num; + secp256k1_num order, half_order; +#endif + unsigned char c[32]; + + /* Set 's' to a random scalar, with value 'snum'. */ + random_scalar_order_test(&s); + + /* Set 's1' to a random scalar, with value 's1num'. */ + random_scalar_order_test(&s1); + + /* Set 's2' to a random scalar, with value 'snum2', and byte array representation 'c'. */ + random_scalar_order_test(&s2); + secp256k1_scalar_get_b32(c, &s2); + +#ifndef USE_NUM_NONE + secp256k1_scalar_get_num(&snum, &s); + secp256k1_scalar_get_num(&s1num, &s1); + secp256k1_scalar_get_num(&s2num, &s2); + + secp256k1_scalar_order_get_num(&order); + half_order = order; + secp256k1_num_shift(&half_order, 1); +#endif + + { + int i; + /* Test that fetching groups of 4 bits from a scalar and recursing n(i)=16*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar n; + secp256k1_scalar_set_int(&n, 0); + for (i = 0; i < 256; i += 4) { + secp256k1_scalar t; + int j; + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits(&s, 256 - 4 - i, 4)); + for (j = 0; j < 4; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + + { + /* Test that fetching groups of randomly-sized bits from a scalar and recursing n(i)=b*n(i-1)+p(i) reconstructs it. */ + secp256k1_scalar n; + int i = 0; + secp256k1_scalar_set_int(&n, 0); + while (i < 256) { + secp256k1_scalar t; + int j; + int now = secp256k1_rand_int(15) + 1; + if (now + i > 256) { + now = 256 - i; + } + secp256k1_scalar_set_int(&t, secp256k1_scalar_get_bits_var(&s, 256 - now - i, now)); + for (j = 0; j < now; j++) { + secp256k1_scalar_add(&n, &n, &n); + } + secp256k1_scalar_add(&n, &n, &t); + i += now; + } + CHECK(secp256k1_scalar_eq(&n, &s)); + } + +#ifndef USE_NUM_NONE + { + /* Test that adding the scalars together is equal to adding their numbers together modulo the order. */ + secp256k1_num rnum; + secp256k1_num r2num; + secp256k1_scalar r; + secp256k1_num_add(&rnum, &snum, &s2num); + secp256k1_num_mod(&rnum, &order); + secp256k1_scalar_add(&r, &s, &s2); + secp256k1_scalar_get_num(&r2num, &r); + CHECK(secp256k1_num_eq(&rnum, &r2num)); + } + + { + /* Test that multiplying the scalars is equal to multiplying their numbers modulo the order. */ + secp256k1_scalar r; + secp256k1_num r2num; + secp256k1_num rnum; + secp256k1_num_mul(&rnum, &snum, &s2num); + secp256k1_num_mod(&rnum, &order); + secp256k1_scalar_mul(&r, &s, &s2); + secp256k1_scalar_get_num(&r2num, &r); + CHECK(secp256k1_num_eq(&rnum, &r2num)); + /* The result can only be zero if at least one of the factors was zero. */ + CHECK(secp256k1_scalar_is_zero(&r) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_zero(&s2))); + /* The results can only be equal to one of the factors if that factor was zero, or the other factor was one. */ + CHECK(secp256k1_num_eq(&rnum, &snum) == (secp256k1_scalar_is_zero(&s) || secp256k1_scalar_is_one(&s2))); + CHECK(secp256k1_num_eq(&rnum, &s2num) == (secp256k1_scalar_is_zero(&s2) || secp256k1_scalar_is_one(&s))); + } + + { + secp256k1_scalar neg; + secp256k1_num negnum; + secp256k1_num negnum2; + /* Check that comparison with zero matches comparison with zero on the number. */ + CHECK(secp256k1_num_is_zero(&snum) == secp256k1_scalar_is_zero(&s)); + /* Check that comparison with the half order is equal to testing for high scalar. */ + CHECK(secp256k1_scalar_is_high(&s) == (secp256k1_num_cmp(&snum, &half_order) > 0)); + secp256k1_scalar_negate(&neg, &s); + secp256k1_num_sub(&negnum, &order, &snum); + secp256k1_num_mod(&negnum, &order); + /* Check that comparison with the half order is equal to testing for high scalar after negation. */ + CHECK(secp256k1_scalar_is_high(&neg) == (secp256k1_num_cmp(&negnum, &half_order) > 0)); + /* Negating should change the high property, unless the value was already zero. */ + CHECK((secp256k1_scalar_is_high(&s) == secp256k1_scalar_is_high(&neg)) == secp256k1_scalar_is_zero(&s)); + secp256k1_scalar_get_num(&negnum2, &neg); + /* Negating a scalar should be equal to (order - n) mod order on the number. */ + CHECK(secp256k1_num_eq(&negnum, &negnum2)); + secp256k1_scalar_add(&neg, &neg, &s); + /* Adding a number to its negation should result in zero. */ + CHECK(secp256k1_scalar_is_zero(&neg)); + secp256k1_scalar_negate(&neg, &neg); + /* Negating zero should still result in zero. */ + CHECK(secp256k1_scalar_is_zero(&neg)); + } + + { + /* Test secp256k1_scalar_mul_shift_var. */ + secp256k1_scalar r; + secp256k1_num one; + secp256k1_num rnum; + secp256k1_num rnum2; + unsigned char cone[1] = {0x01}; + unsigned int shift = 256 + secp256k1_rand_int(257); + secp256k1_scalar_mul_shift_var(&r, &s1, &s2, shift); + secp256k1_num_mul(&rnum, &s1num, &s2num); + secp256k1_num_shift(&rnum, shift - 1); + secp256k1_num_set_bin(&one, cone, 1); + secp256k1_num_add(&rnum, &rnum, &one); + secp256k1_num_shift(&rnum, 1); + secp256k1_scalar_get_num(&rnum2, &r); + CHECK(secp256k1_num_eq(&rnum, &rnum2)); + } + + { + /* test secp256k1_scalar_shr_int */ + secp256k1_scalar r; + int i; + random_scalar_order_test(&r); + for (i = 0; i < 100; ++i) { + int low; + int shift = 1 + secp256k1_rand_int(15); + int expected = r.d[0] % (1 << shift); + low = secp256k1_scalar_shr_int(&r, shift); + CHECK(expected == low); + } + } +#endif + + { + /* Test that scalar inverses are equal to the inverse of their number modulo the order. */ + if (!secp256k1_scalar_is_zero(&s)) { + secp256k1_scalar inv; +#ifndef USE_NUM_NONE + secp256k1_num invnum; + secp256k1_num invnum2; +#endif + secp256k1_scalar_inverse(&inv, &s); +#ifndef USE_NUM_NONE + secp256k1_num_mod_inverse(&invnum, &snum, &order); + secp256k1_scalar_get_num(&invnum2, &inv); + CHECK(secp256k1_num_eq(&invnum, &invnum2)); +#endif + secp256k1_scalar_mul(&inv, &inv, &s); + /* Multiplying a scalar with its inverse must result in one. */ + CHECK(secp256k1_scalar_is_one(&inv)); + secp256k1_scalar_inverse(&inv, &inv); + /* Inverting one must result in one. */ + CHECK(secp256k1_scalar_is_one(&inv)); +#ifndef USE_NUM_NONE + secp256k1_scalar_get_num(&invnum, &inv); + CHECK(secp256k1_num_is_one(&invnum)); +#endif + } + } + + { + /* Test commutativity of add. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + secp256k1_scalar r1, r2; + secp256k1_scalar b; + int i; + /* Test add_bit. */ + int bit = secp256k1_rand_bits(8); + secp256k1_scalar_set_int(&b, 1); + CHECK(secp256k1_scalar_is_one(&b)); + for (i = 0; i < bit; i++) { + secp256k1_scalar_add(&b, &b, &b); + } + r1 = s1; + r2 = s1; + if (!secp256k1_scalar_add(&r1, &r1, &b)) { + /* No overflow happened. */ + secp256k1_scalar_cadd_bit(&r2, bit, 1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + /* cadd is a noop when flag is zero */ + secp256k1_scalar_cadd_bit(&r2, bit, 0); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + } + + { + /* Test commutativity of mul. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r2, &s2, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of add. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_add(&r1, &r1, &s); + secp256k1_scalar_add(&r2, &s2, &s); + secp256k1_scalar_add(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test associativity of mul. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_mul(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s2, &s); + secp256k1_scalar_mul(&r2, &s1, &r2); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test distributitivity of mul over add. */ + secp256k1_scalar r1, r2, t; + secp256k1_scalar_add(&r1, &s1, &s2); + secp256k1_scalar_mul(&r1, &r1, &s); + secp256k1_scalar_mul(&r2, &s1, &s); + secp256k1_scalar_mul(&t, &s2, &s); + secp256k1_scalar_add(&r2, &r2, &t); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test square. */ + secp256k1_scalar r1, r2; + secp256k1_scalar_sqr(&r1, &s1); + secp256k1_scalar_mul(&r2, &s1, &s1); + CHECK(secp256k1_scalar_eq(&r1, &r2)); + } + + { + /* Test multiplicative identity. */ + secp256k1_scalar r1, v1; + secp256k1_scalar_set_int(&v1,1); + secp256k1_scalar_mul(&r1, &s1, &v1); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test additive identity. */ + secp256k1_scalar r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_add(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &s1)); + } + + { + /* Test zero product property. */ + secp256k1_scalar r1, v0; + secp256k1_scalar_set_int(&v0,0); + secp256k1_scalar_mul(&r1, &s1, &v0); + CHECK(secp256k1_scalar_eq(&r1, &v0)); + } + +} + +void run_scalar_set_b32_seckey_tests(void) { + unsigned char b32[32]; + secp256k1_scalar s1; + secp256k1_scalar s2; + + /* Usually set_b32 and set_b32_seckey give the same result */ + random_scalar_order_b32(b32); + secp256k1_scalar_set_b32(&s1, b32, NULL); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 1); + CHECK(secp256k1_scalar_eq(&s1, &s2) == 1); + + memset(b32, 0, sizeof(b32)); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); + memset(b32, 0xFF, sizeof(b32)); + CHECK(secp256k1_scalar_set_b32_seckey(&s2, b32) == 0); +} + +void run_scalar_tests(void) { + int i; + for (i = 0; i < 128 * count; i++) { + scalar_test(); + } + for (i = 0; i < count; i++) { + run_scalar_set_b32_seckey_tests(); + } + + { + /* (-1)+1 should be zero. */ + secp256k1_scalar s, o; + secp256k1_scalar_set_int(&s, 1); + CHECK(secp256k1_scalar_is_one(&s)); + secp256k1_scalar_negate(&o, &s); + secp256k1_scalar_add(&o, &o, &s); + CHECK(secp256k1_scalar_is_zero(&o)); + secp256k1_scalar_negate(&o, &o); + CHECK(secp256k1_scalar_is_zero(&o)); + } + +#ifndef USE_NUM_NONE + { + /* Test secp256k1_scalar_set_b32 boundary conditions */ + secp256k1_num order; + secp256k1_scalar scalar; + unsigned char bin[32]; + unsigned char bin_tmp[32]; + int overflow = 0; + /* 2^256-1 - order */ + static const secp256k1_scalar all_ones_minus_order = SECP256K1_SCALAR_CONST( + 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000001UL, + 0x45512319UL, 0x50B75FC4UL, 0x402DA173UL, 0x2FC9BEBEUL + ); + + /* A scalar set to 0s should be 0. */ + memset(bin, 0, 32); + secp256k1_scalar_set_b32(&scalar, bin, &overflow); + CHECK(overflow == 0); + CHECK(secp256k1_scalar_is_zero(&scalar)); + + /* A scalar with value of the curve order should be 0. */ + secp256k1_scalar_order_get_num(&order); + secp256k1_num_get_bin(bin, 32, &order); + secp256k1_scalar_set_b32(&scalar, bin, &overflow); + CHECK(overflow == 1); + CHECK(secp256k1_scalar_is_zero(&scalar)); + + /* A scalar with value of the curve order minus one should not overflow. */ + bin[31] -= 1; + secp256k1_scalar_set_b32(&scalar, bin, &overflow); + CHECK(overflow == 0); + secp256k1_scalar_get_b32(bin_tmp, &scalar); + CHECK(memcmp(bin, bin_tmp, 32) == 0); + + /* A scalar set to all 1s should overflow. */ + memset(bin, 0xFF, 32); + secp256k1_scalar_set_b32(&scalar, bin, &overflow); + CHECK(overflow == 1); + CHECK(secp256k1_scalar_eq(&scalar, &all_ones_minus_order)); + } +#endif + + { + /* Does check_overflow check catch all ones? */ + static const secp256k1_scalar overflowed = SECP256K1_SCALAR_CONST( + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, + 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL + ); + CHECK(secp256k1_scalar_check_overflow(&overflowed)); + } + + { + /* Static test vectors. + * These were reduced from ~10^12 random vectors based on comparison-decision + * and edge-case coverage on 32-bit and 64-bit implementations. + * The responses were generated with Sage 5.9. + */ + secp256k1_scalar x; + secp256k1_scalar y; + secp256k1_scalar z; + secp256k1_scalar zz; + secp256k1_scalar one; + secp256k1_scalar r1; + secp256k1_scalar r2; +#if defined(USE_SCALAR_INV_NUM) + secp256k1_scalar zzv; +#endif + int overflow; + unsigned char chal[33][2][32] = { + {{0xff, 0xff, 0x03, 0x07, 0x00, 0x00, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0xc0, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff}}, + {{0xef, 0xff, 0x1f, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, + 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x80, 0xff}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x06, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0x3f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0x00}, + {0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x0f, 0x00, 0xe0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x7f, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x1e, 0xf8, 0xff, 0xff, 0xff, 0xfd, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, + 0x00, 0x00, 0x00, 0xf8, 0xff, 0x03, 0x00, 0xe0, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0xf0, 0xff, + 0xf3, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x1c, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, + 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x1f, 0x00, 0x00, 0x80, 0xff, 0xff, 0x3f, + 0x00, 0xfe, 0xff, 0xff, 0xff, 0xdf, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0x00, 0x0f, 0xfc, 0x9f, + 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0x0f, 0xfc, 0xff, 0x7f, 0x00, 0x00, 0x00, + 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0x08, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0x00, 0x00, 0xf8, 0xff, 0x0f, 0xc0, 0xff, 0xff, + 0xff, 0x1f, 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x07, 0x80, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xf7, 0xff, 0xff, 0xef, 0xff, 0xff, 0xff, 0x00, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0xf0}, + {0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0x00, 0xf8, 0xff, 0x03, 0xff, 0xff, 0xff, 0x00, + 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0xc0, 0xff, 0x0f, 0xfc, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xe0, 0xff, 0xff, + 0xff, 0x01, 0x00, 0x00, 0x00, 0x3f, 0x00, 0xc0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0x8f, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x7f, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x80, 0xff, 0x7f}, + {0xff, 0xcf, 0xff, 0xff, 0x01, 0x00, 0x00, 0x00, + 0x00, 0xc0, 0xff, 0xcf, 0xff, 0xff, 0xff, 0xff, + 0xbf, 0xff, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x80, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x80, 0xff, 0xff, + 0xff, 0xff, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0x01, 0xfc, 0xff, 0x01, 0x00, 0xfe, 0xff}, + {0xff, 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc0, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x7f, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0xf8, 0xff, 0x01, 0x00, 0xf0, 0xff, 0xff, + 0xe0, 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, + 0xfc, 0xff, 0xff, 0x3f, 0xf0, 0xff, 0xff, 0x3f, + 0x00, 0x00, 0xf8, 0x07, 0x00, 0x00, 0x00, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x0f, 0x7e, 0x00, 0x00}}, + {{0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x1f, 0x00, 0x00, 0xfe, 0x07, 0x00}, + {0x00, 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xfb, 0xff, 0x07, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x60}}, + {{0xff, 0x01, 0x00, 0xff, 0xff, 0xff, 0x0f, 0x00, + 0x80, 0x7f, 0xfe, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0x1f, 0x00, 0xf0, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x00, 0x00}}, + {{0x80, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf1, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, + 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x7e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0xc0, 0xff, 0xff, 0xcf, 0xff, 0x1f, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x7e, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xfc, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x03, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x7c, 0x00}, + {0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0x7f, 0x00, 0x80, 0x00, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x3f, 0x00, 0x00, 0x80, + 0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, + 0xff, 0x7f, 0xf8, 0xff, 0xff, 0x1f, 0x00, 0xfe}}, + {{0xff, 0xff, 0xff, 0x3f, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0x03, 0xfe, 0x01, 0x00, 0x00, 0x00, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0x01, 0x80, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0xc0, + 0xff, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0x07, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0x01, 0xff, 0xff, 0xff}}, + {{0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x02}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0x7e, 0x00, 0x00, 0xc0, 0xff, 0xff, 0x07, 0x00, + 0x80, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x00, + 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0x01, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x03, 0x00, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}}, + {{0xff, 0xff, 0xf0, 0xff, 0xff, 0xff, 0xff, 0x00, + 0xf0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x00, 0xe0, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0xe0, 0xff, 0xff, + 0xff, 0xff, 0x3f, 0x00, 0xf8, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0x3f, 0x00, 0x00, 0xc0, 0xf1, 0x7f, 0x00}}, + {{0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0xc0, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0xff, 0xff, 0x00}, + {0x00, 0xf8, 0xff, 0xff, 0xff, 0xff, 0xff, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, + 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0x80, 0x1f, + 0x00, 0x00, 0xfc, 0xff, 0xff, 0x01, 0xff, 0xff}}, + {{0x00, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0x00, 0x00, 0x80, 0xff, 0x03, 0xe0, 0x01, + 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, + 0xfe, 0xff, 0xff, 0xf0, 0x07, 0x00, 0x3c, 0x80, + 0xff, 0xff, 0xff, 0xff, 0xfc, 0xff, 0xff, 0xff, + 0xff, 0xff, 0x07, 0xe0, 0xff, 0x00, 0x00, 0x00}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x00, + 0xfc, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x07, 0xf8, + 0x00, 0x00, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80}, + {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x0c, 0x80, 0x00, + 0x00, 0x00, 0x00, 0xc0, 0x7f, 0xfe, 0xff, 0x1f, + 0x00, 0xfe, 0xff, 0x03, 0x00, 0x00, 0xfe, 0xff}}, + {{0xff, 0xff, 0x81, 0xff, 0xff, 0xff, 0xff, 0x00, + 0x80, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x83, + 0xff, 0xff, 0x00, 0x00, 0x80, 0x00, 0x00, 0x80, + 0xff, 0xff, 0x7f, 0x00, 0x00, 0x00, 0x00, 0xf0}, + {0xff, 0x01, 0x00, 0x00, 0x00, 0x00, 0xf8, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x1f, 0x00, 0x00, + 0xf8, 0x07, 0x00, 0x80, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xc7, 0xff, 0xff, 0xe0, 0xff, 0xff, 0xff}}, + {{0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, + 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}, + {0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0x82, 0xc9, 0xfa, 0xb0, 0x68, 0x04, 0xa0, 0x00, + 0xff, 0xff, 0xff, 0xff, 0xff, 0x6f, 0x03, 0xfb, + 0xfa, 0x8a, 0x7d, 0xdf, 0x13, 0x86, 0xe2, 0x03}} + }; + unsigned char res[33][2][32] = { + {{0x0c, 0x3b, 0x0a, 0xca, 0x8d, 0x1a, 0x2f, 0xb9, + 0x8a, 0x7b, 0x53, 0x5a, 0x1f, 0xc5, 0x22, 0xa1, + 0x07, 0x2a, 0x48, 0xea, 0x02, 0xeb, 0xb3, 0xd6, + 0x20, 0x1e, 0x86, 0xd0, 0x95, 0xf6, 0x92, 0x35}, + {0xdc, 0x90, 0x7a, 0x07, 0x2e, 0x1e, 0x44, 0x6d, + 0xf8, 0x15, 0x24, 0x5b, 0x5a, 0x96, 0x37, 0x9c, + 0x37, 0x7b, 0x0d, 0xac, 0x1b, 0x65, 0x58, 0x49, + 0x43, 0xb7, 0x31, 0xbb, 0xa7, 0xf4, 0x97, 0x15}}, + {{0xf1, 0xf7, 0x3a, 0x50, 0xe6, 0x10, 0xba, 0x22, + 0x43, 0x4d, 0x1f, 0x1f, 0x7c, 0x27, 0xca, 0x9c, + 0xb8, 0xb6, 0xa0, 0xfc, 0xd8, 0xc0, 0x05, 0x2f, + 0xf7, 0x08, 0xe1, 0x76, 0xdd, 0xd0, 0x80, 0xc8}, + {0xe3, 0x80, 0x80, 0xb8, 0xdb, 0xe3, 0xa9, 0x77, + 0x00, 0xb0, 0xf5, 0x2e, 0x27, 0xe2, 0x68, 0xc4, + 0x88, 0xe8, 0x04, 0xc1, 0x12, 0xbf, 0x78, 0x59, + 0xe6, 0xa9, 0x7c, 0xe1, 0x81, 0xdd, 0xb9, 0xd5}}, + {{0x96, 0xe2, 0xee, 0x01, 0xa6, 0x80, 0x31, 0xef, + 0x5c, 0xd0, 0x19, 0xb4, 0x7d, 0x5f, 0x79, 0xab, + 0xa1, 0x97, 0xd3, 0x7e, 0x33, 0xbb, 0x86, 0x55, + 0x60, 0x20, 0x10, 0x0d, 0x94, 0x2d, 0x11, 0x7c}, + {0xcc, 0xab, 0xe0, 0xe8, 0x98, 0x65, 0x12, 0x96, + 0x38, 0x5a, 0x1a, 0xf2, 0x85, 0x23, 0x59, 0x5f, + 0xf9, 0xf3, 0xc2, 0x81, 0x70, 0x92, 0x65, 0x12, + 0x9c, 0x65, 0x1e, 0x96, 0x00, 0xef, 0xe7, 0x63}}, + {{0xac, 0x1e, 0x62, 0xc2, 0x59, 0xfc, 0x4e, 0x5c, + 0x83, 0xb0, 0xd0, 0x6f, 0xce, 0x19, 0xf6, 0xbf, + 0xa4, 0xb0, 0xe0, 0x53, 0x66, 0x1f, 0xbf, 0xc9, + 0x33, 0x47, 0x37, 0xa9, 0x3d, 0x5d, 0xb0, 0x48}, + {0x86, 0xb9, 0x2a, 0x7f, 0x8e, 0xa8, 0x60, 0x42, + 0x26, 0x6d, 0x6e, 0x1c, 0xa2, 0xec, 0xe0, 0xe5, + 0x3e, 0x0a, 0x33, 0xbb, 0x61, 0x4c, 0x9f, 0x3c, + 0xd1, 0xdf, 0x49, 0x33, 0xcd, 0x72, 0x78, 0x18}}, + {{0xf7, 0xd3, 0xcd, 0x49, 0x5c, 0x13, 0x22, 0xfb, + 0x2e, 0xb2, 0x2f, 0x27, 0xf5, 0x8a, 0x5d, 0x74, + 0xc1, 0x58, 0xc5, 0xc2, 0x2d, 0x9f, 0x52, 0xc6, + 0x63, 0x9f, 0xba, 0x05, 0x76, 0x45, 0x7a, 0x63}, + {0x8a, 0xfa, 0x55, 0x4d, 0xdd, 0xa3, 0xb2, 0xc3, + 0x44, 0xfd, 0xec, 0x72, 0xde, 0xef, 0xc0, 0x99, + 0xf5, 0x9f, 0xe2, 0x52, 0xb4, 0x05, 0x32, 0x58, + 0x57, 0xc1, 0x8f, 0xea, 0xc3, 0x24, 0x5b, 0x94}}, + {{0x05, 0x83, 0xee, 0xdd, 0x64, 0xf0, 0x14, 0x3b, + 0xa0, 0x14, 0x4a, 0x3a, 0x41, 0x82, 0x7c, 0xa7, + 0x2c, 0xaa, 0xb1, 0x76, 0xbb, 0x59, 0x64, 0x5f, + 0x52, 0xad, 0x25, 0x29, 0x9d, 0x8f, 0x0b, 0xb0}, + {0x7e, 0xe3, 0x7c, 0xca, 0xcd, 0x4f, 0xb0, 0x6d, + 0x7a, 0xb2, 0x3e, 0xa0, 0x08, 0xb9, 0xa8, 0x2d, + 0xc2, 0xf4, 0x99, 0x66, 0xcc, 0xac, 0xd8, 0xb9, + 0x72, 0x2a, 0x4a, 0x3e, 0x0f, 0x7b, 0xbf, 0xf4}}, + {{0x8c, 0x9c, 0x78, 0x2b, 0x39, 0x61, 0x7e, 0xf7, + 0x65, 0x37, 0x66, 0x09, 0x38, 0xb9, 0x6f, 0x70, + 0x78, 0x87, 0xff, 0xcf, 0x93, 0xca, 0x85, 0x06, + 0x44, 0x84, 0xa7, 0xfe, 0xd3, 0xa4, 0xe3, 0x7e}, + {0xa2, 0x56, 0x49, 0x23, 0x54, 0xa5, 0x50, 0xe9, + 0x5f, 0xf0, 0x4d, 0xe7, 0xdc, 0x38, 0x32, 0x79, + 0x4f, 0x1c, 0xb7, 0xe4, 0xbb, 0xf8, 0xbb, 0x2e, + 0x40, 0x41, 0x4b, 0xcc, 0xe3, 0x1e, 0x16, 0x36}}, + {{0x0c, 0x1e, 0xd7, 0x09, 0x25, 0x40, 0x97, 0xcb, + 0x5c, 0x46, 0xa8, 0xda, 0xef, 0x25, 0xd5, 0xe5, + 0x92, 0x4d, 0xcf, 0xa3, 0xc4, 0x5d, 0x35, 0x4a, + 0xe4, 0x61, 0x92, 0xf3, 0xbf, 0x0e, 0xcd, 0xbe}, + {0xe4, 0xaf, 0x0a, 0xb3, 0x30, 0x8b, 0x9b, 0x48, + 0x49, 0x43, 0xc7, 0x64, 0x60, 0x4a, 0x2b, 0x9e, + 0x95, 0x5f, 0x56, 0xe8, 0x35, 0xdc, 0xeb, 0xdc, + 0xc7, 0xc4, 0xfe, 0x30, 0x40, 0xc7, 0xbf, 0xa4}}, + {{0xd4, 0xa0, 0xf5, 0x81, 0x49, 0x6b, 0xb6, 0x8b, + 0x0a, 0x69, 0xf9, 0xfe, 0xa8, 0x32, 0xe5, 0xe0, + 0xa5, 0xcd, 0x02, 0x53, 0xf9, 0x2c, 0xe3, 0x53, + 0x83, 0x36, 0xc6, 0x02, 0xb5, 0xeb, 0x64, 0xb8}, + {0x1d, 0x42, 0xb9, 0xf9, 0xe9, 0xe3, 0x93, 0x2c, + 0x4c, 0xee, 0x6c, 0x5a, 0x47, 0x9e, 0x62, 0x01, + 0x6b, 0x04, 0xfe, 0xa4, 0x30, 0x2b, 0x0d, 0x4f, + 0x71, 0x10, 0xd3, 0x55, 0xca, 0xf3, 0x5e, 0x80}}, + {{0x77, 0x05, 0xf6, 0x0c, 0x15, 0x9b, 0x45, 0xe7, + 0xb9, 0x11, 0xb8, 0xf5, 0xd6, 0xda, 0x73, 0x0c, + 0xda, 0x92, 0xea, 0xd0, 0x9d, 0xd0, 0x18, 0x92, + 0xce, 0x9a, 0xaa, 0xee, 0x0f, 0xef, 0xde, 0x30}, + {0xf1, 0xf1, 0xd6, 0x9b, 0x51, 0xd7, 0x77, 0x62, + 0x52, 0x10, 0xb8, 0x7a, 0x84, 0x9d, 0x15, 0x4e, + 0x07, 0xdc, 0x1e, 0x75, 0x0d, 0x0c, 0x3b, 0xdb, + 0x74, 0x58, 0x62, 0x02, 0x90, 0x54, 0x8b, 0x43}}, + {{0xa6, 0xfe, 0x0b, 0x87, 0x80, 0x43, 0x67, 0x25, + 0x57, 0x5d, 0xec, 0x40, 0x50, 0x08, 0xd5, 0x5d, + 0x43, 0xd7, 0xe0, 0xaa, 0xe0, 0x13, 0xb6, 0xb0, + 0xc0, 0xd4, 0xe5, 0x0d, 0x45, 0x83, 0xd6, 0x13}, + {0x40, 0x45, 0x0a, 0x92, 0x31, 0xea, 0x8c, 0x60, + 0x8c, 0x1f, 0xd8, 0x76, 0x45, 0xb9, 0x29, 0x00, + 0x26, 0x32, 0xd8, 0xa6, 0x96, 0x88, 0xe2, 0xc4, + 0x8b, 0xdb, 0x7f, 0x17, 0x87, 0xcc, 0xc8, 0xf2}}, + {{0xc2, 0x56, 0xe2, 0xb6, 0x1a, 0x81, 0xe7, 0x31, + 0x63, 0x2e, 0xbb, 0x0d, 0x2f, 0x81, 0x67, 0xd4, + 0x22, 0xe2, 0x38, 0x02, 0x25, 0x97, 0xc7, 0x88, + 0x6e, 0xdf, 0xbe, 0x2a, 0xa5, 0x73, 0x63, 0xaa}, + {0x50, 0x45, 0xe2, 0xc3, 0xbd, 0x89, 0xfc, 0x57, + 0xbd, 0x3c, 0xa3, 0x98, 0x7e, 0x7f, 0x36, 0x38, + 0x92, 0x39, 0x1f, 0x0f, 0x81, 0x1a, 0x06, 0x51, + 0x1f, 0x8d, 0x6a, 0xff, 0x47, 0x16, 0x06, 0x9c}}, + {{0x33, 0x95, 0xa2, 0x6f, 0x27, 0x5f, 0x9c, 0x9c, + 0x64, 0x45, 0xcb, 0xd1, 0x3c, 0xee, 0x5e, 0x5f, + 0x48, 0xa6, 0xaf, 0xe3, 0x79, 0xcf, 0xb1, 0xe2, + 0xbf, 0x55, 0x0e, 0xa2, 0x3b, 0x62, 0xf0, 0xe4}, + {0x14, 0xe8, 0x06, 0xe3, 0xbe, 0x7e, 0x67, 0x01, + 0xc5, 0x21, 0x67, 0xd8, 0x54, 0xb5, 0x7f, 0xa4, + 0xf9, 0x75, 0x70, 0x1c, 0xfd, 0x79, 0xdb, 0x86, + 0xad, 0x37, 0x85, 0x83, 0x56, 0x4e, 0xf0, 0xbf}}, + {{0xbc, 0xa6, 0xe0, 0x56, 0x4e, 0xef, 0xfa, 0xf5, + 0x1d, 0x5d, 0x3f, 0x2a, 0x5b, 0x19, 0xab, 0x51, + 0xc5, 0x8b, 0xdd, 0x98, 0x28, 0x35, 0x2f, 0xc3, + 0x81, 0x4f, 0x5c, 0xe5, 0x70, 0xb9, 0xeb, 0x62}, + {0xc4, 0x6d, 0x26, 0xb0, 0x17, 0x6b, 0xfe, 0x6c, + 0x12, 0xf8, 0xe7, 0xc1, 0xf5, 0x2f, 0xfa, 0x91, + 0x13, 0x27, 0xbd, 0x73, 0xcc, 0x33, 0x31, 0x1c, + 0x39, 0xe3, 0x27, 0x6a, 0x95, 0xcf, 0xc5, 0xfb}}, + {{0x30, 0xb2, 0x99, 0x84, 0xf0, 0x18, 0x2a, 0x6e, + 0x1e, 0x27, 0xed, 0xa2, 0x29, 0x99, 0x41, 0x56, + 0xe8, 0xd4, 0x0d, 0xef, 0x99, 0x9c, 0xf3, 0x58, + 0x29, 0x55, 0x1a, 0xc0, 0x68, 0xd6, 0x74, 0xa4}, + {0x07, 0x9c, 0xe7, 0xec, 0xf5, 0x36, 0x73, 0x41, + 0xa3, 0x1c, 0xe5, 0x93, 0x97, 0x6a, 0xfd, 0xf7, + 0x53, 0x18, 0xab, 0xaf, 0xeb, 0x85, 0xbd, 0x92, + 0x90, 0xab, 0x3c, 0xbf, 0x30, 0x82, 0xad, 0xf6}}, + {{0xc6, 0x87, 0x8a, 0x2a, 0xea, 0xc0, 0xa9, 0xec, + 0x6d, 0xd3, 0xdc, 0x32, 0x23, 0xce, 0x62, 0x19, + 0xa4, 0x7e, 0xa8, 0xdd, 0x1c, 0x33, 0xae, 0xd3, + 0x4f, 0x62, 0x9f, 0x52, 0xe7, 0x65, 0x46, 0xf4}, + {0x97, 0x51, 0x27, 0x67, 0x2d, 0xa2, 0x82, 0x87, + 0x98, 0xd3, 0xb6, 0x14, 0x7f, 0x51, 0xd3, 0x9a, + 0x0b, 0xd0, 0x76, 0x81, 0xb2, 0x4f, 0x58, 0x92, + 0xa4, 0x86, 0xa1, 0xa7, 0x09, 0x1d, 0xef, 0x9b}}, + {{0xb3, 0x0f, 0x2b, 0x69, 0x0d, 0x06, 0x90, 0x64, + 0xbd, 0x43, 0x4c, 0x10, 0xe8, 0x98, 0x1c, 0xa3, + 0xe1, 0x68, 0xe9, 0x79, 0x6c, 0x29, 0x51, 0x3f, + 0x41, 0xdc, 0xdf, 0x1f, 0xf3, 0x60, 0xbe, 0x33}, + {0xa1, 0x5f, 0xf7, 0x1d, 0xb4, 0x3e, 0x9b, 0x3c, + 0xe7, 0xbd, 0xb6, 0x06, 0xd5, 0x60, 0x06, 0x6d, + 0x50, 0xd2, 0xf4, 0x1a, 0x31, 0x08, 0xf2, 0xea, + 0x8e, 0xef, 0x5f, 0x7d, 0xb6, 0xd0, 0xc0, 0x27}}, + {{0x62, 0x9a, 0xd9, 0xbb, 0x38, 0x36, 0xce, 0xf7, + 0x5d, 0x2f, 0x13, 0xec, 0xc8, 0x2d, 0x02, 0x8a, + 0x2e, 0x72, 0xf0, 0xe5, 0x15, 0x9d, 0x72, 0xae, + 0xfc, 0xb3, 0x4f, 0x02, 0xea, 0xe1, 0x09, 0xfe}, + {0x00, 0x00, 0x00, 0x00, 0xfa, 0x0a, 0x3d, 0xbc, + 0xad, 0x16, 0x0c, 0xb6, 0xe7, 0x7c, 0x8b, 0x39, + 0x9a, 0x43, 0xbb, 0xe3, 0xc2, 0x55, 0x15, 0x14, + 0x75, 0xac, 0x90, 0x9b, 0x7f, 0x9a, 0x92, 0x00}}, + {{0x8b, 0xac, 0x70, 0x86, 0x29, 0x8f, 0x00, 0x23, + 0x7b, 0x45, 0x30, 0xaa, 0xb8, 0x4c, 0xc7, 0x8d, + 0x4e, 0x47, 0x85, 0xc6, 0x19, 0xe3, 0x96, 0xc2, + 0x9a, 0xa0, 0x12, 0xed, 0x6f, 0xd7, 0x76, 0x16}, + {0x45, 0xaf, 0x7e, 0x33, 0xc7, 0x7f, 0x10, 0x6c, + 0x7c, 0x9f, 0x29, 0xc1, 0xa8, 0x7e, 0x15, 0x84, + 0xe7, 0x7d, 0xc0, 0x6d, 0xab, 0x71, 0x5d, 0xd0, + 0x6b, 0x9f, 0x97, 0xab, 0xcb, 0x51, 0x0c, 0x9f}}, + {{0x9e, 0xc3, 0x92, 0xb4, 0x04, 0x9f, 0xc8, 0xbb, + 0xdd, 0x9e, 0xc6, 0x05, 0xfd, 0x65, 0xec, 0x94, + 0x7f, 0x2c, 0x16, 0xc4, 0x40, 0xac, 0x63, 0x7b, + 0x7d, 0xb8, 0x0c, 0xe4, 0x5b, 0xe3, 0xa7, 0x0e}, + {0x43, 0xf4, 0x44, 0xe8, 0xcc, 0xc8, 0xd4, 0x54, + 0x33, 0x37, 0x50, 0xf2, 0x87, 0x42, 0x2e, 0x00, + 0x49, 0x60, 0x62, 0x02, 0xfd, 0x1a, 0x7c, 0xdb, + 0x29, 0x6c, 0x6d, 0x54, 0x53, 0x08, 0xd1, 0xc8}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}, + {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, + {{0x28, 0x56, 0xac, 0x0e, 0x4f, 0x98, 0x09, 0xf0, + 0x49, 0xfa, 0x7f, 0x84, 0xac, 0x7e, 0x50, 0x5b, + 0x17, 0x43, 0x14, 0x89, 0x9c, 0x53, 0xa8, 0x94, + 0x30, 0xf2, 0x11, 0x4d, 0x92, 0x14, 0x27, 0xe8}, + {0x39, 0x7a, 0x84, 0x56, 0x79, 0x9d, 0xec, 0x26, + 0x2c, 0x53, 0xc1, 0x94, 0xc9, 0x8d, 0x9e, 0x9d, + 0x32, 0x1f, 0xdd, 0x84, 0x04, 0xe8, 0xe2, 0x0a, + 0x6b, 0xbe, 0xbb, 0x42, 0x40, 0x67, 0x30, 0x6c}}, + {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x73, 0x2f, 0xc9, 0xbe, 0xbd}, + {0x27, 0x59, 0xc7, 0x35, 0x60, 0x71, 0xa6, 0xf1, + 0x79, 0xa5, 0xfd, 0x79, 0x16, 0xf3, 0x41, 0xf0, + 0x57, 0xb4, 0x02, 0x97, 0x32, 0xe7, 0xde, 0x59, + 0xe2, 0x2d, 0x9b, 0x11, 0xea, 0x2c, 0x35, 0x92}}, + {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40}, + {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}}, + {{0x1c, 0xc4, 0xf7, 0xda, 0x0f, 0x65, 0xca, 0x39, + 0x70, 0x52, 0x92, 0x8e, 0xc3, 0xc8, 0x15, 0xea, + 0x7f, 0x10, 0x9e, 0x77, 0x4b, 0x6e, 0x2d, 0xdf, + 0xe8, 0x30, 0x9d, 0xda, 0xe8, 0x9a, 0x65, 0xae}, + {0x02, 0xb0, 0x16, 0xb1, 0x1d, 0xc8, 0x57, 0x7b, + 0xa2, 0x3a, 0xa2, 0xa3, 0x38, 0x5c, 0x8f, 0xeb, + 0x66, 0x37, 0x91, 0xa8, 0x5f, 0xef, 0x04, 0xf6, + 0x59, 0x75, 0xe1, 0xee, 0x92, 0xf6, 0x0e, 0x30}}, + {{0x8d, 0x76, 0x14, 0xa4, 0x14, 0x06, 0x9f, 0x9a, + 0xdf, 0x4a, 0x85, 0xa7, 0x6b, 0xbf, 0x29, 0x6f, + 0xbc, 0x34, 0x87, 0x5d, 0xeb, 0xbb, 0x2e, 0xa9, + 0xc9, 0x1f, 0x58, 0xd6, 0x9a, 0x82, 0xa0, 0x56}, + {0xd4, 0xb9, 0xdb, 0x88, 0x1d, 0x04, 0xe9, 0x93, + 0x8d, 0x3f, 0x20, 0xd5, 0x86, 0xa8, 0x83, 0x07, + 0xdb, 0x09, 0xd8, 0x22, 0x1f, 0x7f, 0xf1, 0x71, + 0xc8, 0xe7, 0x5d, 0x47, 0xaf, 0x8b, 0x72, 0xe9}}, + {{0x83, 0xb9, 0x39, 0xb2, 0xa4, 0xdf, 0x46, 0x87, + 0xc2, 0xb8, 0xf1, 0xe6, 0x4c, 0xd1, 0xe2, 0xa9, + 0xe4, 0x70, 0x30, 0x34, 0xbc, 0x52, 0x7c, 0x55, + 0xa6, 0xec, 0x80, 0xa4, 0xe5, 0xd2, 0xdc, 0x73}, + {0x08, 0xf1, 0x03, 0xcf, 0x16, 0x73, 0xe8, 0x7d, + 0xb6, 0x7e, 0x9b, 0xc0, 0xb4, 0xc2, 0xa5, 0x86, + 0x02, 0x77, 0xd5, 0x27, 0x86, 0xa5, 0x15, 0xfb, + 0xae, 0x9b, 0x8c, 0xa9, 0xf9, 0xf8, 0xa8, 0x4a}}, + {{0x8b, 0x00, 0x49, 0xdb, 0xfa, 0xf0, 0x1b, 0xa2, + 0xed, 0x8a, 0x9a, 0x7a, 0x36, 0x78, 0x4a, 0xc7, + 0xf7, 0xad, 0x39, 0xd0, 0x6c, 0x65, 0x7a, 0x41, + 0xce, 0xd6, 0xd6, 0x4c, 0x20, 0x21, 0x6b, 0xc7}, + {0xc6, 0xca, 0x78, 0x1d, 0x32, 0x6c, 0x6c, 0x06, + 0x91, 0xf2, 0x1a, 0xe8, 0x43, 0x16, 0xea, 0x04, + 0x3c, 0x1f, 0x07, 0x85, 0xf7, 0x09, 0x22, 0x08, + 0xba, 0x13, 0xfd, 0x78, 0x1e, 0x3f, 0x6f, 0x62}}, + {{0x25, 0x9b, 0x7c, 0xb0, 0xac, 0x72, 0x6f, 0xb2, + 0xe3, 0x53, 0x84, 0x7a, 0x1a, 0x9a, 0x98, 0x9b, + 0x44, 0xd3, 0x59, 0xd0, 0x8e, 0x57, 0x41, 0x40, + 0x78, 0xa7, 0x30, 0x2f, 0x4c, 0x9c, 0xb9, 0x68}, + {0xb7, 0x75, 0x03, 0x63, 0x61, 0xc2, 0x48, 0x6e, + 0x12, 0x3d, 0xbf, 0x4b, 0x27, 0xdf, 0xb1, 0x7a, + 0xff, 0x4e, 0x31, 0x07, 0x83, 0xf4, 0x62, 0x5b, + 0x19, 0xa5, 0xac, 0xa0, 0x32, 0x58, 0x0d, 0xa7}}, + {{0x43, 0x4f, 0x10, 0xa4, 0xca, 0xdb, 0x38, 0x67, + 0xfa, 0xae, 0x96, 0xb5, 0x6d, 0x97, 0xff, 0x1f, + 0xb6, 0x83, 0x43, 0xd3, 0xa0, 0x2d, 0x70, 0x7a, + 0x64, 0x05, 0x4c, 0xa7, 0xc1, 0xa5, 0x21, 0x51}, + {0xe4, 0xf1, 0x23, 0x84, 0xe1, 0xb5, 0x9d, 0xf2, + 0xb8, 0x73, 0x8b, 0x45, 0x2b, 0x35, 0x46, 0x38, + 0x10, 0x2b, 0x50, 0xf8, 0x8b, 0x35, 0xcd, 0x34, + 0xc8, 0x0e, 0xf6, 0xdb, 0x09, 0x35, 0xf0, 0xda}}, + {{0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, + 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, + 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, + 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}, + {0xdb, 0x21, 0x5c, 0x8d, 0x83, 0x1d, 0xb3, 0x34, + 0xc7, 0x0e, 0x43, 0xa1, 0x58, 0x79, 0x67, 0x13, + 0x1e, 0x86, 0x5d, 0x89, 0x63, 0xe6, 0x0a, 0x46, + 0x5c, 0x02, 0x97, 0x1b, 0x62, 0x43, 0x86, 0xf5}} + }; + secp256k1_scalar_set_int(&one, 1); + for (i = 0; i < 33; i++) { + secp256k1_scalar_set_b32(&x, chal[i][0], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&y, chal[i][1], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&r1, res[i][0], &overflow); + CHECK(!overflow); + secp256k1_scalar_set_b32(&r2, res[i][1], &overflow); + CHECK(!overflow); + secp256k1_scalar_mul(&z, &x, &y); + CHECK(!secp256k1_scalar_check_overflow(&z)); + CHECK(secp256k1_scalar_eq(&r1, &z)); + if (!secp256k1_scalar_is_zero(&y)) { + secp256k1_scalar_inverse(&zz, &y); + CHECK(!secp256k1_scalar_check_overflow(&zz)); +#if defined(USE_SCALAR_INV_NUM) + secp256k1_scalar_inverse_var(&zzv, &y); + CHECK(secp256k1_scalar_eq(&zzv, &zz)); +#endif + secp256k1_scalar_mul(&z, &z, &zz); + CHECK(!secp256k1_scalar_check_overflow(&z)); + CHECK(secp256k1_scalar_eq(&x, &z)); + secp256k1_scalar_mul(&zz, &zz, &y); + CHECK(!secp256k1_scalar_check_overflow(&zz)); + CHECK(secp256k1_scalar_eq(&one, &zz)); + } + secp256k1_scalar_mul(&z, &x, &x); + CHECK(!secp256k1_scalar_check_overflow(&z)); + secp256k1_scalar_sqr(&zz, &x); + CHECK(!secp256k1_scalar_check_overflow(&zz)); + CHECK(secp256k1_scalar_eq(&zz, &z)); + CHECK(secp256k1_scalar_eq(&r2, &zz)); + } + } +} + +/***** FIELD TESTS *****/ + +void random_fe(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_rand256(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +void random_fe_test(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_rand256_test(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} + +void random_fe_non_zero(secp256k1_fe *nz) { + int tries = 10; + while (--tries >= 0) { + random_fe(nz); + secp256k1_fe_normalize(nz); + if (!secp256k1_fe_is_zero(nz)) { + break; + } + } + /* Infinitesimal probability of spurious failure here */ + CHECK(tries >= 0); +} + +void random_fe_non_square(secp256k1_fe *ns) { + secp256k1_fe r; + random_fe_non_zero(ns); + if (secp256k1_fe_sqrt(&r, ns)) { + secp256k1_fe_negate(ns, ns, 1); + } +} + +int check_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe an = *a; + secp256k1_fe bn = *b; + secp256k1_fe_normalize_weak(&an); + secp256k1_fe_normalize_var(&bn); + return secp256k1_fe_equal_var(&an, &bn); +} + +int check_fe_inverse(const secp256k1_fe *a, const secp256k1_fe *ai) { + secp256k1_fe x; + secp256k1_fe one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_fe_mul(&x, a, ai); + return check_fe_equal(&x, &one); +} + +void run_field_convert(void) { + static const unsigned char b32[32] = { + 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, + 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, 0x18, + 0x22, 0x23, 0x24, 0x25, 0x26, 0x27, 0x28, 0x29, + 0x33, 0x34, 0x35, 0x36, 0x37, 0x38, 0x39, 0x40 + }; + static const secp256k1_fe_storage fes = SECP256K1_FE_STORAGE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + static const secp256k1_fe fe = SECP256K1_FE_CONST( + 0x00010203UL, 0x04050607UL, 0x11121314UL, 0x15161718UL, + 0x22232425UL, 0x26272829UL, 0x33343536UL, 0x37383940UL + ); + secp256k1_fe fe2; + unsigned char b322[32]; + secp256k1_fe_storage fes2; + /* Check conversions to fe. */ + CHECK(secp256k1_fe_set_b32(&fe2, b32)); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + secp256k1_fe_from_storage(&fe2, &fes); + CHECK(secp256k1_fe_equal_var(&fe, &fe2)); + /* Check conversion from fe. */ + secp256k1_fe_get_b32(b322, &fe); + CHECK(memcmp(b322, b32, 32) == 0); + secp256k1_fe_to_storage(&fes2, &fe); + CHECK(memcmp(&fes2, &fes, sizeof(fes)) == 0); +} + +int fe_memcmp(const secp256k1_fe *a, const secp256k1_fe *b) { + secp256k1_fe t = *b; +#ifdef VERIFY + t.magnitude = a->magnitude; + t.normalized = a->normalized; +#endif + return memcmp(a, &t, sizeof(secp256k1_fe)); +} + +void run_field_misc(void) { + secp256k1_fe x; + secp256k1_fe y; + secp256k1_fe z; + secp256k1_fe q; + secp256k1_fe fe5 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 5); + int i, j; + for (i = 0; i < 5*count; i++) { + secp256k1_fe_storage xs, ys, zs; + random_fe(&x); + random_fe_non_zero(&y); + /* Test the fe equality and comparison operations. */ + CHECK(secp256k1_fe_cmp_var(&x, &x) == 0); + CHECK(secp256k1_fe_equal_var(&x, &x)); + z = x; + secp256k1_fe_add(&z,&y); + /* Test fe conditional move; z is not normalized here. */ + q = x; + secp256k1_fe_cmov(&x, &z, 0); +#ifdef VERIFY + CHECK(x.normalized && x.magnitude == 1); +#endif + secp256k1_fe_cmov(&x, &x, 1); + CHECK(fe_memcmp(&x, &z) != 0); + CHECK(fe_memcmp(&x, &q) == 0); + secp256k1_fe_cmov(&q, &z, 1); +#ifdef VERIFY + CHECK(!q.normalized && q.magnitude == z.magnitude); +#endif + CHECK(fe_memcmp(&q, &z) == 0); + secp256k1_fe_normalize_var(&x); + secp256k1_fe_normalize_var(&z); + CHECK(!secp256k1_fe_equal_var(&x, &z)); + secp256k1_fe_normalize_var(&q); + secp256k1_fe_cmov(&q, &z, (i&1)); +#ifdef VERIFY + CHECK(q.normalized && q.magnitude == 1); +#endif + for (j = 0; j < 6; j++) { + secp256k1_fe_negate(&z, &z, j+1); + secp256k1_fe_normalize_var(&q); + secp256k1_fe_cmov(&q, &z, (j&1)); +#ifdef VERIFY + CHECK((q.normalized != (j&1)) && q.magnitude == ((j&1) ? z.magnitude : 1)); +#endif + } + secp256k1_fe_normalize_var(&z); + /* Test storage conversion and conditional moves. */ + secp256k1_fe_to_storage(&xs, &x); + secp256k1_fe_to_storage(&ys, &y); + secp256k1_fe_to_storage(&zs, &z); + secp256k1_fe_storage_cmov(&zs, &xs, 0); + secp256k1_fe_storage_cmov(&zs, &zs, 1); + CHECK(memcmp(&xs, &zs, sizeof(xs)) != 0); + secp256k1_fe_storage_cmov(&ys, &xs, 1); + CHECK(memcmp(&xs, &ys, sizeof(xs)) == 0); + secp256k1_fe_from_storage(&x, &xs); + secp256k1_fe_from_storage(&y, &ys); + secp256k1_fe_from_storage(&z, &zs); + /* Test that mul_int, mul, and add agree. */ + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&y, &x); + z = x; + secp256k1_fe_mul_int(&z, 3); + CHECK(check_fe_equal(&y, &z)); + secp256k1_fe_add(&y, &x); + secp256k1_fe_add(&z, &x); + CHECK(check_fe_equal(&z, &y)); + z = x; + secp256k1_fe_mul_int(&z, 5); + secp256k1_fe_mul(&q, &x, &fe5); + CHECK(check_fe_equal(&z, &q)); + secp256k1_fe_negate(&x, &x, 1); + secp256k1_fe_add(&z, &x); + secp256k1_fe_add(&q, &x); + CHECK(check_fe_equal(&y, &z)); + CHECK(check_fe_equal(&q, &y)); + } +} + +void run_field_inv(void) { + secp256k1_fe x, xi, xii; + int i; + for (i = 0; i < 10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_var(void) { + secp256k1_fe x, xi, xii; + int i; + for (i = 0; i < 10*count; i++) { + random_fe_non_zero(&x); + secp256k1_fe_inv_var(&xi, &x); + CHECK(check_fe_inverse(&x, &xi)); + secp256k1_fe_inv_var(&xii, &xi); + CHECK(check_fe_equal(&x, &xii)); + } +} + +void run_field_inv_all_var(void) { + secp256k1_fe x[16], xi[16], xii[16]; + int i; + /* Check it's safe to call for 0 elements */ + secp256k1_fe_inv_all_var(xi, x, 0); + for (i = 0; i < count; i++) { + size_t j; + size_t len = secp256k1_rand_int(15) + 1; + for (j = 0; j < len; j++) { + random_fe_non_zero(&x[j]); + } + secp256k1_fe_inv_all_var(xi, x, len); + for (j = 0; j < len; j++) { + CHECK(check_fe_inverse(&x[j], &xi[j])); + } + secp256k1_fe_inv_all_var(xii, xi, len); + for (j = 0; j < len; j++) { + CHECK(check_fe_equal(&x[j], &xii[j])); + } + } +} + +void run_sqr(void) { + secp256k1_fe x, s; + + { + int i; + secp256k1_fe_set_int(&x, 1); + secp256k1_fe_negate(&x, &x, 1); + + for (i = 1; i <= 512; ++i) { + secp256k1_fe_mul_int(&x, 2); + secp256k1_fe_normalize(&x); + secp256k1_fe_sqr(&s, &x); + } + } +} + +void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) { + secp256k1_fe r1, r2; + int v = secp256k1_fe_sqrt(&r1, a); + CHECK((v == 0) == (k == NULL)); + + if (k != NULL) { + /* Check that the returned root is +/- the given known answer */ + secp256k1_fe_negate(&r2, &r1, 1); + secp256k1_fe_add(&r1, k); secp256k1_fe_add(&r2, k); + secp256k1_fe_normalize(&r1); secp256k1_fe_normalize(&r2); + CHECK(secp256k1_fe_is_zero(&r1) || secp256k1_fe_is_zero(&r2)); + } +} + +void run_sqrt(void) { + secp256k1_fe ns, x, s, t; + int i; + + /* Check sqrt(0) is 0 */ + secp256k1_fe_set_int(&x, 0); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + + /* Check sqrt of small squares (and their negatives) */ + for (i = 1; i <= 100; i++) { + secp256k1_fe_set_int(&x, i); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + } + + /* Consistency checks for large random values */ + for (i = 0; i < 10; i++) { + int j; + random_fe_non_square(&ns); + for (j = 0; j < count; j++) { + random_fe(&x); + secp256k1_fe_sqr(&s, &x); + test_sqrt(&s, &x); + secp256k1_fe_negate(&t, &s, 1); + test_sqrt(&t, NULL); + secp256k1_fe_mul(&t, &s, &ns); + test_sqrt(&t, NULL); + } + } +} + +/***** GROUP TESTS *****/ + +void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) { + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + CHECK(secp256k1_fe_equal_var(&a->x, &b->x)); + CHECK(secp256k1_fe_equal_var(&a->y, &b->y)); +} + +/* This compares jacobian points including their Z, not just their geometric meaning. */ +int gej_xyz_equals_gej(const secp256k1_gej *a, const secp256k1_gej *b) { + secp256k1_gej a2; + secp256k1_gej b2; + int ret = 1; + ret &= a->infinity == b->infinity; + if (ret && !a->infinity) { + a2 = *a; + b2 = *b; + secp256k1_fe_normalize(&a2.x); + secp256k1_fe_normalize(&a2.y); + secp256k1_fe_normalize(&a2.z); + secp256k1_fe_normalize(&b2.x); + secp256k1_fe_normalize(&b2.y); + secp256k1_fe_normalize(&b2.z); + ret &= secp256k1_fe_cmp_var(&a2.x, &b2.x) == 0; + ret &= secp256k1_fe_cmp_var(&a2.y, &b2.y) == 0; + ret &= secp256k1_fe_cmp_var(&a2.z, &b2.z) == 0; + } + return ret; +} + +void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) { + secp256k1_fe z2s; + secp256k1_fe u1, u2, s1, s2; + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */ + secp256k1_fe_sqr(&z2s, &b->z); + secp256k1_fe_mul(&u1, &a->x, &z2s); + u2 = b->x; secp256k1_fe_normalize_weak(&u2); + secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z); + s2 = b->y; secp256k1_fe_normalize_weak(&s2); + CHECK(secp256k1_fe_equal_var(&u1, &u2)); + CHECK(secp256k1_fe_equal_var(&s1, &s2)); +} + +void test_ge(void) { + int i, i1; +#ifdef USE_ENDOMORPHISM + int runs = 6; +#else + int runs = 4; +#endif + /* Points: (infinity, p1, p1, -p1, -p1, p2, p2, -p2, -p2, p3, p3, -p3, -p3, p4, p4, -p4, -p4). + * The second in each pair of identical points uses a random Z coordinate in the Jacobian form. + * All magnitudes are randomized. + * All 17*17 combinations of points are added to each other, using all applicable methods. + * + * When the endomorphism code is compiled in, p5 = lambda*p1 and p6 = lambda^2*p1 are added as well. + */ + secp256k1_ge *ge = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * (1 + 4 * runs)); + secp256k1_gej *gej = (secp256k1_gej *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_gej) * (1 + 4 * runs)); + secp256k1_fe *zinv = (secp256k1_fe *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs)); + secp256k1_fe zf; + secp256k1_fe zfi2, zfi3; + + secp256k1_gej_set_infinity(&gej[0]); + secp256k1_ge_clear(&ge[0]); + secp256k1_ge_set_gej_var(&ge[0], &gej[0]); + for (i = 0; i < runs; i++) { + int j; + secp256k1_ge g; + random_group_element_test(&g); +#ifdef USE_ENDOMORPHISM + if (i >= runs - 2) { + secp256k1_ge_mul_lambda(&g, &ge[1]); + } + if (i >= runs - 1) { + secp256k1_ge_mul_lambda(&g, &g); + } +#endif + ge[1 + 4 * i] = g; + ge[2 + 4 * i] = g; + secp256k1_ge_neg(&ge[3 + 4 * i], &g); + secp256k1_ge_neg(&ge[4 + 4 * i], &g); + secp256k1_gej_set_ge(&gej[1 + 4 * i], &ge[1 + 4 * i]); + random_group_element_jacobian_test(&gej[2 + 4 * i], &ge[2 + 4 * i]); + secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]); + random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]); + for (j = 0; j < 4; j++) { + random_field_element_magnitude(&ge[1 + j + 4 * i].x); + random_field_element_magnitude(&ge[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].x); + random_field_element_magnitude(&gej[1 + j + 4 * i].y); + random_field_element_magnitude(&gej[1 + j + 4 * i].z); + } + } + + /* Compute z inverses. */ + { + secp256k1_fe *zs = checked_malloc(&ctx->error_callback, sizeof(secp256k1_fe) * (1 + 4 * runs)); + for (i = 0; i < 4 * runs + 1; i++) { + if (i == 0) { + /* The point at infinity does not have a meaningful z inverse. Any should do. */ + do { + random_field_element_test(&zs[i]); + } while(secp256k1_fe_is_zero(&zs[i])); + } else { + zs[i] = gej[i].z; + } + } + secp256k1_fe_inv_all_var(zinv, zs, 4 * runs + 1); + free(zs); + } + + /* Generate random zf, and zfi2 = 1/zf^2, zfi3 = 1/zf^3 */ + do { + random_field_element_test(&zf); + } while(secp256k1_fe_is_zero(&zf)); + random_field_element_magnitude(&zf); + secp256k1_fe_inv_var(&zfi3, &zf); + secp256k1_fe_sqr(&zfi2, &zfi3); + secp256k1_fe_mul(&zfi3, &zfi3, &zfi2); + + for (i1 = 0; i1 < 1 + 4 * runs; i1++) { + int i2; + for (i2 = 0; i2 < 1 + 4 * runs; i2++) { + /* Compute reference result using gej + gej (var). */ + secp256k1_gej refj, resj; + secp256k1_ge ref; + secp256k1_fe zr; + secp256k1_gej_add_var(&refj, &gej[i1], &gej[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr); + /* Check Z ratio. */ + if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&refj)) { + secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zrz, &refj.z)); + } + secp256k1_ge_set_gej_var(&ref, &refj); + + /* Test gej + ge with Z ratio result (var). */ + secp256k1_gej_add_ge_var(&resj, &gej[i1], &ge[i2], secp256k1_gej_is_infinity(&gej[i1]) ? NULL : &zr); + ge_equals_gej(&ref, &resj); + if (!secp256k1_gej_is_infinity(&gej[i1]) && !secp256k1_gej_is_infinity(&resj)) { + secp256k1_fe zrz; secp256k1_fe_mul(&zrz, &zr, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zrz, &resj.z)); + } + + /* Test gej + ge (var, with additional Z factor). */ + { + secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */ + secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2); + secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3); + random_field_element_magnitude(&ge2_zfi.x); + random_field_element_magnitude(&ge2_zfi.y); + secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf); + ge_equals_gej(&ref, &resj); + } + + /* Test gej + ge (const). */ + if (i2 != 0) { + /* secp256k1_gej_add_ge does not support its second argument being infinity. */ + secp256k1_gej_add_ge(&resj, &gej[i1], &ge[i2]); + ge_equals_gej(&ref, &resj); + } + + /* Test doubling (var). */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 == ((i2 + 3)%4)/2)) { + secp256k1_fe zr2; + /* Normal doubling with Z ratio result. */ + secp256k1_gej_double_var(&resj, &gej[i1], &zr2); + ge_equals_gej(&ref, &resj); + /* Check Z ratio. */ + secp256k1_fe_mul(&zr2, &zr2, &gej[i1].z); + CHECK(secp256k1_fe_equal_var(&zr2, &resj.z)); + /* Normal doubling. */ + secp256k1_gej_double_var(&resj, &gej[i2], NULL); + ge_equals_gej(&ref, &resj); + } + + /* Test adding opposites. */ + if ((i1 == 0 && i2 == 0) || ((i1 + 3)/4 == (i2 + 3)/4 && ((i1 + 3)%4)/2 != ((i2 + 3)%4)/2)) { + CHECK(secp256k1_ge_is_infinity(&ref)); + } + + /* Test adding infinity. */ + if (i1 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i1])); + CHECK(secp256k1_gej_is_infinity(&gej[i1])); + ge_equals_gej(&ref, &gej[i2]); + } + if (i2 == 0) { + CHECK(secp256k1_ge_is_infinity(&ge[i2])); + CHECK(secp256k1_gej_is_infinity(&gej[i2])); + ge_equals_gej(&ref, &gej[i1]); + } + } + } + + /* Test adding all points together in random order equals infinity. */ + { + secp256k1_gej sum = SECP256K1_GEJ_CONST_INFINITY; + secp256k1_gej *gej_shuffled = (secp256k1_gej *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_gej)); + for (i = 0; i < 4 * runs + 1; i++) { + gej_shuffled[i] = gej[i]; + } + for (i = 0; i < 4 * runs + 1; i++) { + int swap = i + secp256k1_rand_int(4 * runs + 1 - i); + if (swap != i) { + secp256k1_gej t = gej_shuffled[i]; + gej_shuffled[i] = gej_shuffled[swap]; + gej_shuffled[swap] = t; + } + } + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_gej_add_var(&sum, &sum, &gej_shuffled[i], NULL); + } + CHECK(secp256k1_gej_is_infinity(&sum)); + free(gej_shuffled); + } + + /* Test batch gej -> ge conversion with and without known z ratios. */ + { + secp256k1_fe *zr = (secp256k1_fe *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_fe)); + secp256k1_ge *ge_set_all = (secp256k1_ge *)checked_malloc(&ctx->error_callback, (4 * runs + 1) * sizeof(secp256k1_ge)); + for (i = 0; i < 4 * runs + 1; i++) { + /* Compute gej[i + 1].z / gez[i].z (with gej[n].z taken to be 1). */ + if (i < 4 * runs) { + secp256k1_fe_mul(&zr[i + 1], &zinv[i], &gej[i + 1].z); + } + } + secp256k1_ge_set_all_gej_var(ge_set_all, gej, 4 * runs + 1); + for (i = 0; i < 4 * runs + 1; i++) { + secp256k1_fe s; + random_fe_non_zero(&s); + secp256k1_gej_rescale(&gej[i], &s); + ge_equals_gej(&ge_set_all[i], &gej[i]); + } + free(ge_set_all); + free(zr); + } + + /* Test batch gej -> ge conversion with many infinities. */ + for (i = 0; i < 4 * runs + 1; i++) { + random_group_element_test(&ge[i]); + /* randomly set half the points to infinity */ + if(secp256k1_fe_is_odd(&ge[i].x)) { + secp256k1_ge_set_infinity(&ge[i]); + } + secp256k1_gej_set_ge(&gej[i], &ge[i]); + } + /* batch invert */ + secp256k1_ge_set_all_gej_var(ge, gej, 4 * runs + 1); + /* check result */ + for (i = 0; i < 4 * runs + 1; i++) { + ge_equals_gej(&ge[i], &gej[i]); + } + + free(ge); + free(gej); + free(zinv); +} + +void test_add_neg_y_diff_x(void) { + /* The point of this test is to check that we can add two points + * whose y-coordinates are negatives of each other but whose x + * coordinates differ. If the x-coordinates were the same, these + * points would be negatives of each other and their sum is + * infinity. This is cool because it "covers up" any degeneracy + * in the addition algorithm that would cause the xy coordinates + * of the sum to be wrong (since infinity has no xy coordinates). + * HOWEVER, if the x-coordinates are different, infinity is the + * wrong answer, and such degeneracies are exposed. This is the + * root of https://github.com/bitcoin-core/secp256k1/issues/257 + * which this test is a regression test for. + * + * These points were generated in sage as + * # secp256k1 params + * F = FiniteField (0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F) + * C = EllipticCurve ([F (0), F (7)]) + * G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798) + * N = FiniteField(G.order()) + * + * # endomorphism values (lambda is 1^{1/3} in N, beta is 1^{1/3} in F) + * x = polygen(N) + * lam = (1 - x^3).roots()[1][0] + * + * # random "bad pair" + * P = C.random_element() + * Q = -int(lam) * P + * print " P: %x %x" % P.xy() + * print " Q: %x %x" % Q.xy() + * print "P + Q: %x %x" % (P + Q).xy() + */ + secp256k1_gej aj = SECP256K1_GEJ_CONST( + 0x8d24cd95, 0x0a355af1, 0x3c543505, 0x44238d30, + 0x0643d79f, 0x05a59614, 0x2f8ec030, 0xd58977cb, + 0x001e337a, 0x38093dcd, 0x6c0f386d, 0x0b1293a8, + 0x4d72c879, 0xd7681924, 0x44e6d2f3, 0x9190117d + ); + secp256k1_gej bj = SECP256K1_GEJ_CONST( + 0xc7b74206, 0x1f788cd9, 0xabd0937d, 0x164a0d86, + 0x95f6ff75, 0xf19a4ce9, 0xd013bd7b, 0xbf92d2a7, + 0xffe1cc85, 0xc7f6c232, 0x93f0c792, 0xf4ed6c57, + 0xb28d3786, 0x2897e6db, 0xbb192d0b, 0x6e6feab2 + ); + secp256k1_gej sumj = SECP256K1_GEJ_CONST( + 0x671a63c0, 0x3efdad4c, 0x389a7798, 0x24356027, + 0xb3d69010, 0x278625c3, 0x5c86d390, 0x184a8f7a, + 0x5f6409c2, 0x2ce01f2b, 0x511fd375, 0x25071d08, + 0xda651801, 0x70e95caf, 0x8f0d893c, 0xbed8fbbe + ); + secp256k1_ge b; + secp256k1_gej resj; + secp256k1_ge res; + secp256k1_ge_set_gej(&b, &bj); + + secp256k1_gej_add_var(&resj, &aj, &bj, NULL); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); + + secp256k1_gej_add_ge(&resj, &aj, &b); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); + + secp256k1_gej_add_ge_var(&resj, &aj, &b, NULL); + secp256k1_ge_set_gej(&res, &resj); + ge_equals_gej(&res, &sumj); +} + +void run_ge(void) { + int i; + for (i = 0; i < count * 32; i++) { + test_ge(); + } + test_add_neg_y_diff_x(); +} + +void test_ec_combine(void) { + secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_pubkey data[6]; + const secp256k1_pubkey* d[6]; + secp256k1_pubkey sd; + secp256k1_pubkey sd2; + secp256k1_gej Qj; + secp256k1_ge Q; + int i; + for (i = 1; i <= 6; i++) { + secp256k1_scalar s; + random_scalar_order_test(&s); + secp256k1_scalar_add(&sum, &sum, &s); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &s); + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(&data[i - 1], &Q); + d[i - 1] = &data[i - 1]; + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &Qj, &sum); + secp256k1_ge_set_gej(&Q, &Qj); + secp256k1_pubkey_save(&sd, &Q); + CHECK(secp256k1_ec_pubkey_combine(ctx, &sd2, d, i) == 1); + CHECK(memcmp(&sd, &sd2, sizeof(sd)) == 0); + } +} + +void run_ec_combine(void) { + int i; + for (i = 0; i < count * 8; i++) { + test_ec_combine(); + } +} + +void test_group_decompress(const secp256k1_fe* x) { + /* The input itself, normalized. */ + secp256k1_fe fex = *x; + secp256k1_fe fez; + /* Results of set_xquad_var, set_xo_var(..., 0), set_xo_var(..., 1). */ + secp256k1_ge ge_quad, ge_even, ge_odd; + secp256k1_gej gej_quad; + /* Return values of the above calls. */ + int res_quad, res_even, res_odd; + + secp256k1_fe_normalize_var(&fex); + + res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex); + res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0); + res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1); + + CHECK(res_quad == res_even); + CHECK(res_quad == res_odd); + + if (res_quad) { + secp256k1_fe_normalize_var(&ge_quad.x); + secp256k1_fe_normalize_var(&ge_odd.x); + secp256k1_fe_normalize_var(&ge_even.x); + secp256k1_fe_normalize_var(&ge_quad.y); + secp256k1_fe_normalize_var(&ge_odd.y); + secp256k1_fe_normalize_var(&ge_even.y); + + /* No infinity allowed. */ + CHECK(!ge_quad.infinity); + CHECK(!ge_even.infinity); + CHECK(!ge_odd.infinity); + + /* Check that the x coordinates check out. */ + CHECK(secp256k1_fe_equal_var(&ge_quad.x, x)); + CHECK(secp256k1_fe_equal_var(&ge_even.x, x)); + CHECK(secp256k1_fe_equal_var(&ge_odd.x, x)); + + /* Check that the Y coordinate result in ge_quad is a square. */ + CHECK(secp256k1_fe_is_quad_var(&ge_quad.y)); + + /* Check odd/even Y in ge_odd, ge_even. */ + CHECK(secp256k1_fe_is_odd(&ge_odd.y)); + CHECK(!secp256k1_fe_is_odd(&ge_even.y)); + + /* Check secp256k1_gej_has_quad_y_var. */ + secp256k1_gej_set_ge(&gej_quad, &ge_quad); + CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); + do { + random_fe_test(&fez); + } while (secp256k1_fe_is_zero(&fez)); + secp256k1_gej_rescale(&gej_quad, &fez); + CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); + secp256k1_gej_neg(&gej_quad, &gej_quad); + CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); + do { + random_fe_test(&fez); + } while (secp256k1_fe_is_zero(&fez)); + secp256k1_gej_rescale(&gej_quad, &fez); + CHECK(!secp256k1_gej_has_quad_y_var(&gej_quad)); + secp256k1_gej_neg(&gej_quad, &gej_quad); + CHECK(secp256k1_gej_has_quad_y_var(&gej_quad)); + } +} + +void run_group_decompress(void) { + int i; + for (i = 0; i < count * 4; i++) { + secp256k1_fe fe; + random_fe_test(&fe); + test_group_decompress(&fe); + } +} + +/***** ECMULT TESTS *****/ + +void run_ecmult_chain(void) { + /* random starting point A (on the curve) */ + secp256k1_gej a = SECP256K1_GEJ_CONST( + 0x8b30bbe9, 0xae2a9906, 0x96b22f67, 0x0709dff3, + 0x727fd8bc, 0x04d3362c, 0x6c7bf458, 0xe2846004, + 0xa357ae91, 0x5c4a6528, 0x1309edf2, 0x0504740f, + 0x0eb33439, 0x90216b4f, 0x81063cb6, 0x5f2f7e0f + ); + /* two random initial factors xn and gn */ + secp256k1_scalar xn = SECP256K1_SCALAR_CONST( + 0x84cc5452, 0xf7fde1ed, 0xb4d38a8c, 0xe9b1b84c, + 0xcef31f14, 0x6e569be9, 0x705d357a, 0x42985407 + ); + secp256k1_scalar gn = SECP256K1_SCALAR_CONST( + 0xa1e58d22, 0x553dcd42, 0xb2398062, 0x5d4c57a9, + 0x6e9323d4, 0x2b3152e5, 0xca2c3990, 0xedc7c9de + ); + /* two small multipliers to be applied to xn and gn in every iteration: */ + static const secp256k1_scalar xf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x1337); + static const secp256k1_scalar gf = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0x7113); + /* accumulators with the resulting coefficients to A and G */ + secp256k1_scalar ae = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_scalar ge = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + /* actual points */ + secp256k1_gej x; + secp256k1_gej x2; + int i; + + /* the point being computed */ + x = a; + for (i = 0; i < 200*count; i++) { + /* in each iteration, compute X = xn*X + gn*G; */ + secp256k1_ecmult(&ctx->ecmult_ctx, &x, &x, &xn, &gn); + /* also compute ae and ge: the actual accumulated factors for A and G */ + /* if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G) */ + secp256k1_scalar_mul(&ae, &ae, &xn); + secp256k1_scalar_mul(&ge, &ge, &xn); + secp256k1_scalar_add(&ge, &ge, &gn); + /* modify xn and gn */ + secp256k1_scalar_mul(&xn, &xn, &xf); + secp256k1_scalar_mul(&gn, &gn, &gf); + + /* verify */ + if (i == 19999) { + /* expected result after 19999 iterations */ + secp256k1_gej rp = SECP256K1_GEJ_CONST( + 0xD6E96687, 0xF9B10D09, 0x2A6F3543, 0x9D86CEBE, + 0xA4535D0D, 0x409F5358, 0x6440BD74, 0xB933E830, + 0xB95CBCA2, 0xC77DA786, 0x539BE8FD, 0x53354D2D, + 0x3B4F566A, 0xE6580454, 0x07ED6015, 0xEE1B2A88 + ); + + secp256k1_gej_neg(&rp, &rp); + secp256k1_gej_add_var(&rp, &rp, &x, NULL); + CHECK(secp256k1_gej_is_infinity(&rp)); + } + } + /* redo the computation, but directly with the resulting ae and ge coefficients: */ + secp256k1_ecmult(&ctx->ecmult_ctx, &x2, &a, &ae, &ge); + secp256k1_gej_neg(&x2, &x2); + secp256k1_gej_add_var(&x2, &x2, &x, NULL); + CHECK(secp256k1_gej_is_infinity(&x2)); +} + +void test_point_times_order(const secp256k1_gej *point) { + /* X * (point + G) + (order-X) * (pointer + G) = 0 */ + secp256k1_scalar x; + secp256k1_scalar nx; + secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_gej res1, res2; + secp256k1_ge res3; + unsigned char pub[65]; + size_t psize = 65; + random_scalar_order_test(&x); + secp256k1_scalar_negate(&nx, &x); + secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &x, &x); /* calc res1 = x * point + x * G; */ + secp256k1_ecmult(&ctx->ecmult_ctx, &res2, point, &nx, &nx); /* calc res2 = (order - x) * point + (order - x) * G; */ + secp256k1_gej_add_var(&res1, &res1, &res2, NULL); + CHECK(secp256k1_gej_is_infinity(&res1)); + CHECK(secp256k1_gej_is_valid_var(&res1) == 0); + secp256k1_ge_set_gej(&res3, &res1); + CHECK(secp256k1_ge_is_infinity(&res3)); + CHECK(secp256k1_ge_is_valid_var(&res3) == 0); + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 0) == 0); + psize = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&res3, pub, &psize, 1) == 0); + /* check zero/one edge cases */ + secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &zero); + secp256k1_ge_set_gej(&res3, &res1); + CHECK(secp256k1_ge_is_infinity(&res3)); + secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &one, &zero); + secp256k1_ge_set_gej(&res3, &res1); + ge_equals_gej(&res3, point); + secp256k1_ecmult(&ctx->ecmult_ctx, &res1, point, &zero, &one); + secp256k1_ge_set_gej(&res3, &res1); + ge_equals_ge(&res3, &secp256k1_ge_const_g); +} + +void run_point_times_order(void) { + int i; + secp256k1_fe x = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 2); + static const secp256k1_fe xr = SECP256K1_FE_CONST( + 0x7603CB59, 0xB0EF6C63, 0xFE608479, 0x2A0C378C, + 0xDB3233A8, 0x0F8A9A09, 0xA877DEAD, 0x31B38C45 + ); + for (i = 0; i < 500; i++) { + secp256k1_ge p; + if (secp256k1_ge_set_xo_var(&p, &x, 1)) { + secp256k1_gej j; + CHECK(secp256k1_ge_is_valid_var(&p)); + secp256k1_gej_set_ge(&j, &p); + CHECK(secp256k1_gej_is_valid_var(&j)); + test_point_times_order(&j); + } + secp256k1_fe_sqr(&x, &x); + } + secp256k1_fe_normalize_var(&x); + CHECK(secp256k1_fe_equal_var(&x, &xr)); +} + +void ecmult_const_random_mult(void) { + /* random starting point A (on the curve) */ + secp256k1_ge a = SECP256K1_GE_CONST( + 0x6d986544, 0x57ff52b8, 0xcf1b8126, 0x5b802a5b, + 0xa97f9263, 0xb1e88044, 0x93351325, 0x91bc450a, + 0x535c59f7, 0x325e5d2b, 0xc391fbe8, 0x3c12787c, + 0x337e4a98, 0xe82a9011, 0x0123ba37, 0xdd769c7d + ); + /* random initial factor xn */ + secp256k1_scalar xn = SECP256K1_SCALAR_CONST( + 0x649d4f77, 0xc4242df7, 0x7f2079c9, 0x14530327, + 0xa31b876a, 0xd2d8ce2a, 0x2236d5c6, 0xd7b2029b + ); + /* expected xn * A (from sage) */ + secp256k1_ge expected_b = SECP256K1_GE_CONST( + 0x23773684, 0x4d209dc7, 0x098a786f, 0x20d06fcd, + 0x070a38bf, 0xc11ac651, 0x03004319, 0x1e2a8786, + 0xed8c3b8e, 0xc06dd57b, 0xd06ea66e, 0x45492b0f, + 0xb84e4e1b, 0xfb77e21f, 0x96baae2a, 0x63dec956 + ); + secp256k1_gej b; + secp256k1_ecmult_const(&b, &a, &xn, 256); + + CHECK(secp256k1_ge_is_valid_var(&a)); + ge_equals_gej(&expected_b, &b); +} + +void ecmult_const_commutativity(void) { + secp256k1_scalar a; + secp256k1_scalar b; + secp256k1_gej res1; + secp256k1_gej res2; + secp256k1_ge mid1; + secp256k1_ge mid2; + random_scalar_order_test(&a); + random_scalar_order_test(&b); + + secp256k1_ecmult_const(&res1, &secp256k1_ge_const_g, &a, 256); + secp256k1_ecmult_const(&res2, &secp256k1_ge_const_g, &b, 256); + secp256k1_ge_set_gej(&mid1, &res1); + secp256k1_ge_set_gej(&mid2, &res2); + secp256k1_ecmult_const(&res1, &mid1, &b, 256); + secp256k1_ecmult_const(&res2, &mid2, &a, 256); + secp256k1_ge_set_gej(&mid1, &res1); + secp256k1_ge_set_gej(&mid2, &res2); + ge_equals_ge(&mid1, &mid2); +} + +void ecmult_const_mult_zero_one(void) { + secp256k1_scalar zero = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar one = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 1); + secp256k1_scalar negone; + secp256k1_gej res1; + secp256k1_ge res2; + secp256k1_ge point; + secp256k1_scalar_negate(&negone, &one); + + random_group_element_test(&point); + secp256k1_ecmult_const(&res1, &point, &zero, 3); + secp256k1_ge_set_gej(&res2, &res1); + CHECK(secp256k1_ge_is_infinity(&res2)); + secp256k1_ecmult_const(&res1, &point, &one, 2); + secp256k1_ge_set_gej(&res2, &res1); + ge_equals_ge(&res2, &point); + secp256k1_ecmult_const(&res1, &point, &negone, 256); + secp256k1_gej_neg(&res1, &res1); + secp256k1_ge_set_gej(&res2, &res1); + ge_equals_ge(&res2, &point); +} + +void ecmult_const_chain_multiply(void) { + /* Check known result (randomly generated test problem from sage) */ + const secp256k1_scalar scalar = SECP256K1_SCALAR_CONST( + 0x4968d524, 0x2abf9b7a, 0x466abbcf, 0x34b11b6d, + 0xcd83d307, 0x827bed62, 0x05fad0ce, 0x18fae63b + ); + const secp256k1_gej expected_point = SECP256K1_GEJ_CONST( + 0x5494c15d, 0x32099706, 0xc2395f94, 0x348745fd, + 0x757ce30e, 0x4e8c90fb, 0xa2bad184, 0xf883c69f, + 0x5d195d20, 0xe191bf7f, 0x1be3e55f, 0x56a80196, + 0x6071ad01, 0xf1462f66, 0xc997fa94, 0xdb858435 + ); + secp256k1_gej point; + secp256k1_ge res; + int i; + + secp256k1_gej_set_ge(&point, &secp256k1_ge_const_g); + for (i = 0; i < 100; ++i) { + secp256k1_ge tmp; + secp256k1_ge_set_gej(&tmp, &point); + secp256k1_ecmult_const(&point, &tmp, &scalar, 256); + } + secp256k1_ge_set_gej(&res, &point); + ge_equals_gej(&res, &expected_point); +} + +void run_ecmult_const_tests(void) { + ecmult_const_mult_zero_one(); + ecmult_const_random_mult(); + ecmult_const_commutativity(); + ecmult_const_chain_multiply(); +} + +typedef struct { + secp256k1_scalar *sc; + secp256k1_ge *pt; +} ecmult_multi_data; + +static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + ecmult_multi_data *data = (ecmult_multi_data*) cbdata; + *sc = data->sc[idx]; + *pt = data->pt[idx]; + return 1; +} + +static int ecmult_multi_false_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + (void)sc; + (void)pt; + (void)idx; + (void)cbdata; + return 0; +} + +void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func ecmult_multi) { + int ncount; + secp256k1_scalar szero; + secp256k1_scalar sc[32]; + secp256k1_ge pt[32]; + secp256k1_gej r; + secp256k1_gej r2; + ecmult_multi_data data; + + data.sc = sc; + data.pt = pt; + secp256k1_scalar_set_int(&szero, 0); + + /* No points to multiply */ + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, NULL, ecmult_multi_callback, &data, 0)); + + /* Check 1- and 2-point multiplies against ecmult */ + for (ncount = 0; ncount < count; ncount++) { + secp256k1_ge ptg; + secp256k1_gej ptgj; + random_scalar_order(&sc[0]); + random_scalar_order(&sc[1]); + + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + pt[0] = ptg; + pt[1] = secp256k1_ge_const_g; + + /* only G scalar */ + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &szero, &sc[0]); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[0], ecmult_multi_callback, &data, 0)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + + /* 1-point */ + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &szero); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 1)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + + /* Try to multiply 1 point, but callback returns false */ + CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_false_callback, &data, 1)); + + /* 2-point */ + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 2)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + + /* 2-point with G scalar */ + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &ptgj, &sc[0], &sc[1]); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &sc[1], ecmult_multi_callback, &data, 1)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + /* Check infinite outputs of various forms */ + for (ncount = 0; ncount < count; ncount++) { + secp256k1_ge ptg; + size_t i, j; + size_t sizes[] = { 2, 10, 32 }; + + for (j = 0; j < 3; j++) { + for (i = 0; i < 32; i++) { + random_scalar_order(&sc[i]); + secp256k1_ge_set_infinity(&pt[i]); + } + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + for (j = 0; j < 3; j++) { + for (i = 0; i < 32; i++) { + random_group_element_test(&ptg); + pt[i] = ptg; + secp256k1_scalar_set_int(&sc[i], 0); + } + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + for (j = 0; j < 3; j++) { + random_group_element_test(&ptg); + for (i = 0; i < 16; i++) { + random_scalar_order(&sc[2*i]); + secp256k1_scalar_negate(&sc[2*i + 1], &sc[2*i]); + pt[2 * i] = ptg; + pt[2 * i + 1] = ptg; + } + + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + + random_scalar_order(&sc[0]); + for (i = 0; i < 16; i++) { + random_group_element_test(&ptg); + + sc[2*i] = sc[0]; + sc[2*i+1] = sc[0]; + pt[2 * i] = ptg; + secp256k1_ge_neg(&pt[2*i+1], &pt[2*i]); + } + + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, sizes[j])); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + random_group_element_test(&ptg); + secp256k1_scalar_set_int(&sc[0], 0); + pt[0] = ptg; + for (i = 1; i < 32; i++) { + pt[i] = ptg; + + random_scalar_order(&sc[i]); + secp256k1_scalar_add(&sc[0], &sc[0], &sc[i]); + secp256k1_scalar_negate(&sc[i], &sc[i]); + } + + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 32)); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + /* Check random points, constant scalar */ + for (ncount = 0; ncount < count; ncount++) { + size_t i; + secp256k1_gej_set_infinity(&r); + + random_scalar_order(&sc[0]); + for (i = 0; i < 20; i++) { + secp256k1_ge ptg; + sc[i] = sc[0]; + random_group_element_test(&ptg); + pt[i] = ptg; + secp256k1_gej_add_ge_var(&r, &r, &pt[i], NULL); + } + + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r, &sc[0], &szero); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + /* Check random scalars, constant point */ + for (ncount = 0; ncount < count; ncount++) { + size_t i; + secp256k1_ge ptg; + secp256k1_gej p0j; + secp256k1_scalar rs; + secp256k1_scalar_set_int(&rs, 0); + + random_group_element_test(&ptg); + for (i = 0; i < 20; i++) { + random_scalar_order(&sc[i]); + pt[i] = ptg; + secp256k1_scalar_add(&rs, &rs, &sc[i]); + } + + secp256k1_gej_set_ge(&p0j, &pt[0]); + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &p0j, &rs, &szero); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + secp256k1_gej_neg(&r2, &r2); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + } + + /* Sanity check that zero scalars don't cause problems */ + for (ncount = 0; ncount < 20; ncount++) { + random_scalar_order(&sc[ncount]); + random_group_element_test(&pt[ncount]); + } + + secp256k1_scalar_clear(&sc[0]); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 20)); + secp256k1_scalar_clear(&sc[1]); + secp256k1_scalar_clear(&sc[2]); + secp256k1_scalar_clear(&sc[3]); + secp256k1_scalar_clear(&sc[4]); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 6)); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &szero, ecmult_multi_callback, &data, 5)); + CHECK(secp256k1_gej_is_infinity(&r)); + + /* Run through s0*(t0*P) + s1*(t1*P) exhaustively for many small values of s0, s1, t0, t1 */ + { + const size_t TOP = 8; + size_t s0i, s1i; + size_t t0i, t1i; + secp256k1_ge ptg; + secp256k1_gej ptgj; + + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + + for(t0i = 0; t0i < TOP; t0i++) { + for(t1i = 0; t1i < TOP; t1i++) { + secp256k1_gej t0p, t1p; + secp256k1_scalar t0, t1; + + secp256k1_scalar_set_int(&t0, (t0i + 1) / 2); + secp256k1_scalar_cond_negate(&t0, t0i & 1); + secp256k1_scalar_set_int(&t1, (t1i + 1) / 2); + secp256k1_scalar_cond_negate(&t1, t1i & 1); + + secp256k1_ecmult(&ctx->ecmult_ctx, &t0p, &ptgj, &t0, &szero); + secp256k1_ecmult(&ctx->ecmult_ctx, &t1p, &ptgj, &t1, &szero); + + for(s0i = 0; s0i < TOP; s0i++) { + for(s1i = 0; s1i < TOP; s1i++) { + secp256k1_scalar tmp1, tmp2; + secp256k1_gej expected, actual; + + secp256k1_ge_set_gej(&pt[0], &t0p); + secp256k1_ge_set_gej(&pt[1], &t1p); + + secp256k1_scalar_set_int(&sc[0], (s0i + 1) / 2); + secp256k1_scalar_cond_negate(&sc[0], s0i & 1); + secp256k1_scalar_set_int(&sc[1], (s1i + 1) / 2); + secp256k1_scalar_cond_negate(&sc[1], s1i & 1); + + secp256k1_scalar_mul(&tmp1, &t0, &sc[0]); + secp256k1_scalar_mul(&tmp2, &t1, &sc[1]); + secp256k1_scalar_add(&tmp1, &tmp1, &tmp2); + + secp256k1_ecmult(&ctx->ecmult_ctx, &expected, &ptgj, &tmp1, &szero); + CHECK(ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &actual, &szero, ecmult_multi_callback, &data, 2)); + secp256k1_gej_neg(&expected, &expected); + secp256k1_gej_add_var(&actual, &actual, &expected, NULL); + CHECK(secp256k1_gej_is_infinity(&actual)); + } + } + } + } + } +} + +void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) { + secp256k1_scalar szero; + secp256k1_scalar sc[32]; + secp256k1_ge pt[32]; + secp256k1_gej r; + ecmult_multi_data data; + secp256k1_scratch *scratch_empty; + + data.sc = sc; + data.pt = pt; + secp256k1_scalar_set_int(&szero, 0); + + /* Try to multiply 1 point, but scratch space is empty.*/ + scratch_empty = secp256k1_scratch_create(&ctx->error_callback, 0); + CHECK(!ecmult_multi(&ctx->error_callback, &ctx->ecmult_ctx, scratch_empty, &r, &szero, ecmult_multi_callback, &data, 1)); + secp256k1_scratch_destroy(&ctx->error_callback, scratch_empty); +} + +void test_secp256k1_pippenger_bucket_window_inv(void) { + int i; + + CHECK(secp256k1_pippenger_bucket_window_inv(0) == 0); + for(i = 1; i <= PIPPENGER_MAX_BUCKET_WINDOW; i++) { +#ifdef USE_ENDOMORPHISM + /* Bucket_window of 8 is not used with endo */ + if (i == 8) { + continue; + } +#endif + CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)) == i); + if (i != PIPPENGER_MAX_BUCKET_WINDOW) { + CHECK(secp256k1_pippenger_bucket_window(secp256k1_pippenger_bucket_window_inv(i)+1) > i); + } + } +} + +/** + * Probabilistically test the function returning the maximum number of possible points + * for a given scratch space. + */ +void test_ecmult_multi_pippenger_max_points(void) { + size_t scratch_size = secp256k1_rand_int(256); + size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12); + secp256k1_scratch *scratch; + size_t n_points_supported; + int bucket_window = 0; + + for(; scratch_size < max_size; scratch_size+=256) { + size_t i; + size_t total_alloc; + size_t checkpoint; + scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size); + CHECK(scratch != NULL); + checkpoint = secp256k1_scratch_checkpoint(&ctx->error_callback, scratch); + n_points_supported = secp256k1_pippenger_max_points(&ctx->error_callback, scratch); + if (n_points_supported == 0) { + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + continue; + } + bucket_window = secp256k1_pippenger_bucket_window(n_points_supported); + /* allocate `total_alloc` bytes over `PIPPENGER_SCRATCH_OBJECTS` many allocations */ + total_alloc = secp256k1_pippenger_scratch_size(n_points_supported, bucket_window); + for (i = 0; i < PIPPENGER_SCRATCH_OBJECTS - 1; i++) { + CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, 1)); + total_alloc--; + } + CHECK(secp256k1_scratch_alloc(&ctx->error_callback, scratch, total_alloc)); + secp256k1_scratch_apply_checkpoint(&ctx->error_callback, scratch, checkpoint); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + } + CHECK(bucket_window == PIPPENGER_MAX_BUCKET_WINDOW); +} + +void test_ecmult_multi_batch_size_helper(void) { + size_t n_batches, n_batch_points, max_n_batch_points, n; + + max_n_batch_points = 0; + n = 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 0); + + max_n_batch_points = 1; + n = 0; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 0); + CHECK(n_batch_points == 0); + + max_n_batch_points = 2; + n = 5; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 3); + CHECK(n_batch_points == 2); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH; + n = ECMULT_MAX_POINTS_PER_BATCH; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 1); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH); + + max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH + 1; + n = ECMULT_MAX_POINTS_PER_BATCH + 1; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == 2); + CHECK(n_batch_points == ECMULT_MAX_POINTS_PER_BATCH/2 + 1); + + max_n_batch_points = 1; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX); + CHECK(n_batch_points == 1); + + max_n_batch_points = 2; + n = SIZE_MAX; + CHECK(secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, max_n_batch_points, n) == 1); + CHECK(n_batches == SIZE_MAX/2 + 1); + CHECK(n_batch_points == 2); +} + +/** + * Run secp256k1_ecmult_multi_var with num points and a scratch space restricted to + * 1 <= i <= num points. + */ +void test_ecmult_multi_batching(void) { + static const int n_points = 2*ECMULT_PIPPENGER_THRESHOLD; + secp256k1_scalar scG; + secp256k1_scalar szero; + secp256k1_scalar *sc = (secp256k1_scalar *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_scalar) * n_points); + secp256k1_ge *pt = (secp256k1_ge *)checked_malloc(&ctx->error_callback, sizeof(secp256k1_ge) * n_points); + secp256k1_gej r; + secp256k1_gej r2; + ecmult_multi_data data; + int i; + secp256k1_scratch *scratch; + + secp256k1_gej_set_infinity(&r2); + secp256k1_scalar_set_int(&szero, 0); + + /* Get random scalars and group elements and compute result */ + random_scalar_order(&scG); + secp256k1_ecmult(&ctx->ecmult_ctx, &r2, &r2, &szero, &scG); + for(i = 0; i < n_points; i++) { + secp256k1_ge ptg; + secp256k1_gej ptgj; + random_group_element_test(&ptg); + secp256k1_gej_set_ge(&ptgj, &ptg); + pt[i] = ptg; + random_scalar_order(&sc[i]); + secp256k1_ecmult(&ctx->ecmult_ctx, &ptgj, &ptgj, &sc[i], NULL); + secp256k1_gej_add_var(&r2, &r2, &ptgj, NULL); + } + data.sc = sc; + data.pt = pt; + secp256k1_gej_neg(&r2, &r2); + + /* Test with empty scratch space. It should compute the correct result using + * ecmult_mult_simple algorithm which doesn't require a scratch space. */ + scratch = secp256k1_scratch_create(&ctx->error_callback, 0); + CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + + /* Test with space for 1 point in pippenger. That's not enough because + * ecmult_multi selects strauss which requires more memory. It should + * therefore select the simple algorithm. */ + scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_pippenger_scratch_size(1, 1) + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); + CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + + for(i = 1; i <= n_points; i++) { + if (i > ECMULT_PIPPENGER_THRESHOLD) { + int bucket_window = secp256k1_pippenger_bucket_window(i); + size_t scratch_size = secp256k1_pippenger_scratch_size(i, bucket_window); + scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + PIPPENGER_SCRATCH_OBJECTS*ALIGNMENT); + } else { + size_t scratch_size = secp256k1_strauss_scratch_size(i); + scratch = secp256k1_scratch_create(&ctx->error_callback, scratch_size + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); + } + CHECK(secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &r, &scG, ecmult_multi_callback, &data, n_points)); + secp256k1_gej_add_var(&r, &r, &r2, NULL); + CHECK(secp256k1_gej_is_infinity(&r)); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + } + free(sc); + free(pt); +} + +void run_ecmult_multi_tests(void) { + secp256k1_scratch *scratch; + + test_secp256k1_pippenger_bucket_window_inv(); + test_ecmult_multi_pippenger_max_points(); + scratch = secp256k1_scratch_create(&ctx->error_callback, 819200); + test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); + test_ecmult_multi(NULL, secp256k1_ecmult_multi_var); + test_ecmult_multi(scratch, secp256k1_ecmult_pippenger_batch_single); + test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single); + test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single); + test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + + /* Run test_ecmult_multi with space for exactly one point */ + scratch = secp256k1_scratch_create(&ctx->error_callback, secp256k1_strauss_scratch_size(1) + STRAUSS_SCRATCH_OBJECTS*ALIGNMENT); + test_ecmult_multi(scratch, secp256k1_ecmult_multi_var); + secp256k1_scratch_destroy(&ctx->error_callback, scratch); + + test_ecmult_multi_batch_size_helper(); + test_ecmult_multi_batching(); +} + +void test_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, two, t; + int wnaf[256]; + int zeroes = -1; + int i; + int bits; + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&two, 2); + bits = secp256k1_ecmult_wnaf(wnaf, 256, number, w); + CHECK(bits <= 256); + for (i = bits-1; i >= 0; i--) { + int v = wnaf[i]; + secp256k1_scalar_mul(&x, &x, &two); + if (v) { + CHECK(zeroes == -1 || zeroes >= w-1); /* check that distance between non-zero elements is at least w-1 */ + zeroes=0; + CHECK((v & 1) == 1); /* check non-zero elements are odd */ + CHECK(v <= (1 << (w-1)) - 1); /* check range below */ + CHECK(v >= -(1 << (w-1)) - 1); /* check range above */ + } else { + CHECK(zeroes != -1); /* check that no unnecessary zero padding exists */ + zeroes++; + } + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + CHECK(secp256k1_scalar_eq(&x, number)); /* check that wnaf represents number */ +} + +void test_constant_wnaf_negate(const secp256k1_scalar *number) { + secp256k1_scalar neg1 = *number; + secp256k1_scalar neg2 = *number; + int sign1 = 1; + int sign2 = 1; + + if (!secp256k1_scalar_get_bits(&neg1, 0, 1)) { + secp256k1_scalar_negate(&neg1, &neg1); + sign1 = -1; + } + sign2 = secp256k1_scalar_cond_negate(&neg2, secp256k1_scalar_is_even(&neg2)); + CHECK(sign1 == sign2); + CHECK(secp256k1_scalar_eq(&neg1, &neg2)); +} + +void test_constant_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, shift; + int wnaf[256] = {0}; + int i; + int skew; + int bits = 256; + secp256k1_scalar num = *number; + + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&shift, 1 << w); + /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */ +#ifdef USE_ENDOMORPHISM + for (i = 0; i < 16; ++i) { + secp256k1_scalar_shr_int(&num, 8); + } + bits = 128; +#endif + skew = secp256k1_wnaf_const(wnaf, &num, w, bits); + + for (i = WNAF_SIZE_BITS(bits, w); i >= 0; --i) { + secp256k1_scalar t; + int v = wnaf[i]; + CHECK(v != 0); /* check nonzero */ + CHECK(v & 1); /* check parity */ + CHECK(v > -(1 << w)); /* check range above */ + CHECK(v < (1 << w)); /* check range below */ + + secp256k1_scalar_mul(&x, &x, &shift); + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + /* Skew num because when encoding numbers as odd we use an offset */ + secp256k1_scalar_cadd_bit(&num, skew == 2, 1); + CHECK(secp256k1_scalar_eq(&x, &num)); +} + +void test_fixed_wnaf(const secp256k1_scalar *number, int w) { + secp256k1_scalar x, shift; + int wnaf[256] = {0}; + int i; + int skew; + secp256k1_scalar num = *number; + + secp256k1_scalar_set_int(&x, 0); + secp256k1_scalar_set_int(&shift, 1 << w); + /* With USE_ENDOMORPHISM on we only consider 128-bit numbers */ +#ifdef USE_ENDOMORPHISM + for (i = 0; i < 16; ++i) { + secp256k1_scalar_shr_int(&num, 8); + } +#endif + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + + for (i = WNAF_SIZE(w)-1; i >= 0; --i) { + secp256k1_scalar t; + int v = wnaf[i]; + CHECK(v == 0 || v & 1); /* check parity */ + CHECK(v > -(1 << w)); /* check range above */ + CHECK(v < (1 << w)); /* check range below */ + + secp256k1_scalar_mul(&x, &x, &shift); + if (v >= 0) { + secp256k1_scalar_set_int(&t, v); + } else { + secp256k1_scalar_set_int(&t, -v); + secp256k1_scalar_negate(&t, &t); + } + secp256k1_scalar_add(&x, &x, &t); + } + /* If skew is 1 then add 1 to num */ + secp256k1_scalar_cadd_bit(&num, 0, skew == 1); + CHECK(secp256k1_scalar_eq(&x, &num)); +} + +/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the + * rest is 0.*/ +void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) { + int i; + for (i = WNAF_SIZE(w)-1; i >= 8; --i) { + CHECK(wnaf[i] == 0); + } + for (i = 7; i >= 0; --i) { + CHECK(wnaf[i] == wnaf_expected[i]); + } +} + +void test_fixed_wnaf_small(void) { + int w = 4; + int wnaf[256] = {0}; + int i; + int skew; + secp256k1_scalar num; + + secp256k1_scalar_set_int(&num, 0); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + for (i = WNAF_SIZE(w)-1; i >= 0; --i) { + int v = wnaf[i]; + CHECK(v == 0); + } + CHECK(skew == 0); + + secp256k1_scalar_set_int(&num, 1); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + for (i = WNAF_SIZE(w)-1; i >= 1; --i) { + int v = wnaf[i]; + CHECK(v == 0); + } + CHECK(wnaf[0] == 1); + CHECK(skew == 0); + + { + int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf }; + secp256k1_scalar_set_int(&num, 0xffffffff); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } + { + int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf }; + secp256k1_scalar_set_int(&num, 0xeeeeeeee); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 1); + } + { + int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 }; + secp256k1_scalar_set_int(&num, 0x01010101); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } + { + int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 }; + secp256k1_scalar_set_int(&num, 0x01ef1ef1); + skew = secp256k1_wnaf_fixed(wnaf, &num, w); + test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w); + CHECK(skew == 0); + } +} + +void run_wnaf(void) { + int i; + secp256k1_scalar n = {{0}}; + + /* Sanity check: 1 and 2 are the smallest odd and even numbers and should + * have easier-to-diagnose failure modes */ + n.d[0] = 1; + test_constant_wnaf(&n, 4); + n.d[0] = 2; + test_constant_wnaf(&n, 4); + /* Test 0 */ + test_fixed_wnaf_small(); + /* Random tests */ + for (i = 0; i < count; i++) { + random_scalar_order(&n); + test_wnaf(&n, 4+(i%10)); + test_constant_wnaf_negate(&n); + test_constant_wnaf(&n, 4 + (i % 10)); + test_fixed_wnaf(&n, 4 + (i % 10)); + } + secp256k1_scalar_set_int(&n, 0); + CHECK(secp256k1_scalar_cond_negate(&n, 1) == -1); + CHECK(secp256k1_scalar_is_zero(&n)); + CHECK(secp256k1_scalar_cond_negate(&n, 0) == 1); + CHECK(secp256k1_scalar_is_zero(&n)); +} + +void test_ecmult_constants(void) { + /* Test ecmult_gen() for [0..36) and [order-36..0). */ + secp256k1_scalar x; + secp256k1_gej r; + secp256k1_ge ng; + int i; + int j; + secp256k1_ge_neg(&ng, &secp256k1_ge_const_g); + for (i = 0; i < 36; i++ ) { + secp256k1_scalar_set_int(&x, i); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x); + for (j = 0; j < i; j++) { + if (j == i - 1) { + ge_equals_gej(&secp256k1_ge_const_g, &r); + } + secp256k1_gej_add_ge(&r, &r, &ng); + } + CHECK(secp256k1_gej_is_infinity(&r)); + } + for (i = 1; i <= 36; i++ ) { + secp256k1_scalar_set_int(&x, i); + secp256k1_scalar_negate(&x, &x); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &r, &x); + for (j = 0; j < i; j++) { + if (j == i - 1) { + ge_equals_gej(&ng, &r); + } + secp256k1_gej_add_ge(&r, &r, &secp256k1_ge_const_g); + } + CHECK(secp256k1_gej_is_infinity(&r)); + } +} + +void run_ecmult_constants(void) { + test_ecmult_constants(); +} + +void test_ecmult_gen_blind(void) { + /* Test ecmult_gen() blinding and confirm that the blinding changes, the affine points match, and the z's don't match. */ + secp256k1_scalar key; + secp256k1_scalar b; + unsigned char seed32[32]; + secp256k1_gej pgej; + secp256k1_gej pgej2; + secp256k1_gej i; + secp256k1_ge pge; + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej, &key); + secp256k1_rand256(seed32); + b = ctx->ecmult_gen_ctx.blind; + i = ctx->ecmult_gen_ctx.initial; + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, seed32); + CHECK(!secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind)); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pgej2, &key); + CHECK(!gej_xyz_equals_gej(&pgej, &pgej2)); + CHECK(!gej_xyz_equals_gej(&i, &ctx->ecmult_gen_ctx.initial)); + secp256k1_ge_set_gej(&pge, &pgej); + ge_equals_gej(&pge, &pgej2); +} + +void test_ecmult_gen_blind_reset(void) { + /* Test ecmult_gen() blinding reset and confirm that the blinding is consistent. */ + secp256k1_scalar b; + secp256k1_gej initial; + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0); + b = ctx->ecmult_gen_ctx.blind; + initial = ctx->ecmult_gen_ctx.initial; + secp256k1_ecmult_gen_blind(&ctx->ecmult_gen_ctx, 0); + CHECK(secp256k1_scalar_eq(&b, &ctx->ecmult_gen_ctx.blind)); + CHECK(gej_xyz_equals_gej(&initial, &ctx->ecmult_gen_ctx.initial)); +} + +void run_ecmult_gen_blind(void) { + int i; + test_ecmult_gen_blind_reset(); + for (i = 0; i < 10; i++) { + test_ecmult_gen_blind(); + } +} + +#ifdef USE_ENDOMORPHISM +/***** ENDOMORPHISH TESTS *****/ +void test_scalar_split(void) { + secp256k1_scalar full; + secp256k1_scalar s1, slam; + const unsigned char zero[32] = {0}; + unsigned char tmp[32]; + + random_scalar_order_test(&full); + secp256k1_scalar_split_lambda(&s1, &slam, &full); + + /* check that both are <= 128 bits in size */ + if (secp256k1_scalar_is_high(&s1)) { + secp256k1_scalar_negate(&s1, &s1); + } + if (secp256k1_scalar_is_high(&slam)) { + secp256k1_scalar_negate(&slam, &slam); + } + + secp256k1_scalar_get_b32(tmp, &s1); + CHECK(memcmp(zero, tmp, 16) == 0); + secp256k1_scalar_get_b32(tmp, &slam); + CHECK(memcmp(zero, tmp, 16) == 0); +} + +void run_endomorphism_tests(void) { + test_scalar_split(); +} +#endif + +void ec_pubkey_parse_pointtest(const unsigned char *input, int xvalid, int yvalid) { + unsigned char pubkeyc[65]; + secp256k1_pubkey pubkey; + secp256k1_ge ge; + size_t pubkeyclen; + int32_t ecount; + ecount = 0; + secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); + for (pubkeyclen = 3; pubkeyclen <= 65; pubkeyclen++) { + /* Smaller sizes are tested exhaustively elsewhere. */ + int32_t i; + memcpy(&pubkeyc[1], input, 64); + VG_UNDEF(&pubkeyc[pubkeyclen], 65 - pubkeyclen); + for (i = 0; i < 256; i++) { + /* Try all type bytes. */ + int xpass; + int ypass; + int ysign; + pubkeyc[0] = i; + /* What sign does this point have? */ + ysign = (input[63] & 1) + 2; + /* For the current type (i) do we expect parsing to work? Handled all of compressed/uncompressed/hybrid. */ + xpass = xvalid && (pubkeyclen == 33) && ((i & 254) == 2); + /* Do we expect a parse and re-serialize as uncompressed to give a matching y? */ + ypass = xvalid && yvalid && ((i & 4) == ((pubkeyclen == 65) << 2)) && + ((i == 4) || ((i & 251) == ysign)) && ((pubkeyclen == 33) || (pubkeyclen == 65)); + if (xpass || ypass) { + /* These cases must parse. */ + unsigned char pubkeyo[65]; + size_t outl; + memset(&pubkey, 0, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + ecount = 0; + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1); + VG_CHECK(&pubkey, sizeof(pubkey)); + outl = 65; + VG_UNDEF(pubkeyo, 65); + CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + VG_CHECK(pubkeyo, outl); + CHECK(outl == 33); + CHECK(memcmp(&pubkeyo[1], &pubkeyc[1], 32) == 0); + CHECK((pubkeyclen != 33) || (pubkeyo[0] == pubkeyc[0])); + if (ypass) { + /* This test isn't always done because we decode with alternative signs, so the y won't match. */ + CHECK(pubkeyo[0] == ysign); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + secp256k1_pubkey_save(&pubkey, &ge); + VG_CHECK(&pubkey, sizeof(pubkey)); + outl = 65; + VG_UNDEF(pubkeyo, 65); + CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyo, &outl, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); + VG_CHECK(pubkeyo, outl); + CHECK(outl == 65); + CHECK(pubkeyo[0] == 4); + CHECK(memcmp(&pubkeyo[1], input, 64) == 0); + } + CHECK(ecount == 0); + } else { + /* These cases must fail to parse. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + } + } + secp256k1_context_set_illegal_callback(ctx, NULL, NULL); +} + +void run_ec_pubkey_parse_test(void) { +#define SECP256K1_EC_PARSE_TEST_NVALID (12) + const unsigned char valid[SECP256K1_EC_PARSE_TEST_NVALID][64] = { + { + /* Point with leading and trailing zeros in x and y serialization. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x42, 0x52, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x64, 0xef, 0xa1, 0x7b, 0x77, 0x61, 0xe1, 0xe4, 0x27, 0x06, 0x98, 0x9f, 0xb4, 0x83, + 0xb8, 0xd2, 0xd4, 0x9b, 0xf7, 0x8f, 0xae, 0x98, 0x03, 0xf0, 0x99, 0xb8, 0x34, 0xed, 0xeb, 0x00 + }, + { + /* Point with x equal to a 3rd root of unity.*/ + 0x7a, 0xe9, 0x6a, 0x2b, 0x65, 0x7c, 0x07, 0x10, 0x6e, 0x64, 0x47, 0x9e, 0xac, 0x34, 0x34, 0xe9, + 0x9c, 0xf0, 0x49, 0x75, 0x12, 0xf5, 0x89, 0x95, 0xc1, 0x39, 0x6c, 0x28, 0x71, 0x95, 0x01, 0xee, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Point with largest x. (1/2) */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c, + 0x0e, 0x99, 0x4b, 0x14, 0xea, 0x72, 0xf8, 0xc3, 0xeb, 0x95, 0xc7, 0x1e, 0xf6, 0x92, 0x57, 0x5e, + 0x77, 0x50, 0x58, 0x33, 0x2d, 0x7e, 0x52, 0xd0, 0x99, 0x5c, 0xf8, 0x03, 0x88, 0x71, 0xb6, 0x7d, + }, + { + /* Point with largest x. (2/2) */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2c, + 0xf1, 0x66, 0xb4, 0xeb, 0x15, 0x8d, 0x07, 0x3c, 0x14, 0x6a, 0x38, 0xe1, 0x09, 0x6d, 0xa8, 0xa1, + 0x88, 0xaf, 0xa7, 0xcc, 0xd2, 0x81, 0xad, 0x2f, 0x66, 0xa3, 0x07, 0xfb, 0x77, 0x8e, 0x45, 0xb2, + }, + { + /* Point with smallest x. (1/2) */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Point with smallest x. (2/2) */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, + 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41, + }, + { + /* Point with largest y. (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with largest y. (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with largest y. (3/3) */ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + }, + { + /* Point with smallest y. (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Point with smallest y. (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Point with smallest y. (3/3) */ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01 + } + }; +#define SECP256K1_EC_PARSE_TEST_NXVALID (4) + const unsigned char onlyxvalid[SECP256K1_EC_PARSE_TEST_NXVALID][64] = { + { + /* Valid if y overflow ignored (y = 1 mod p). (1/3) */ + 0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, + 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* Valid if y overflow ignored (y = 1 mod p). (2/3) */ + 0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, + 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* Valid if y overflow ignored (y = 1 mod p). (3/3)*/ + 0x14, 0x6d, 0x3b, 0x65, 0xad, 0xd9, 0xf5, 0x4c, 0xcc, 0xa2, 0x85, 0x33, 0xc8, 0x8e, 0x2c, 0xbc, + 0x63, 0xf7, 0x44, 0x3e, 0x16, 0x58, 0x78, 0x3a, 0xb4, 0x1f, 0x8e, 0xf9, 0x7c, 0x2a, 0x10, 0xb5, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + }, + { + /* x on curve, y is from y^2 = x^3 + 8. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x03 + } + }; +#define SECP256K1_EC_PARSE_TEST_NINVALID (7) + const unsigned char invalid[SECP256K1_EC_PARSE_TEST_NINVALID][64] = { + { + /* x is third root of -8, y is -1 * (x^3+7); also on the curve for y^2 = x^3 + 9. */ + 0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, + 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }, + { + /* Valid if x overflow ignored (x = 1 mod p). */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, + 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee, + }, + { + /* Valid if x overflow ignored (x = 1 mod p). */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x30, + 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, + 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41, + }, + { + /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + 0xf4, 0x84, 0x14, 0x5c, 0xb0, 0x14, 0x9b, 0x82, 0x5d, 0xff, 0x41, 0x2f, 0xa0, 0x52, 0xa8, 0x3f, + 0xcb, 0x72, 0xdb, 0x61, 0xd5, 0x6f, 0x37, 0x70, 0xce, 0x06, 0x6b, 0x73, 0x49, 0xa2, 0xaa, 0x28, + }, + { + /* x is -1, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 5. */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2e, + 0x0b, 0x7b, 0xeb, 0xa3, 0x4f, 0xeb, 0x64, 0x7d, 0xa2, 0x00, 0xbe, 0xd0, 0x5f, 0xad, 0x57, 0xc0, + 0x34, 0x8d, 0x24, 0x9e, 0x2a, 0x90, 0xc8, 0x8f, 0x31, 0xf9, 0x94, 0x8b, 0xb6, 0x5d, 0x52, 0x07, + }, + { + /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x8f, 0x53, 0x7e, 0xef, 0xdf, 0xc1, 0x60, 0x6a, 0x07, 0x27, 0xcd, 0x69, 0xb4, 0xa7, 0x33, 0x3d, + 0x38, 0xed, 0x44, 0xe3, 0x93, 0x2a, 0x71, 0x79, 0xee, 0xcb, 0x4b, 0x6f, 0xba, 0x93, 0x60, 0xdc, + }, + { + /* x is zero, y is the result of the sqrt ladder; also on the curve for y^2 = x^3 - 7. */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x70, 0xac, 0x81, 0x10, 0x20, 0x3e, 0x9f, 0x95, 0xf8, 0xd8, 0x32, 0x96, 0x4b, 0x58, 0xcc, 0xc2, + 0xc7, 0x12, 0xbb, 0x1c, 0x6c, 0xd5, 0x8e, 0x86, 0x11, 0x34, 0xb4, 0x8f, 0x45, 0x6c, 0x9b, 0x53 + } + }; + const unsigned char pubkeyc[66] = { + /* Serialization of G. */ + 0x04, 0x79, 0xBE, 0x66, 0x7E, 0xF9, 0xDC, 0xBB, 0xAC, 0x55, 0xA0, 0x62, 0x95, 0xCE, 0x87, 0x0B, + 0x07, 0x02, 0x9B, 0xFC, 0xDB, 0x2D, 0xCE, 0x28, 0xD9, 0x59, 0xF2, 0x81, 0x5B, 0x16, 0xF8, 0x17, + 0x98, 0x48, 0x3A, 0xDA, 0x77, 0x26, 0xA3, 0xC4, 0x65, 0x5D, 0xA4, 0xFB, 0xFC, 0x0E, 0x11, 0x08, + 0xA8, 0xFD, 0x17, 0xB4, 0x48, 0xA6, 0x85, 0x54, 0x19, 0x9C, 0x47, 0xD0, 0x8F, 0xFB, 0x10, 0xD4, + 0xB8, 0x00 + }; + unsigned char sout[65]; + unsigned char shortkey[2]; + secp256k1_ge ge; + secp256k1_pubkey pubkey; + size_t len; + int32_t i; + int32_t ecount; + int32_t ecount2; + ecount = 0; + /* Nothing should be reading this far into pubkeyc. */ + VG_UNDEF(&pubkeyc[65], 1); + secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); + /* Zero length claimed, fail, zeroize, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(shortkey, 2); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 0) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* Length one claimed, fail, zeroize, no illegal arg error. */ + for (i = 0; i < 256 ; i++) { + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + shortkey[0] = i; + VG_UNDEF(&shortkey[1], 1); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 1) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + /* Length two claimed, fail, zeroize, no illegal arg error. */ + for (i = 0; i < 65536 ; i++) { + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + shortkey[0] = i & 255; + shortkey[1] = i >> 8; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, shortkey, 2) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + } + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + /* 33 bytes claimed on otherwise valid input starting with 0x04, fail, zeroize output, no illegal arg error. */ + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 33) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* NULL pubkey, illegal arg error. Pubkey isn't rewritten before this step, since it's NULL into the parser. */ + CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, pubkeyc, 65) == 0); + CHECK(ecount == 2); + /* NULL input string. Illegal arg and zeroize output. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, NULL, 65) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 1); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 2); + /* 64 bytes claimed on input starting with 0x04, fail, zeroize output, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 64) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* 66 bytes claimed, fail, zeroize output, no illegal arg error. */ + memset(&pubkey, 0xfe, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 66) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 0); + CHECK(ecount == 1); + /* Valid parse. */ + memset(&pubkey, 0, sizeof(pubkey)); + ecount = 0; + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, 65) == 1); + CHECK(secp256k1_ec_pubkey_parse(secp256k1_context_no_precomp, &pubkey, pubkeyc, 65) == 1); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(ecount == 0); + VG_UNDEF(&ge, sizeof(ge)); + CHECK(secp256k1_pubkey_load(ctx, &ge, &pubkey) == 1); + VG_CHECK(&ge.x, sizeof(ge.x)); + VG_CHECK(&ge.y, sizeof(ge.y)); + VG_CHECK(&ge.infinity, sizeof(ge.infinity)); + ge_equals_ge(&secp256k1_ge_const_g, &ge); + CHECK(ecount == 0); + /* secp256k1_ec_pubkey_serialize illegal args. */ + ecount = 0; + len = 65; + CHECK(secp256k1_ec_pubkey_serialize(ctx, NULL, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); + CHECK(ecount == 1); + CHECK(len == 0); + CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, NULL, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 0); + CHECK(ecount == 2); + len = 65; + VG_UNDEF(sout, 65); + CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, NULL, SECP256K1_EC_UNCOMPRESSED) == 0); + VG_CHECK(sout, 65); + CHECK(ecount == 3); + CHECK(len == 0); + len = 65; + CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, ~0) == 0); + CHECK(ecount == 4); + CHECK(len == 0); + len = 65; + VG_UNDEF(sout, 65); + CHECK(secp256k1_ec_pubkey_serialize(ctx, sout, &len, &pubkey, SECP256K1_EC_UNCOMPRESSED) == 1); + VG_CHECK(sout, 65); + CHECK(ecount == 4); + CHECK(len == 65); + /* Multiple illegal args. Should still set arg error only once. */ + ecount = 0; + ecount2 = 11; + CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); + CHECK(ecount == 1); + /* Does the illegal arg callback actually change the behavior? */ + secp256k1_context_set_illegal_callback(ctx, uncounting_illegal_callback_fn, &ecount2); + CHECK(secp256k1_ec_pubkey_parse(ctx, NULL, NULL, 65) == 0); + CHECK(ecount == 1); + CHECK(ecount2 == 10); + secp256k1_context_set_illegal_callback(ctx, NULL, NULL); + /* Try a bunch of prefabbed points with all possible encodings. */ + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NVALID; i++) { + ec_pubkey_parse_pointtest(valid[i], 1, 1); + } + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NXVALID; i++) { + ec_pubkey_parse_pointtest(onlyxvalid[i], 1, 0); + } + for (i = 0; i < SECP256K1_EC_PARSE_TEST_NINVALID; i++) { + ec_pubkey_parse_pointtest(invalid[i], 0, 0); + } +} + +void run_eckey_edge_case_test(void) { + const unsigned char orderc[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41 + }; + const unsigned char zeros[sizeof(secp256k1_pubkey)] = {0x00}; + unsigned char ctmp[33]; + unsigned char ctmp2[33]; + secp256k1_pubkey pubkey; + secp256k1_pubkey pubkey2; + secp256k1_pubkey pubkey_one; + secp256k1_pubkey pubkey_negone; + const secp256k1_pubkey *pubkeys[3]; + size_t len; + int32_t ecount; + /* Group order is too large, reject. */ + CHECK(secp256k1_ec_seckey_verify(ctx, orderc) == 0); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, orderc) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* Maximum value is too large, reject. */ + memset(ctmp, 255, 32); + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* Zero is too small, reject. */ + memset(ctmp, 0, 32); + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* One must be accepted. */ + ctmp[31] = 0x01; + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + pubkey_one = pubkey; + /* Group order + 1 is too large, reject. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x42; + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); + memset(&pubkey, 1, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 0); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* -1 must be accepted. */ + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); + memset(&pubkey, 0, sizeof(pubkey)); + VG_UNDEF(&pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, ctmp) == 1); + VG_CHECK(&pubkey, sizeof(pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + pubkey_negone = pubkey; + /* Tweak of zero leaves the value unchanged. */ + memset(ctmp2, 0, 32); + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 1); + CHECK(memcmp(orderc, ctmp, 31) == 0 && ctmp[31] == 0x40); + memcpy(&pubkey2, &pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); + CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Multiply tweak of zero zeroizes the output. */ + CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); + CHECK(memcmp(zeros, ctmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, ctmp2) == 0); + CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing + seckey, the seckey is zeroized. */ + memcpy(ctmp, orderc, 32); + memset(ctmp2, 0, 32); + ctmp2[31] = 0x01; + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp2) == 1); + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 0); + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, ctmp2) == 0); + CHECK(memcmp(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, ctmp2) == 0); + CHECK(memcmp(zeros, ctmp, 32) == 0); + /* If seckey_tweak_add or seckey_tweak_mul are called with an overflowing + tweak, the seckey is zeroized. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, orderc) == 0); + CHECK(memcmp(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, orderc) == 0); + CHECK(memcmp(zeros, ctmp, 32) == 0); + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + /* If pubkey_tweak_add or pubkey_tweak_mul are called with an overflowing + tweak, the pubkey is zeroized. */ + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, orderc) == 0); + CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, orderc) == 0); + CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* If the resulting key in secp256k1_ec_seckey_tweak_add and + * secp256k1_ec_pubkey_tweak_add is 0 the functions fail and in the latter + * case the pubkey is zeroized. */ + memcpy(ctmp, orderc, 32); + ctmp[31] = 0x40; + memset(ctmp2, 0, 32); + ctmp2[31] = 1; + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 0); + CHECK(memcmp(zeros, ctmp2, 32) == 0); + ctmp2[31] = 1; + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); + CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + /* Tweak computation wraps and results in a key of 1. */ + ctmp2[31] = 2; + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp2, ctmp) == 1); + CHECK(memcmp(ctmp2, zeros, 31) == 0 && ctmp2[31] == 1); + ctmp2[31] = 2; + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); + ctmp2[31] = 1; + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, ctmp2) == 1); + CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Tweak mul * 2 = 1+1. */ + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 1); + ctmp2[31] = 2; + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 1); + CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + /* Test argument errors. */ + ecount = 0; + secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); + CHECK(ecount == 0); + /* Zeroize pubkey on parse error. */ + memset(&pubkey, 0, 32); + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(memcmp(&pubkey, zeros, sizeof(pubkey)) == 0); + memcpy(&pubkey, &pubkey2, sizeof(pubkey)); + memset(&pubkey2, 0, 32); + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey2, ctmp2) == 0); + CHECK(ecount == 2); + CHECK(memcmp(&pubkey2, zeros, sizeof(pubkey2)) == 0); + /* Plain argument errors. */ + ecount = 0; + CHECK(secp256k1_ec_seckey_verify(ctx, ctmp) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ec_seckey_verify(ctx, NULL) == 0); + CHECK(ecount == 1); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 4; + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 4; + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + CHECK(secp256k1_ec_seckey_tweak_add(ctx, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_seckey_tweak_add(ctx, ctmp, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + memset(ctmp2, 0, 32); + ctmp2[31] = 1; + CHECK(secp256k1_ec_seckey_tweak_mul(ctx, NULL, ctmp2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_seckey_tweak_mul(ctx, ctmp, NULL) == 0); + CHECK(ecount == 2); + ecount = 0; + CHECK(secp256k1_ec_pubkey_create(ctx, NULL, ctmp) == 0); + CHECK(ecount == 1); + memset(&pubkey, 1, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0); + CHECK(ecount == 2); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + /* secp256k1_ec_pubkey_combine tests. */ + ecount = 0; + pubkeys[0] = &pubkey_one; + VG_UNDEF(&pubkeys[0], sizeof(secp256k1_pubkey *)); + VG_UNDEF(&pubkeys[1], sizeof(secp256k1_pubkey *)); + VG_UNDEF(&pubkeys[2], sizeof(secp256k1_pubkey *)); + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 0) == 0); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ec_pubkey_combine(ctx, NULL, pubkeys, 1) == 0); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 2); + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, NULL, 1) == 0); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 3); + pubkeys[0] = &pubkey_negone; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 1) == 1); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + len = 33; + CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_negone, SECP256K1_EC_COMPRESSED) == 1); + CHECK(memcmp(ctmp, ctmp2, 33) == 0); + /* Result is infinity. */ + pubkeys[0] = &pubkey_one; + pubkeys[1] = &pubkey_negone; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 0); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) == 0); + CHECK(ecount == 3); + /* Passes through infinity but comes out one. */ + pubkeys[2] = &pubkey_one; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 3) == 1); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + len = 33; + CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp, &len, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + CHECK(secp256k1_ec_pubkey_serialize(ctx, ctmp2, &len, &pubkey_one, SECP256K1_EC_COMPRESSED) == 1); + CHECK(memcmp(ctmp, ctmp2, 33) == 0); + /* Adds to two. */ + pubkeys[1] = &pubkey_one; + memset(&pubkey, 255, sizeof(secp256k1_pubkey)); + VG_UNDEF(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(secp256k1_ec_pubkey_combine(ctx, &pubkey, pubkeys, 2) == 1); + VG_CHECK(&pubkey, sizeof(secp256k1_pubkey)); + CHECK(memcmp(&pubkey, zeros, sizeof(secp256k1_pubkey)) > 0); + CHECK(ecount == 3); + secp256k1_context_set_illegal_callback(ctx, NULL, NULL); +} + +void run_eckey_negate_test(void) { + unsigned char seckey[32]; + unsigned char seckey_tmp[32]; + + random_scalar_order_b32(seckey); + memcpy(seckey_tmp, seckey, 32); + + /* Verify negation changes the key and changes it back */ + CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); + CHECK(memcmp(seckey, seckey_tmp, 32) != 0); + CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); + CHECK(memcmp(seckey, seckey_tmp, 32) == 0); + + /* Check that privkey alias gives same result */ + CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 1); + CHECK(secp256k1_ec_privkey_negate(ctx, seckey_tmp) == 1); + CHECK(memcmp(seckey, seckey_tmp, 32) == 0); + + /* Negating all 0s fails */ + memset(seckey, 0, 32); + memset(seckey_tmp, 0, 32); + CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0); + /* Check that seckey is not modified */ + CHECK(memcmp(seckey, seckey_tmp, 32) == 0); + + /* Negating an overflowing seckey fails and the seckey is zeroed. In this + * test, the seckey has 16 random bytes to ensure that ec_seckey_negate + * doesn't just set seckey to a constant value in case of failure. */ + random_scalar_order_b32(seckey); + memset(seckey, 0xFF, 16); + memset(seckey_tmp, 0, 32); + CHECK(secp256k1_ec_seckey_negate(ctx, seckey) == 0); + CHECK(memcmp(seckey, seckey_tmp, 32) == 0); +} + +void random_sign(secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *key, const secp256k1_scalar *msg, int *recid) { + secp256k1_scalar nonce; + do { + random_scalar_order_test(&nonce); + } while(!secp256k1_ecdsa_sig_sign(&ctx->ecmult_gen_ctx, sigr, sigs, key, msg, &nonce, recid)); +} + +void test_ecdsa_sign_verify(void) { + secp256k1_gej pubj; + secp256k1_ge pub; + secp256k1_scalar one; + secp256k1_scalar msg, key; + secp256k1_scalar sigr, sigs; + int recid; + int getrec; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &pubj, &key); + secp256k1_ge_set_gej(&pub, &pubj); + getrec = secp256k1_rand_bits(1); + random_sign(&sigr, &sigs, &key, &msg, getrec?&recid:NULL); + if (getrec) { + CHECK(recid >= 0 && recid < 4); + } + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg)); + secp256k1_scalar_set_int(&one, 1); + secp256k1_scalar_add(&msg, &msg, &one); + CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &pub, &msg)); +} + +void run_ecdsa_sign_verify(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_ecdsa_sign_verify(); + } +} + +/** Dummy nonce generation function that just uses a precomputed nonce, and fails if it is not accepted. Use only for testing. */ +static int precomputed_nonce_function(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + (void)msg32; + (void)key32; + (void)algo16; + memcpy(nonce32, data, 32); + return (counter == 0); +} + +static int nonce_function_test_fail(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + /* Dummy nonce generator that has a fatal error on the first counter value. */ + if (counter == 0) { + return 0; + } + return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 1); +} + +static int nonce_function_test_retry(unsigned char *nonce32, const unsigned char *msg32, const unsigned char *key32, const unsigned char *algo16, void *data, unsigned int counter) { + /* Dummy nonce generator that produces unacceptable nonces for the first several counter values. */ + if (counter < 3) { + memset(nonce32, counter==0 ? 0 : 255, 32); + if (counter == 2) { + nonce32[31]--; + } + return 1; + } + if (counter < 5) { + static const unsigned char order[] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41 + }; + memcpy(nonce32, order, 32); + if (counter == 4) { + nonce32[31]++; + } + return 1; + } + /* Retry rate of 6979 is negligible esp. as we only call this in deterministic tests. */ + /* If someone does fine a case where it retries for secp256k1, we'd like to know. */ + if (counter > 5) { + return 0; + } + return nonce_function_rfc6979(nonce32, msg32, key32, algo16, data, counter - 5); +} + +int is_empty_signature(const secp256k1_ecdsa_signature *sig) { + static const unsigned char res[sizeof(secp256k1_ecdsa_signature)] = {0}; + return memcmp(sig, res, sizeof(secp256k1_ecdsa_signature)) == 0; +} + +void test_ecdsa_end_to_end(void) { + unsigned char extra[32] = {0x00}; + unsigned char privkey[32]; + unsigned char message[32]; + unsigned char privkey2[32]; + secp256k1_ecdsa_signature signature[6]; + secp256k1_scalar r, s; + unsigned char sig[74]; + size_t siglen = 74; + unsigned char pubkeyc[65]; + size_t pubkeyclen = 65; + secp256k1_pubkey pubkey; + secp256k1_pubkey pubkey_tmp; + unsigned char seckey[300]; + size_t seckeylen = 300; + + /* Generate a random key and message. */ + { + secp256k1_scalar msg, key; + random_scalar_order_test(&msg); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(privkey, &key); + secp256k1_scalar_get_b32(message, &msg); + } + + /* Construct and verify corresponding public key. */ + CHECK(secp256k1_ec_seckey_verify(ctx, privkey) == 1); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, privkey) == 1); + + /* Verify exporting and importing public key. */ + CHECK(secp256k1_ec_pubkey_serialize(ctx, pubkeyc, &pubkeyclen, &pubkey, secp256k1_rand_bits(1) == 1 ? SECP256K1_EC_COMPRESSED : SECP256K1_EC_UNCOMPRESSED)); + memset(&pubkey, 0, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_parse(ctx, &pubkey, pubkeyc, pubkeyclen) == 1); + + /* Verify negation changes the key and changes it back */ + memcpy(&pubkey_tmp, &pubkey, sizeof(pubkey)); + CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); + CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) != 0); + CHECK(secp256k1_ec_pubkey_negate(ctx, &pubkey_tmp) == 1); + CHECK(memcmp(&pubkey_tmp, &pubkey, sizeof(pubkey)) == 0); + + /* Verify private key import and export. */ + CHECK(ec_privkey_export_der(ctx, seckey, &seckeylen, privkey, secp256k1_rand_bits(1) == 1)); + CHECK(ec_privkey_import_der(ctx, privkey2, seckey, seckeylen) == 1); + CHECK(memcmp(privkey, privkey2, 32) == 0); + + /* Optionally tweak the keys using addition. */ + if (secp256k1_rand_int(3) == 0) { + int ret1; + int ret2; + int ret3; + unsigned char rnd[32]; + unsigned char privkey_tmp[32]; + secp256k1_pubkey pubkey2; + secp256k1_rand256_test(rnd); + memcpy(privkey_tmp, privkey, 32); + ret1 = secp256k1_ec_seckey_tweak_add(ctx, privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_add(ctx, &pubkey, rnd); + /* Check that privkey alias gives same result */ + ret3 = secp256k1_ec_privkey_tweak_add(ctx, privkey_tmp, rnd); + CHECK(ret1 == ret2); + CHECK(ret2 == ret3); + if (ret1 == 0) { + return; + } + CHECK(memcmp(privkey, privkey_tmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); + CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + } + + /* Optionally tweak the keys using multiplication. */ + if (secp256k1_rand_int(3) == 0) { + int ret1; + int ret2; + int ret3; + unsigned char rnd[32]; + unsigned char privkey_tmp[32]; + secp256k1_pubkey pubkey2; + secp256k1_rand256_test(rnd); + memcpy(privkey_tmp, privkey, 32); + ret1 = secp256k1_ec_seckey_tweak_mul(ctx, privkey, rnd); + ret2 = secp256k1_ec_pubkey_tweak_mul(ctx, &pubkey, rnd); + /* Check that privkey alias gives same result */ + ret3 = secp256k1_ec_privkey_tweak_mul(ctx, privkey_tmp, rnd); + CHECK(ret1 == ret2); + CHECK(ret2 == ret3); + if (ret1 == 0) { + return; + } + CHECK(memcmp(privkey, privkey_tmp, 32) == 0); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey2, privkey) == 1); + CHECK(memcmp(&pubkey, &pubkey2, sizeof(pubkey)) == 0); + } + + /* Sign. */ + CHECK(secp256k1_ecdsa_sign(ctx, &signature[0], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(ctx, &signature[4], message, privkey, NULL, NULL) == 1); + CHECK(secp256k1_ecdsa_sign(ctx, &signature[1], message, privkey, NULL, extra) == 1); + extra[31] = 1; + CHECK(secp256k1_ecdsa_sign(ctx, &signature[2], message, privkey, NULL, extra) == 1); + extra[31] = 0; + extra[0] = 1; + CHECK(secp256k1_ecdsa_sign(ctx, &signature[3], message, privkey, NULL, extra) == 1); + CHECK(memcmp(&signature[0], &signature[4], sizeof(signature[0])) == 0); + CHECK(memcmp(&signature[0], &signature[1], sizeof(signature[0])) != 0); + CHECK(memcmp(&signature[0], &signature[2], sizeof(signature[0])) != 0); + CHECK(memcmp(&signature[0], &signature[3], sizeof(signature[0])) != 0); + CHECK(memcmp(&signature[1], &signature[2], sizeof(signature[0])) != 0); + CHECK(memcmp(&signature[1], &signature[3], sizeof(signature[0])) != 0); + CHECK(memcmp(&signature[2], &signature[3], sizeof(signature[0])) != 0); + /* Verify. */ + CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[1], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[2], message, &pubkey) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[3], message, &pubkey) == 1); + /* Test lower-S form, malleate, verify and fail, test again, malleate again */ + CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[0])); + secp256k1_ecdsa_signature_load(ctx, &r, &s, &signature[0]); + secp256k1_scalar_negate(&s, &s); + secp256k1_ecdsa_signature_save(&signature[5], &r, &s); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 0); + CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); + CHECK(secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); + CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); + CHECK(!secp256k1_ecdsa_signature_normalize(ctx, &signature[5], &signature[5])); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); + secp256k1_scalar_negate(&s, &s); + secp256k1_ecdsa_signature_save(&signature[5], &r, &s); + CHECK(!secp256k1_ecdsa_signature_normalize(ctx, NULL, &signature[5])); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[5], message, &pubkey) == 1); + CHECK(memcmp(&signature[5], &signature[0], 64) == 0); + + /* Serialize/parse DER and verify again */ + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); + memset(&signature[0], 0, sizeof(signature[0])); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 1); + /* Serialize/destroy/parse DER and verify again. */ + siglen = 74; + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature[0]) == 1); + sig[secp256k1_rand_int(siglen)] += 1 + secp256k1_rand_int(255); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &signature[0], sig, siglen) == 0 || + secp256k1_ecdsa_verify(ctx, &signature[0], message, &pubkey) == 0); +} + +void test_random_pubkeys(void) { + secp256k1_ge elem; + secp256k1_ge elem2; + unsigned char in[65]; + /* Generate some randomly sized pubkeys. */ + size_t len = secp256k1_rand_bits(2) == 0 ? 65 : 33; + if (secp256k1_rand_bits(2) == 0) { + len = secp256k1_rand_bits(6); + } + if (len == 65) { + in[0] = secp256k1_rand_bits(1) ? 4 : (secp256k1_rand_bits(1) ? 6 : 7); + } else { + in[0] = secp256k1_rand_bits(1) ? 2 : 3; + } + if (secp256k1_rand_bits(3) == 0) { + in[0] = secp256k1_rand_bits(8); + } + if (len > 1) { + secp256k1_rand256(&in[1]); + } + if (len > 33) { + secp256k1_rand256(&in[33]); + } + if (secp256k1_eckey_pubkey_parse(&elem, in, len)) { + unsigned char out[65]; + unsigned char firstb; + int res; + size_t size = len; + firstb = in[0]; + /* If the pubkey can be parsed, it should round-trip... */ + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, len == 33)); + CHECK(size == len); + CHECK(memcmp(&in[1], &out[1], len-1) == 0); + /* ... except for the type of hybrid inputs. */ + if ((in[0] != 6) && (in[0] != 7)) { + CHECK(in[0] == out[0]); + } + size = 65; + CHECK(secp256k1_eckey_pubkey_serialize(&elem, in, &size, 0)); + CHECK(size == 65); + CHECK(secp256k1_eckey_pubkey_parse(&elem2, in, size)); + ge_equals_ge(&elem,&elem2); + /* Check that the X9.62 hybrid type is checked. */ + in[0] = secp256k1_rand_bits(1) ? 6 : 7; + res = secp256k1_eckey_pubkey_parse(&elem2, in, size); + if (firstb == 2 || firstb == 3) { + if (in[0] == firstb + 4) { + CHECK(res); + } else { + CHECK(!res); + } + } + if (res) { + ge_equals_ge(&elem,&elem2); + CHECK(secp256k1_eckey_pubkey_serialize(&elem, out, &size, 0)); + CHECK(memcmp(&in[1], &out[1], 64) == 0); + } + } +} + +void run_random_pubkeys(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_random_pubkeys(); + } +} + +void run_ecdsa_end_to_end(void) { + int i; + for (i = 0; i < 64*count; i++) { + test_ecdsa_end_to_end(); + } +} + +int test_ecdsa_der_parse(const unsigned char *sig, size_t siglen, int certainly_der, int certainly_not_der) { + static const unsigned char zeroes[32] = {0}; +#ifdef ENABLE_OPENSSL_TESTS + static const unsigned char max_scalar[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x40 + }; +#endif + + int ret = 0; + + secp256k1_ecdsa_signature sig_der; + unsigned char roundtrip_der[2048]; + unsigned char compact_der[64]; + size_t len_der = 2048; + int parsed_der = 0, valid_der = 0, roundtrips_der = 0; + + secp256k1_ecdsa_signature sig_der_lax; + unsigned char roundtrip_der_lax[2048]; + unsigned char compact_der_lax[64]; + size_t len_der_lax = 2048; + int parsed_der_lax = 0, valid_der_lax = 0, roundtrips_der_lax = 0; + +#ifdef ENABLE_OPENSSL_TESTS + ECDSA_SIG *sig_openssl; + const BIGNUM *r = NULL, *s = NULL; + const unsigned char *sigptr; + unsigned char roundtrip_openssl[2048]; + int len_openssl = 2048; + int parsed_openssl, valid_openssl = 0, roundtrips_openssl = 0; +#endif + + parsed_der = secp256k1_ecdsa_signature_parse_der(ctx, &sig_der, sig, siglen); + if (parsed_der) { + ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der, &sig_der)) << 0; + valid_der = (memcmp(compact_der, zeroes, 32) != 0) && (memcmp(compact_der + 32, zeroes, 32) != 0); + } + if (valid_der) { + ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der, &len_der, &sig_der)) << 1; + roundtrips_der = (len_der == siglen) && memcmp(roundtrip_der, sig, siglen) == 0; + } + + parsed_der_lax = ecdsa_signature_parse_der_lax(ctx, &sig_der_lax, sig, siglen); + if (parsed_der_lax) { + ret |= (!secp256k1_ecdsa_signature_serialize_compact(ctx, compact_der_lax, &sig_der_lax)) << 10; + valid_der_lax = (memcmp(compact_der_lax, zeroes, 32) != 0) && (memcmp(compact_der_lax + 32, zeroes, 32) != 0); + } + if (valid_der_lax) { + ret |= (!secp256k1_ecdsa_signature_serialize_der(ctx, roundtrip_der_lax, &len_der_lax, &sig_der_lax)) << 11; + roundtrips_der_lax = (len_der_lax == siglen) && memcmp(roundtrip_der_lax, sig, siglen) == 0; + } + + if (certainly_der) { + ret |= (!parsed_der) << 2; + } + if (certainly_not_der) { + ret |= (parsed_der) << 17; + } + if (valid_der) { + ret |= (!roundtrips_der) << 3; + } + + if (valid_der) { + ret |= (!roundtrips_der_lax) << 12; + ret |= (len_der != len_der_lax) << 13; + ret |= ((len_der != len_der_lax) || (memcmp(roundtrip_der_lax, roundtrip_der, len_der) != 0)) << 14; + } + ret |= (roundtrips_der != roundtrips_der_lax) << 15; + if (parsed_der) { + ret |= (!parsed_der_lax) << 16; + } + +#ifdef ENABLE_OPENSSL_TESTS + sig_openssl = ECDSA_SIG_new(); + sigptr = sig; + parsed_openssl = (d2i_ECDSA_SIG(&sig_openssl, &sigptr, siglen) != NULL); + if (parsed_openssl) { + ECDSA_SIG_get0(sig_openssl, &r, &s); + valid_openssl = !BN_is_negative(r) && !BN_is_negative(s) && BN_num_bits(r) > 0 && BN_num_bits(r) <= 256 && BN_num_bits(s) > 0 && BN_num_bits(s) <= 256; + if (valid_openssl) { + unsigned char tmp[32] = {0}; + BN_bn2bin(r, tmp + 32 - BN_num_bytes(r)); + valid_openssl = memcmp(tmp, max_scalar, 32) < 0; + } + if (valid_openssl) { + unsigned char tmp[32] = {0}; + BN_bn2bin(s, tmp + 32 - BN_num_bytes(s)); + valid_openssl = memcmp(tmp, max_scalar, 32) < 0; + } + } + len_openssl = i2d_ECDSA_SIG(sig_openssl, NULL); + if (len_openssl <= 2048) { + unsigned char *ptr = roundtrip_openssl; + CHECK(i2d_ECDSA_SIG(sig_openssl, &ptr) == len_openssl); + roundtrips_openssl = valid_openssl && ((size_t)len_openssl == siglen) && (memcmp(roundtrip_openssl, sig, siglen) == 0); + } else { + len_openssl = 0; + } + ECDSA_SIG_free(sig_openssl); + + ret |= (parsed_der && !parsed_openssl) << 4; + ret |= (valid_der && !valid_openssl) << 5; + ret |= (roundtrips_openssl && !parsed_der) << 6; + ret |= (roundtrips_der != roundtrips_openssl) << 7; + if (roundtrips_openssl) { + ret |= (len_der != (size_t)len_openssl) << 8; + ret |= ((len_der != (size_t)len_openssl) || (memcmp(roundtrip_der, roundtrip_openssl, len_der) != 0)) << 9; + } +#endif + return ret; +} + +static void assign_big_endian(unsigned char *ptr, size_t ptrlen, uint32_t val) { + size_t i; + for (i = 0; i < ptrlen; i++) { + int shift = ptrlen - 1 - i; + if (shift >= 4) { + ptr[i] = 0; + } else { + ptr[i] = (val >> shift) & 0xFF; + } + } +} + +static void damage_array(unsigned char *sig, size_t *len) { + int pos; + int action = secp256k1_rand_bits(3); + if (action < 1 && *len > 3) { + /* Delete a byte. */ + pos = secp256k1_rand_int(*len); + memmove(sig + pos, sig + pos + 1, *len - pos - 1); + (*len)--; + return; + } else if (action < 2 && *len < 2048) { + /* Insert a byte. */ + pos = secp256k1_rand_int(1 + *len); + memmove(sig + pos + 1, sig + pos, *len - pos); + sig[pos] = secp256k1_rand_bits(8); + (*len)++; + return; + } else if (action < 4) { + /* Modify a byte. */ + sig[secp256k1_rand_int(*len)] += 1 + secp256k1_rand_int(255); + return; + } else { /* action < 8 */ + /* Modify a bit. */ + sig[secp256k1_rand_int(*len)] ^= 1 << secp256k1_rand_bits(3); + return; + } +} + +static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly_der, int* certainly_not_der) { + int der; + int nlow[2], nlen[2], nlenlen[2], nhbit[2], nhbyte[2], nzlen[2]; + size_t tlen, elen, glen; + int indet; + int n; + + *len = 0; + der = secp256k1_rand_bits(2) == 0; + *certainly_der = der; + *certainly_not_der = 0; + indet = der ? 0 : secp256k1_rand_int(10) == 0; + + for (n = 0; n < 2; n++) { + /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */ + nlow[n] = der ? 1 : (secp256k1_rand_bits(3) != 0); + /* The length of the number in bytes (the first byte of which will always be nonzero) */ + nlen[n] = nlow[n] ? secp256k1_rand_int(33) : 32 + secp256k1_rand_int(200) * secp256k1_rand_int(8) / 8; + CHECK(nlen[n] <= 232); + /* The top bit of the number. */ + nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_rand_bits(1)); + /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */ + nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_rand_bits(7) : 1 + secp256k1_rand_int(127)); + /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */ + nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_rand_int(3) : secp256k1_rand_int(300 - nlen[n]) * secp256k1_rand_int(8) / 8); + if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) { + *certainly_not_der = 1; + } + CHECK(nlen[n] + nzlen[n] <= 300); + /* The length of the length descriptor for the number. 0 means short encoding, anything else is long encoding. */ + nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2); + if (!der) { + /* nlenlen[n] max 127 bytes */ + int add = secp256k1_rand_int(127 - nlenlen[n]) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256; + nlenlen[n] += add; + if (add != 0) { + *certainly_not_der = 1; + } + } + CHECK(nlen[n] + nzlen[n] + nlenlen[n] <= 427); + } + + /* The total length of the data to go, so far */ + tlen = 2 + nlenlen[0] + nlen[0] + nzlen[0] + 2 + nlenlen[1] + nlen[1] + nzlen[1]; + CHECK(tlen <= 856); + + /* The length of the garbage inside the tuple. */ + elen = (der || indet) ? 0 : secp256k1_rand_int(980 - tlen) * secp256k1_rand_int(8) / 8; + if (elen != 0) { + *certainly_not_der = 1; + } + tlen += elen; + CHECK(tlen <= 980); + + /* The length of the garbage after the end of the tuple. */ + glen = der ? 0 : secp256k1_rand_int(990 - tlen) * secp256k1_rand_int(8) / 8; + if (glen != 0) { + *certainly_not_der = 1; + } + CHECK(tlen + glen <= 990); + + /* Write the tuple header. */ + sig[(*len)++] = 0x30; + if (indet) { + /* Indeterminate length */ + sig[(*len)++] = 0x80; + *certainly_not_der = 1; + } else { + int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2); + if (!der) { + int add = secp256k1_rand_int(127 - tlenlen) * secp256k1_rand_int(16) * secp256k1_rand_int(16) / 256; + tlenlen += add; + if (add != 0) { + *certainly_not_der = 1; + } + } + if (tlenlen == 0) { + /* Short length notation */ + sig[(*len)++] = tlen; + } else { + /* Long length notation */ + sig[(*len)++] = 128 + tlenlen; + assign_big_endian(sig + *len, tlenlen, tlen); + *len += tlenlen; + } + tlen += tlenlen; + } + tlen += 2; + CHECK(tlen + glen <= 1119); + + for (n = 0; n < 2; n++) { + /* Write the integer header. */ + sig[(*len)++] = 0x02; + if (nlenlen[n] == 0) { + /* Short length notation */ + sig[(*len)++] = nlen[n] + nzlen[n]; + } else { + /* Long length notation. */ + sig[(*len)++] = 128 + nlenlen[n]; + assign_big_endian(sig + *len, nlenlen[n], nlen[n] + nzlen[n]); + *len += nlenlen[n]; + } + /* Write zero padding */ + while (nzlen[n] > 0) { + sig[(*len)++] = 0x00; + nzlen[n]--; + } + if (nlen[n] == 32 && !nlow[n]) { + /* Special extra 16 0xFF bytes in "high" 32-byte numbers */ + int i; + for (i = 0; i < 16; i++) { + sig[(*len)++] = 0xFF; + } + nlen[n] -= 16; + } + /* Write first byte of number */ + if (nlen[n] > 0) { + sig[(*len)++] = nhbyte[n]; + nlen[n]--; + } + /* Generate remaining random bytes of number */ + secp256k1_rand_bytes_test(sig + *len, nlen[n]); + *len += nlen[n]; + nlen[n] = 0; + } + + /* Generate random garbage inside tuple. */ + secp256k1_rand_bytes_test(sig + *len, elen); + *len += elen; + + /* Generate end-of-contents bytes. */ + if (indet) { + sig[(*len)++] = 0; + sig[(*len)++] = 0; + tlen += 2; + } + CHECK(tlen + glen <= 1121); + + /* Generate random garbage outside tuple. */ + secp256k1_rand_bytes_test(sig + *len, glen); + *len += glen; + tlen += glen; + CHECK(tlen <= 1121); + CHECK(tlen == *len); +} + +void run_ecdsa_der_parse(void) { + int i,j; + for (i = 0; i < 200 * count; i++) { + unsigned char buffer[2048]; + size_t buflen = 0; + int certainly_der = 0; + int certainly_not_der = 0; + random_ber_signature(buffer, &buflen, &certainly_der, &certainly_not_der); + CHECK(buflen <= 2048); + for (j = 0; j < 16; j++) { + int ret = 0; + if (j > 0) { + damage_array(buffer, &buflen); + /* We don't know anything anymore about the DERness of the result */ + certainly_der = 0; + certainly_not_der = 0; + } + ret = test_ecdsa_der_parse(buffer, buflen, certainly_der, certainly_not_der); + if (ret != 0) { + size_t k; + fprintf(stderr, "Failure %x on ", ret); + for (k = 0; k < buflen; k++) { + fprintf(stderr, "%02x ", buffer[k]); + } + fprintf(stderr, "\n"); + } + CHECK(ret == 0); + } + } +} + +/* Tests several edge cases. */ +void test_ecdsa_edge_cases(void) { + int t; + secp256k1_ecdsa_signature sig; + + /* Test the case where ECDSA recomputes a point that is infinity. */ + { + secp256k1_gej keyj; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_negate(&ss, &ss); + secp256k1_scalar_inverse(&ss, &ss); + secp256k1_scalar_set_int(&sr, 1); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &keyj, &sr); + secp256k1_ge_set_gej(&key, &keyj); + msg = ss; + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with r of zero fails. */ + { + const unsigned char pubkey_mods_zero[33] = { + 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, + 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, + 0x41 + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 0); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey_mods_zero, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with s of zero fails. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x01 + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 0); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 1); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + } + + /* Verify signature with message 0 passes. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x02 + }; + const unsigned char pubkey2[33] = { + 0x02, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xfe, 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, + 0x3b, 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, + 0x43 + }; + secp256k1_ge key; + secp256k1_ge key2; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 2); + secp256k1_scalar_set_int(&msg, 0); + secp256k1_scalar_set_int(&sr, 2); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_set_int(&ss, 1); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0); + } + + /* Verify signature with message 1 passes. */ + { + const unsigned char pubkey[33] = { + 0x02, 0x14, 0x4e, 0x5a, 0x58, 0xef, 0x5b, 0x22, + 0x6f, 0xd2, 0xe2, 0x07, 0x6a, 0x77, 0xcf, 0x05, + 0xb4, 0x1d, 0xe7, 0x4a, 0x30, 0x98, 0x27, 0x8c, + 0x93, 0xe6, 0xe6, 0x3c, 0x0b, 0xc4, 0x73, 0x76, + 0x25 + }; + const unsigned char pubkey2[33] = { + 0x02, 0x8a, 0xd5, 0x37, 0xed, 0x73, 0xd9, 0x40, + 0x1d, 0xa0, 0x33, 0xd2, 0xdc, 0xf0, 0xaf, 0xae, + 0x34, 0xcf, 0x5f, 0x96, 0x4c, 0x73, 0x28, 0x0f, + 0x92, 0xc0, 0xf6, 0x9d, 0xd9, 0xb2, 0x09, 0x10, + 0x62 + }; + const unsigned char csr[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xeb + }; + secp256k1_ge key; + secp256k1_ge key2; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 1); + secp256k1_scalar_set_b32(&sr, csr, NULL); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_eckey_pubkey_parse(&key2, pubkey2, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 1); + secp256k1_scalar_set_int(&ss, 2); + secp256k1_scalar_inverse_var(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key2, &msg) == 0); + } + + /* Verify signature with message -1 passes. */ + { + const unsigned char pubkey[33] = { + 0x03, 0xaf, 0x97, 0xff, 0x7d, 0x3a, 0xf6, 0xa0, + 0x02, 0x94, 0xbd, 0x9f, 0x4b, 0x2e, 0xd7, 0x52, + 0x28, 0xdb, 0x49, 0x2a, 0x65, 0xcb, 0x1e, 0x27, + 0x57, 0x9c, 0xba, 0x74, 0x20, 0xd5, 0x1d, 0x20, + 0xf1 + }; + const unsigned char csr[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + 0x45, 0x51, 0x23, 0x19, 0x50, 0xb7, 0x5f, 0xc4, + 0x40, 0x2d, 0xa1, 0x72, 0x2f, 0xc9, 0xba, 0xee + }; + secp256k1_ge key; + secp256k1_scalar msg; + secp256k1_scalar sr, ss; + secp256k1_scalar_set_int(&ss, 1); + secp256k1_scalar_set_int(&msg, 1); + secp256k1_scalar_negate(&msg, &msg); + secp256k1_scalar_set_b32(&sr, csr, NULL); + CHECK(secp256k1_eckey_pubkey_parse(&key, pubkey, 33)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + secp256k1_scalar_negate(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 1); + secp256k1_scalar_set_int(&ss, 3); + secp256k1_scalar_inverse_var(&ss, &ss); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sr, &ss, &key, &msg) == 0); + } + + /* Signature where s would be zero. */ + { + secp256k1_pubkey pubkey; + size_t siglen; + int32_t ecount; + unsigned char signature[72]; + static const unsigned char nonce[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + static const unsigned char nonce2[32] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B, + 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40 + }; + const unsigned char key[32] = { + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, + }; + unsigned char msg[32] = { + 0x86, 0x41, 0x99, 0x81, 0x06, 0x23, 0x44, 0x53, + 0xaa, 0x5f, 0x9d, 0x6a, 0x31, 0x78, 0xf4, 0xf7, + 0xb8, 0x12, 0xe0, 0x0b, 0x81, 0x7a, 0x77, 0x62, + 0x65, 0xdf, 0xdd, 0x31, 0xb9, 0x3e, 0x29, 0xa9, + }; + ecount = 0; + secp256k1_context_set_illegal_callback(ctx, counting_illegal_callback_fn, &ecount); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 0); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 0); + msg[31] = 0xaa; + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce) == 1); + CHECK(ecount == 0); + CHECK(secp256k1_ecdsa_sign(ctx, NULL, msg, key, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, NULL, key, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, NULL, precomputed_nonce_function, nonce2) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, precomputed_nonce_function, nonce2) == 1); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, key) == 1); + CHECK(secp256k1_ecdsa_verify(ctx, NULL, msg, &pubkey) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, NULL, &pubkey) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, NULL) == 0); + CHECK(ecount == 6); + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 1); + CHECK(ecount == 6); + CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, NULL) == 0); + CHECK(ecount == 7); + /* That pubkeyload fails via an ARGCHECK is a little odd but makes sense because pubkeys are an opaque data type. */ + CHECK(secp256k1_ecdsa_verify(ctx, &sig, msg, &pubkey) == 0); + CHECK(ecount == 8); + siglen = 72; + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, NULL, &siglen, &sig) == 0); + CHECK(ecount == 9); + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, NULL, &sig) == 0); + CHECK(ecount == 10); + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, NULL) == 0); + CHECK(ecount == 11); + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 1); + CHECK(ecount == 11); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, NULL, signature, siglen) == 0); + CHECK(ecount == 12); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, NULL, siglen) == 0); + CHECK(ecount == 13); + CHECK(secp256k1_ecdsa_signature_parse_der(ctx, &sig, signature, siglen) == 1); + CHECK(ecount == 13); + siglen = 10; + /* Too little room for a signature does not fail via ARGCHECK. */ + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, signature, &siglen, &sig) == 0); + CHECK(ecount == 13); + ecount = 0; + CHECK(secp256k1_ecdsa_signature_normalize(ctx, NULL, NULL) == 0); + CHECK(ecount == 1); + CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, NULL, &sig) == 0); + CHECK(ecount == 2); + CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, NULL) == 0); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_signature_serialize_compact(ctx, signature, &sig) == 1); + CHECK(ecount == 3); + CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, NULL, signature) == 0); + CHECK(ecount == 4); + CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, NULL) == 0); + CHECK(ecount == 5); + CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 1); + CHECK(ecount == 5); + memset(signature, 255, 64); + CHECK(secp256k1_ecdsa_signature_parse_compact(ctx, &sig, signature) == 0); + CHECK(ecount == 5); + secp256k1_context_set_illegal_callback(ctx, NULL, NULL); + } + + /* Nonce function corner cases. */ + for (t = 0; t < 2; t++) { + static const unsigned char zero[32] = {0x00}; + int i; + unsigned char key[32]; + unsigned char msg[32]; + secp256k1_ecdsa_signature sig2; + secp256k1_scalar sr[512], ss; + const unsigned char *extra; + extra = t == 0 ? NULL : zero; + memset(msg, 0, 32); + msg[31] = 1; + /* High key results in signature failure. */ + memset(key, 0xFF, 32); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* Zero key results in signature failure. */ + memset(key, 0, 32); + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, NULL, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* Nonce function failure results in signature failure. */ + key[31] = 1; + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_fail, extra) == 0); + CHECK(is_empty_signature(&sig)); + /* The retry loop successfully makes its way to the first good value. */ + CHECK(secp256k1_ecdsa_sign(ctx, &sig, msg, key, nonce_function_test_retry, extra) == 1); + CHECK(!is_empty_signature(&sig)); + CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, nonce_function_rfc6979, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0); + /* The default nonce function is deterministic. */ + CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + CHECK(memcmp(&sig, &sig2, sizeof(sig)) == 0); + /* The default nonce function changes output with different messages. */ + for(i = 0; i < 256; i++) { + int j; + msg[0] = i; + CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); + } + } + msg[0] = 0; + msg[31] = 2; + /* The default nonce function changes output with different keys. */ + for(i = 256; i < 512; i++) { + int j; + key[0] = i - 256; + CHECK(secp256k1_ecdsa_sign(ctx, &sig2, msg, key, NULL, extra) == 1); + CHECK(!is_empty_signature(&sig2)); + secp256k1_ecdsa_signature_load(ctx, &sr[i], &ss, &sig2); + for (j = 0; j < i; j++) { + CHECK(!secp256k1_scalar_eq(&sr[i], &sr[j])); + } + } + key[0] = 0; + } + + { + /* Check that optional nonce arguments do not have equivalent effect. */ + const unsigned char zeros[32] = {0}; + unsigned char nonce[32]; + unsigned char nonce2[32]; + unsigned char nonce3[32]; + unsigned char nonce4[32]; + VG_UNDEF(nonce,32); + VG_UNDEF(nonce2,32); + VG_UNDEF(nonce3,32); + VG_UNDEF(nonce4,32); + CHECK(nonce_function_rfc6979(nonce, zeros, zeros, NULL, NULL, 0) == 1); + VG_CHECK(nonce,32); + CHECK(nonce_function_rfc6979(nonce2, zeros, zeros, zeros, NULL, 0) == 1); + VG_CHECK(nonce2,32); + CHECK(nonce_function_rfc6979(nonce3, zeros, zeros, NULL, (void *)zeros, 0) == 1); + VG_CHECK(nonce3,32); + CHECK(nonce_function_rfc6979(nonce4, zeros, zeros, zeros, (void *)zeros, 0) == 1); + VG_CHECK(nonce4,32); + CHECK(memcmp(nonce, nonce2, 32) != 0); + CHECK(memcmp(nonce, nonce3, 32) != 0); + CHECK(memcmp(nonce, nonce4, 32) != 0); + CHECK(memcmp(nonce2, nonce3, 32) != 0); + CHECK(memcmp(nonce2, nonce4, 32) != 0); + CHECK(memcmp(nonce3, nonce4, 32) != 0); + } + + + /* Privkey export where pubkey is the point at infinity. */ + { + unsigned char privkey[300]; + unsigned char seckey[32] = { + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, + 0xba, 0xae, 0xdc, 0xe6, 0xaf, 0x48, 0xa0, 0x3b, + 0xbf, 0xd2, 0x5e, 0x8c, 0xd0, 0x36, 0x41, 0x41, + }; + size_t outlen = 300; + CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 0)); + outlen = 300; + CHECK(!ec_privkey_export_der(ctx, privkey, &outlen, seckey, 1)); + } +} + +void run_ecdsa_edge_cases(void) { + test_ecdsa_edge_cases(); +} + +#ifdef ENABLE_OPENSSL_TESTS +EC_KEY *get_openssl_key(const unsigned char *key32) { + unsigned char privkey[300]; + size_t privkeylen; + const unsigned char* pbegin = privkey; + int compr = secp256k1_rand_bits(1); + EC_KEY *ec_key = EC_KEY_new_by_curve_name(NID_secp256k1); + CHECK(ec_privkey_export_der(ctx, privkey, &privkeylen, key32, compr)); + CHECK(d2i_ECPrivateKey(&ec_key, &pbegin, privkeylen)); + CHECK(EC_KEY_check_key(ec_key)); + return ec_key; +} + +void test_ecdsa_openssl(void) { + secp256k1_gej qj; + secp256k1_ge q; + secp256k1_scalar sigr, sigs; + secp256k1_scalar one; + secp256k1_scalar msg2; + secp256k1_scalar key, msg; + EC_KEY *ec_key; + unsigned int sigsize = 80; + size_t secp_sigsize = 80; + unsigned char message[32]; + unsigned char signature[80]; + unsigned char key32[32]; + secp256k1_rand256_test(message); + secp256k1_scalar_set_b32(&msg, message, NULL); + random_scalar_order_test(&key); + secp256k1_scalar_get_b32(key32, &key); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &qj, &key); + secp256k1_ge_set_gej(&q, &qj); + ec_key = get_openssl_key(key32); + CHECK(ec_key != NULL); + CHECK(ECDSA_sign(0, message, sizeof(message), signature, &sigsize, ec_key)); + CHECK(secp256k1_ecdsa_sig_parse(&sigr, &sigs, signature, sigsize)); + CHECK(secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg)); + secp256k1_scalar_set_int(&one, 1); + secp256k1_scalar_add(&msg2, &msg, &one); + CHECK(!secp256k1_ecdsa_sig_verify(&ctx->ecmult_ctx, &sigr, &sigs, &q, &msg2)); + + random_sign(&sigr, &sigs, &key, &msg, NULL); + CHECK(secp256k1_ecdsa_sig_serialize(signature, &secp_sigsize, &sigr, &sigs)); + CHECK(ECDSA_verify(0, message, sizeof(message), signature, secp_sigsize, ec_key) == 1); + + EC_KEY_free(ec_key); +} + +void run_ecdsa_openssl(void) { + int i; + for (i = 0; i < 10*count; i++) { + test_ecdsa_openssl(); + } +} +#endif + +#ifdef ENABLE_MODULE_ECDH +# include "modules/ecdh/tests_impl.h" +#endif + +#ifdef ENABLE_MODULE_RECOVERY +# include "modules/recovery/tests_impl.h" +#endif + +void run_memczero_test(void) { + unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; + unsigned char buf2[sizeof(buf1)]; + + /* memczero(..., ..., 0) is a noop. */ + memcpy(buf2, buf1, sizeof(buf1)); + memczero(buf1, sizeof(buf1), 0); + CHECK(memcmp(buf1, buf2, sizeof(buf1)) == 0); + + /* memczero(..., ..., 1) zeros the buffer. */ + memset(buf2, 0, sizeof(buf2)); + memczero(buf1, sizeof(buf1) , 1); + CHECK(memcmp(buf1, buf2, sizeof(buf1)) == 0); +} + +int main(int argc, char **argv) { + unsigned char seed16[16] = {0}; + unsigned char run32[32] = {0}; + + /* Disable buffering for stdout to improve reliability of getting + * diagnostic information. Happens right at the start of main because + * setbuf must be used before any other operation on the stream. */ + setbuf(stdout, NULL); + /* Also disable buffering for stderr because it's not guaranteed that it's + * unbuffered on all systems. */ + setbuf(stderr, NULL); + + /* find iteration count */ + if (argc > 1) { + count = strtol(argv[1], NULL, 0); + } + + /* find random seed */ + if (argc > 2) { + int pos = 0; + const char* ch = argv[2]; + while (pos < 16 && ch[0] != 0 && ch[1] != 0) { + unsigned short sh; + if ((sscanf(ch, "%2hx", &sh)) == 1) { + seed16[pos] = sh; + } else { + break; + } + ch += 2; + pos++; + } + } else { + FILE *frand = fopen("/dev/urandom", "r"); + if ((frand == NULL) || fread(&seed16, 1, sizeof(seed16), frand) != sizeof(seed16)) { + uint64_t t = time(NULL) * (uint64_t)1337; + fprintf(stderr, "WARNING: could not read 16 bytes from /dev/urandom; falling back to insecure PRNG\n"); + seed16[0] ^= t; + seed16[1] ^= t >> 8; + seed16[2] ^= t >> 16; + seed16[3] ^= t >> 24; + seed16[4] ^= t >> 32; + seed16[5] ^= t >> 40; + seed16[6] ^= t >> 48; + seed16[7] ^= t >> 56; + } + if (frand) { + fclose(frand); + } + } + secp256k1_rand_seed(seed16); + + printf("test count = %i\n", count); + printf("random seed = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", seed16[0], seed16[1], seed16[2], seed16[3], seed16[4], seed16[5], seed16[6], seed16[7], seed16[8], seed16[9], seed16[10], seed16[11], seed16[12], seed16[13], seed16[14], seed16[15]); + + /* initialize */ + run_context_tests(0); + run_context_tests(1); + run_scratch_tests(); + ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + if (secp256k1_rand_bits(1)) { + secp256k1_rand256(run32); + CHECK(secp256k1_context_randomize(ctx, secp256k1_rand_bits(1) ? run32 : NULL)); + } + + run_rand_bits(); + run_rand_int(); + + run_sha256_tests(); + run_hmac_sha256_tests(); + run_rfc6979_hmac_sha256_tests(); + +#ifndef USE_NUM_NONE + /* num tests */ + run_num_smalltests(); +#endif + + /* scalar tests */ + run_scalar_tests(); + + /* field tests */ + run_field_inv(); + run_field_inv_var(); + run_field_inv_all_var(); + run_field_misc(); + run_field_convert(); + run_sqr(); + run_sqrt(); + + /* group tests */ + run_ge(); + run_group_decompress(); + + /* ecmult tests */ + run_wnaf(); + run_point_times_order(); + run_ecmult_chain(); + run_ecmult_constants(); + run_ecmult_gen_blind(); + run_ecmult_const_tests(); + run_ecmult_multi_tests(); + run_ec_combine(); + + /* endomorphism tests */ +#ifdef USE_ENDOMORPHISM + run_endomorphism_tests(); +#endif + + /* EC point parser test */ + run_ec_pubkey_parse_test(); + + /* EC key edge cases */ + run_eckey_edge_case_test(); + + /* EC key arithmetic test */ + run_eckey_negate_test(); + +#ifdef ENABLE_MODULE_ECDH + /* ecdh tests */ + run_ecdh_tests(); +#endif + + /* ecdsa tests */ + run_random_pubkeys(); + run_ecdsa_der_parse(); + run_ecdsa_sign_verify(); + run_ecdsa_end_to_end(); + run_ecdsa_edge_cases(); +#ifdef ENABLE_OPENSSL_TESTS + run_ecdsa_openssl(); +#endif + +#ifdef ENABLE_MODULE_RECOVERY + /* ECDSA pubkey recovery tests */ + run_recovery_tests(); +#endif + + /* util tests */ + run_memczero_test(); + + secp256k1_rand256(run32); + printf("random run = %02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x%02x\n", run32[0], run32[1], run32[2], run32[3], run32[4], run32[5], run32[6], run32[7], run32[8], run32[9], run32[10], run32[11], run32[12], run32[13], run32[14], run32[15]); + + /* shutdown */ + secp256k1_context_destroy(ctx); + + printf("no problems found\n"); + return 0; +} diff --git a/libsecp256k1/src/tests_exhaustive.c b/libsecp256k1/src/tests_exhaustive.c new file mode 100644 index 0000000..8cca1ce --- /dev/null +++ b/libsecp256k1/src/tests_exhaustive.c @@ -0,0 +1,511 @@ +/*********************************************************************** + * Copyright (c) 2016 Andrew Poelstra * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include + +#include + +#undef USE_ECMULT_STATIC_PRECOMPUTATION + +#ifndef EXHAUSTIVE_TEST_ORDER +/* see group_impl.h for allowable values */ +#define EXHAUSTIVE_TEST_ORDER 13 +#define EXHAUSTIVE_TEST_LAMBDA 9 /* cube root of 1 mod 13 */ +#endif + +#include "include/secp256k1.h" +#include "group.h" +#include "secp256k1.c" +#include "testrand_impl.h" + +#ifdef ENABLE_MODULE_RECOVERY +#include "src/modules/recovery/main_impl.h" +#include "include/secp256k1_recovery.h" +#endif + +/** stolen from tests.c */ +void ge_equals_ge(const secp256k1_ge *a, const secp256k1_ge *b) { + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + CHECK(secp256k1_fe_equal_var(&a->x, &b->x)); + CHECK(secp256k1_fe_equal_var(&a->y, &b->y)); +} + +void ge_equals_gej(const secp256k1_ge *a, const secp256k1_gej *b) { + secp256k1_fe z2s; + secp256k1_fe u1, u2, s1, s2; + CHECK(a->infinity == b->infinity); + if (a->infinity) { + return; + } + /* Check a.x * b.z^2 == b.x && a.y * b.z^3 == b.y, to avoid inverses. */ + secp256k1_fe_sqr(&z2s, &b->z); + secp256k1_fe_mul(&u1, &a->x, &z2s); + u2 = b->x; secp256k1_fe_normalize_weak(&u2); + secp256k1_fe_mul(&s1, &a->y, &z2s); secp256k1_fe_mul(&s1, &s1, &b->z); + s2 = b->y; secp256k1_fe_normalize_weak(&s2); + CHECK(secp256k1_fe_equal_var(&u1, &u2)); + CHECK(secp256k1_fe_equal_var(&s1, &s2)); +} + +void random_fe(secp256k1_fe *x) { + unsigned char bin[32]; + do { + secp256k1_rand256(bin); + if (secp256k1_fe_set_b32(x, bin)) { + return; + } + } while(1); +} +/** END stolen from tests.c */ + +int secp256k1_nonce_function_smallint(unsigned char *nonce32, const unsigned char *msg32, + const unsigned char *key32, const unsigned char *algo16, + void *data, unsigned int attempt) { + secp256k1_scalar s; + int *idata = data; + (void)msg32; + (void)key32; + (void)algo16; + /* Some nonces cannot be used because they'd cause s and/or r to be zero. + * The signing function has retry logic here that just re-calls the nonce + * function with an increased `attempt`. So if attempt > 0 this means we + * need to change the nonce to avoid an infinite loop. */ + if (attempt > 0) { + *idata = (*idata + 1) % EXHAUSTIVE_TEST_ORDER; + } + secp256k1_scalar_set_int(&s, *idata); + secp256k1_scalar_get_b32(nonce32, &s); + return 1; +} + +#ifdef USE_ENDOMORPHISM +void test_exhaustive_endomorphism(const secp256k1_ge *group, int order) { + int i; + for (i = 0; i < order; i++) { + secp256k1_ge res; + secp256k1_ge_mul_lambda(&res, &group[i]); + ge_equals_ge(&group[i * EXHAUSTIVE_TEST_LAMBDA % EXHAUSTIVE_TEST_ORDER], &res); + } +} +#endif + +void test_exhaustive_addition(const secp256k1_ge *group, const secp256k1_gej *groupj, int order) { + int i, j; + + /* Sanity-check (and check infinity functions) */ + CHECK(secp256k1_ge_is_infinity(&group[0])); + CHECK(secp256k1_gej_is_infinity(&groupj[0])); + for (i = 1; i < order; i++) { + CHECK(!secp256k1_ge_is_infinity(&group[i])); + CHECK(!secp256k1_gej_is_infinity(&groupj[i])); + } + + /* Check all addition formulae */ + for (j = 0; j < order; j++) { + secp256k1_fe fe_inv; + secp256k1_fe_inv(&fe_inv, &groupj[j].z); + for (i = 0; i < order; i++) { + secp256k1_ge zless_gej; + secp256k1_gej tmp; + /* add_var */ + secp256k1_gej_add_var(&tmp, &groupj[i], &groupj[j], NULL); + ge_equals_gej(&group[(i + j) % order], &tmp); + /* add_ge */ + if (j > 0) { + secp256k1_gej_add_ge(&tmp, &groupj[i], &group[j]); + ge_equals_gej(&group[(i + j) % order], &tmp); + } + /* add_ge_var */ + secp256k1_gej_add_ge_var(&tmp, &groupj[i], &group[j], NULL); + ge_equals_gej(&group[(i + j) % order], &tmp); + /* add_zinv_var */ + zless_gej.infinity = groupj[j].infinity; + zless_gej.x = groupj[j].x; + zless_gej.y = groupj[j].y; + secp256k1_gej_add_zinv_var(&tmp, &groupj[i], &zless_gej, &fe_inv); + ge_equals_gej(&group[(i + j) % order], &tmp); + } + } + + /* Check doubling */ + for (i = 0; i < order; i++) { + secp256k1_gej tmp; + if (i > 0) { + secp256k1_gej_double_nonzero(&tmp, &groupj[i]); + ge_equals_gej(&group[(2 * i) % order], &tmp); + } + secp256k1_gej_double_var(&tmp, &groupj[i], NULL); + ge_equals_gej(&group[(2 * i) % order], &tmp); + } + + /* Check negation */ + for (i = 1; i < order; i++) { + secp256k1_ge tmp; + secp256k1_gej tmpj; + secp256k1_ge_neg(&tmp, &group[i]); + ge_equals_ge(&group[order - i], &tmp); + secp256k1_gej_neg(&tmpj, &groupj[i]); + ge_equals_gej(&group[order - i], &tmpj); + } +} + +void test_exhaustive_ecmult(const secp256k1_context *ctx, const secp256k1_ge *group, const secp256k1_gej *groupj, int order) { + int i, j, r_log; + for (r_log = 1; r_log < order; r_log++) { + for (j = 0; j < order; j++) { + for (i = 0; i < order; i++) { + secp256k1_gej tmp; + secp256k1_scalar na, ng; + secp256k1_scalar_set_int(&na, i); + secp256k1_scalar_set_int(&ng, j); + + secp256k1_ecmult(&ctx->ecmult_ctx, &tmp, &groupj[r_log], &na, &ng); + ge_equals_gej(&group[(i * r_log + j) % order], &tmp); + + if (i > 0) { + secp256k1_ecmult_const(&tmp, &group[i], &ng, 256); + ge_equals_gej(&group[(i * j) % order], &tmp); + } + } + } + } +} + +typedef struct { + secp256k1_scalar sc[2]; + secp256k1_ge pt[2]; +} ecmult_multi_data; + +static int ecmult_multi_callback(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *cbdata) { + ecmult_multi_data *data = (ecmult_multi_data*) cbdata; + *sc = data->sc[idx]; + *pt = data->pt[idx]; + return 1; +} + +void test_exhaustive_ecmult_multi(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + int i, j, k, x, y; + secp256k1_scratch *scratch = secp256k1_scratch_create(&ctx->error_callback, 4096); + for (i = 0; i < order; i++) { + for (j = 0; j < order; j++) { + for (k = 0; k < order; k++) { + for (x = 0; x < order; x++) { + for (y = 0; y < order; y++) { + secp256k1_gej tmp; + secp256k1_scalar g_sc; + ecmult_multi_data data; + + secp256k1_scalar_set_int(&data.sc[0], i); + secp256k1_scalar_set_int(&data.sc[1], j); + secp256k1_scalar_set_int(&g_sc, k); + data.pt[0] = group[x]; + data.pt[1] = group[y]; + + secp256k1_ecmult_multi_var(&ctx->error_callback, &ctx->ecmult_ctx, scratch, &tmp, &g_sc, ecmult_multi_callback, &data, 2); + ge_equals_gej(&group[(i * x + j * y + k) % order], &tmp); + } + } + } + } + } + secp256k1_scratch_destroy(&ctx->error_callback, scratch); +} + +void r_from_k(secp256k1_scalar *r, const secp256k1_ge *group, int k) { + secp256k1_fe x; + unsigned char x_bin[32]; + k %= EXHAUSTIVE_TEST_ORDER; + x = group[k].x; + secp256k1_fe_normalize(&x); + secp256k1_fe_get_b32(x_bin, &x); + secp256k1_scalar_set_b32(r, x_bin, NULL); +} + +void test_exhaustive_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + int s, r, msg, key; + for (s = 1; s < order; s++) { + for (r = 1; r < order; r++) { + for (msg = 1; msg < order; msg++) { + for (key = 1; key < order; key++) { + secp256k1_ge nonconst_ge; + secp256k1_ecdsa_signature sig; + secp256k1_pubkey pk; + secp256k1_scalar sk_s, msg_s, r_s, s_s; + secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s; + int k, should_verify; + unsigned char msg32[32]; + + secp256k1_scalar_set_int(&s_s, s); + secp256k1_scalar_set_int(&r_s, r); + secp256k1_scalar_set_int(&msg_s, msg); + secp256k1_scalar_set_int(&sk_s, key); + + /* Verify by hand */ + /* Run through every k value that gives us this r and check that *one* works. + * Note there could be none, there could be multiple, ECDSA is weird. */ + should_verify = 0; + for (k = 0; k < order; k++) { + secp256k1_scalar check_x_s; + r_from_k(&check_x_s, group, k); + if (r_s == check_x_s) { + secp256k1_scalar_set_int(&s_times_k_s, k); + secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s); + secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s); + secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s); + should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s); + } + } + /* nb we have a "high s" rule */ + should_verify &= !secp256k1_scalar_is_high(&s_s); + + /* Verify by calling verify */ + secp256k1_ecdsa_signature_save(&sig, &r_s, &s_s); + memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge)); + secp256k1_pubkey_save(&pk, &nonconst_ge); + secp256k1_scalar_get_b32(msg32, &msg_s); + CHECK(should_verify == + secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk)); + } + } + } + } +} + +void test_exhaustive_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + int i, j, k; + + /* Loop */ + for (i = 1; i < order; i++) { /* message */ + for (j = 1; j < order; j++) { /* key */ + for (k = 1; k < order; k++) { /* nonce */ + const int starting_k = k; + secp256k1_ecdsa_signature sig; + secp256k1_scalar sk, msg, r, s, expected_r; + unsigned char sk32[32], msg32[32]; + secp256k1_scalar_set_int(&msg, i); + secp256k1_scalar_set_int(&sk, j); + secp256k1_scalar_get_b32(sk32, &sk); + secp256k1_scalar_get_b32(msg32, &msg); + + secp256k1_ecdsa_sign(ctx, &sig, msg32, sk32, secp256k1_nonce_function_smallint, &k); + + secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig); + /* Note that we compute expected_r *after* signing -- this is important + * because our nonce-computing function function might change k during + * signing. */ + r_from_k(&expected_r, group, k); + CHECK(r == expected_r); + CHECK((k * s) % order == (i + r * j) % order || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order); + + /* Overflow means we've tried every possible nonce */ + if (k < starting_k) { + break; + } + } + } + } + + /* We would like to verify zero-knowledge here by counting how often every + * possible (s, r) tuple appears, but because the group order is larger + * than the field order, when coercing the x-values to scalar values, some + * appear more often than others, so we are actually not zero-knowledge. + * (This effect also appears in the real code, but the difference is on the + * order of 1/2^128th the field order, so the deviation is not useful to a + * computationally bounded attacker.) + */ +} + +#ifdef ENABLE_MODULE_RECOVERY +void test_exhaustive_recovery_sign(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + int i, j, k; + + /* Loop */ + for (i = 1; i < order; i++) { /* message */ + for (j = 1; j < order; j++) { /* key */ + for (k = 1; k < order; k++) { /* nonce */ + const int starting_k = k; + secp256k1_fe r_dot_y_normalized; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + secp256k1_scalar sk, msg, r, s, expected_r; + unsigned char sk32[32], msg32[32]; + int expected_recid; + int recid; + secp256k1_scalar_set_int(&msg, i); + secp256k1_scalar_set_int(&sk, j); + secp256k1_scalar_get_b32(sk32, &sk); + secp256k1_scalar_get_b32(msg32, &msg); + + secp256k1_ecdsa_sign_recoverable(ctx, &rsig, msg32, sk32, secp256k1_nonce_function_smallint, &k); + + /* Check directly */ + secp256k1_ecdsa_recoverable_signature_load(ctx, &r, &s, &recid, &rsig); + r_from_k(&expected_r, group, k); + CHECK(r == expected_r); + CHECK((k * s) % order == (i + r * j) % order || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order); + /* In computing the recid, there is an overflow condition that is disabled in + * scalar_low_impl.h `secp256k1_scalar_set_b32` because almost every r.y value + * will exceed the group order, and our signing code always holds out for r + * values that don't overflow, so with a proper overflow check the tests would + * loop indefinitely. */ + r_dot_y_normalized = group[k].y; + secp256k1_fe_normalize(&r_dot_y_normalized); + /* Also the recovery id is flipped depending if we hit the low-s branch */ + if ((k * s) % order == (i + r * j) % order) { + expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 1 : 0; + } else { + expected_recid = secp256k1_fe_is_odd(&r_dot_y_normalized) ? 0 : 1; + } + CHECK(recid == expected_recid); + + /* Convert to a standard sig then check */ + secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig); + secp256k1_ecdsa_signature_load(ctx, &r, &s, &sig); + /* Note that we compute expected_r *after* signing -- this is important + * because our nonce-computing function function might change k during + * signing. */ + r_from_k(&expected_r, group, k); + CHECK(r == expected_r); + CHECK((k * s) % order == (i + r * j) % order || + (k * (EXHAUSTIVE_TEST_ORDER - s)) % order == (i + r * j) % order); + + /* Overflow means we've tried every possible nonce */ + if (k < starting_k) { + break; + } + } + } + } +} + +void test_exhaustive_recovery_verify(const secp256k1_context *ctx, const secp256k1_ge *group, int order) { + /* This is essentially a copy of test_exhaustive_verify, with recovery added */ + int s, r, msg, key; + for (s = 1; s < order; s++) { + for (r = 1; r < order; r++) { + for (msg = 1; msg < order; msg++) { + for (key = 1; key < order; key++) { + secp256k1_ge nonconst_ge; + secp256k1_ecdsa_recoverable_signature rsig; + secp256k1_ecdsa_signature sig; + secp256k1_pubkey pk; + secp256k1_scalar sk_s, msg_s, r_s, s_s; + secp256k1_scalar s_times_k_s, msg_plus_r_times_sk_s; + int recid = 0; + int k, should_verify; + unsigned char msg32[32]; + + secp256k1_scalar_set_int(&s_s, s); + secp256k1_scalar_set_int(&r_s, r); + secp256k1_scalar_set_int(&msg_s, msg); + secp256k1_scalar_set_int(&sk_s, key); + secp256k1_scalar_get_b32(msg32, &msg_s); + + /* Verify by hand */ + /* Run through every k value that gives us this r and check that *one* works. + * Note there could be none, there could be multiple, ECDSA is weird. */ + should_verify = 0; + for (k = 0; k < order; k++) { + secp256k1_scalar check_x_s; + r_from_k(&check_x_s, group, k); + if (r_s == check_x_s) { + secp256k1_scalar_set_int(&s_times_k_s, k); + secp256k1_scalar_mul(&s_times_k_s, &s_times_k_s, &s_s); + secp256k1_scalar_mul(&msg_plus_r_times_sk_s, &r_s, &sk_s); + secp256k1_scalar_add(&msg_plus_r_times_sk_s, &msg_plus_r_times_sk_s, &msg_s); + should_verify |= secp256k1_scalar_eq(&s_times_k_s, &msg_plus_r_times_sk_s); + } + } + /* nb we have a "high s" rule */ + should_verify &= !secp256k1_scalar_is_high(&s_s); + + /* We would like to try recovering the pubkey and checking that it matches, + * but pubkey recovery is impossible in the exhaustive tests (the reason + * being that there are 12 nonzero r values, 12 nonzero points, and no + * overlap between the sets, so there are no valid signatures). */ + + /* Verify by converting to a standard signature and calling verify */ + secp256k1_ecdsa_recoverable_signature_save(&rsig, &r_s, &s_s, recid); + secp256k1_ecdsa_recoverable_signature_convert(ctx, &sig, &rsig); + memcpy(&nonconst_ge, &group[sk_s], sizeof(nonconst_ge)); + secp256k1_pubkey_save(&pk, &nonconst_ge); + CHECK(should_verify == + secp256k1_ecdsa_verify(ctx, &sig, msg32, &pk)); + } + } + } + } +} +#endif + +int main(void) { + int i; + secp256k1_gej groupj[EXHAUSTIVE_TEST_ORDER]; + secp256k1_ge group[EXHAUSTIVE_TEST_ORDER]; + + /* Build context */ + secp256k1_context *ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY); + + /* TODO set z = 1, then do num_tests runs with random z values */ + + /* Generate the entire group */ + secp256k1_gej_set_infinity(&groupj[0]); + secp256k1_ge_set_gej(&group[0], &groupj[0]); + for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) { + /* Set a different random z-value for each Jacobian point */ + secp256k1_fe z; + random_fe(&z); + + secp256k1_gej_add_ge(&groupj[i], &groupj[i - 1], &secp256k1_ge_const_g); + secp256k1_ge_set_gej(&group[i], &groupj[i]); + secp256k1_gej_rescale(&groupj[i], &z); + + /* Verify against ecmult_gen */ + { + secp256k1_scalar scalar_i; + secp256k1_gej generatedj; + secp256k1_ge generated; + + secp256k1_scalar_set_int(&scalar_i, i); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &generatedj, &scalar_i); + secp256k1_ge_set_gej(&generated, &generatedj); + + CHECK(group[i].infinity == 0); + CHECK(generated.infinity == 0); + CHECK(secp256k1_fe_equal_var(&generated.x, &group[i].x)); + CHECK(secp256k1_fe_equal_var(&generated.y, &group[i].y)); + } + } + + /* Run the tests */ +#ifdef USE_ENDOMORPHISM + test_exhaustive_endomorphism(group, EXHAUSTIVE_TEST_ORDER); +#endif + test_exhaustive_addition(group, groupj, EXHAUSTIVE_TEST_ORDER); + test_exhaustive_ecmult(ctx, group, groupj, EXHAUSTIVE_TEST_ORDER); + test_exhaustive_ecmult_multi(ctx, group, EXHAUSTIVE_TEST_ORDER); + test_exhaustive_sign(ctx, group, EXHAUSTIVE_TEST_ORDER); + test_exhaustive_verify(ctx, group, EXHAUSTIVE_TEST_ORDER); + +#ifdef ENABLE_MODULE_RECOVERY + test_exhaustive_recovery_sign(ctx, group, EXHAUSTIVE_TEST_ORDER); + test_exhaustive_recovery_verify(ctx, group, EXHAUSTIVE_TEST_ORDER); +#endif + + secp256k1_context_destroy(ctx); + return 0; +} + diff --git a/libsecp256k1/src/util.h b/libsecp256k1/src/util.h new file mode 100644 index 0000000..9a86e78 --- /dev/null +++ b/libsecp256k1/src/util.h @@ -0,0 +1,178 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef SECP256K1_UTIL_H +#define SECP256K1_UTIL_H + +#if defined HAVE_CONFIG_H +#include "libsecp256k1-config.h" +#endif + +#include +#include +#include +#include + +typedef struct { + void (*fn)(const char *text, void* data); + const void* data; +} secp256k1_callback; + +static SECP256K1_INLINE void secp256k1_callback_call(const secp256k1_callback * const cb, const char * const text) { + cb->fn(text, (void*)cb->data); +} + +#ifdef DETERMINISTIC +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s\n", msg); \ + abort(); \ +} while(0); +#else +#define TEST_FAILURE(msg) do { \ + fprintf(stderr, "%s:%d: %s\n", __FILE__, __LINE__, msg); \ + abort(); \ +} while(0) +#endif + +#if SECP256K1_GNUC_PREREQ(3, 0) +#define EXPECT(x,c) __builtin_expect((x),(c)) +#else +#define EXPECT(x,c) (x) +#endif + +#ifdef DETERMINISTIC +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed"); \ + } \ +} while(0) +#else +#define CHECK(cond) do { \ + if (EXPECT(!(cond), 0)) { \ + TEST_FAILURE("test condition failed: " #cond); \ + } \ +} while(0) +#endif + +/* Like assert(), but when VERIFY is defined, and side-effect safe. */ +#if defined(COVERAGE) +#define VERIFY_CHECK(check) +#define VERIFY_SETUP(stmt) +#elif defined(VERIFY) +#define VERIFY_CHECK CHECK +#define VERIFY_SETUP(stmt) do { stmt; } while(0) +#else +#define VERIFY_CHECK(cond) do { (void)(cond); } while(0) +#define VERIFY_SETUP(stmt) +#endif + +static SECP256K1_INLINE void *checked_malloc(const secp256k1_callback* cb, size_t size) { + void *ret = malloc(size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +static SECP256K1_INLINE void *checked_realloc(const secp256k1_callback* cb, void *ptr, size_t size) { + void *ret = realloc(ptr, size); + if (ret == NULL) { + secp256k1_callback_call(cb, "Out of memory"); + } + return ret; +} + +#if defined(__BIGGEST_ALIGNMENT__) +#define ALIGNMENT __BIGGEST_ALIGNMENT__ +#else +/* Using 16 bytes alignment because common architectures never have alignment + * requirements above 8 for any of the types we care about. In addition we + * leave some room because currently we don't care about a few bytes. */ +#define ALIGNMENT 16 +#endif + +#define ROUND_TO_ALIGN(size) (((size + ALIGNMENT - 1) / ALIGNMENT) * ALIGNMENT) + +/* Assume there is a contiguous memory object with bounds [base, base + max_size) + * of which the memory range [base, *prealloc_ptr) is already allocated for usage, + * where *prealloc_ptr is an aligned pointer. In that setting, this functions + * reserves the subobject [*prealloc_ptr, *prealloc_ptr + alloc_size) of + * alloc_size bytes by increasing *prealloc_ptr accordingly, taking into account + * alignment requirements. + * + * The function returns an aligned pointer to the newly allocated subobject. + * + * This is useful for manual memory management: if we're simply given a block + * [base, base + max_size), the caller can use this function to allocate memory + * in this block and keep track of the current allocation state with *prealloc_ptr. + * + * It is VERIFY_CHECKed that there is enough space left in the memory object and + * *prealloc_ptr is aligned relative to base. + */ +static SECP256K1_INLINE void *manual_alloc(void** prealloc_ptr, size_t alloc_size, void* base, size_t max_size) { + size_t aligned_alloc_size = ROUND_TO_ALIGN(alloc_size); + void* ret; + VERIFY_CHECK(prealloc_ptr != NULL); + VERIFY_CHECK(*prealloc_ptr != NULL); + VERIFY_CHECK(base != NULL); + VERIFY_CHECK((unsigned char*)*prealloc_ptr >= (unsigned char*)base); + VERIFY_CHECK(((unsigned char*)*prealloc_ptr - (unsigned char*)base) % ALIGNMENT == 0); + VERIFY_CHECK((unsigned char*)*prealloc_ptr - (unsigned char*)base + aligned_alloc_size <= max_size); + ret = *prealloc_ptr; + *((unsigned char**)prealloc_ptr) += aligned_alloc_size; + return ret; +} + +/* Macro for restrict, when available and not in a VERIFY build. */ +#if defined(SECP256K1_BUILD) && defined(VERIFY) +# define SECP256K1_RESTRICT +#else +# if (!defined(__STDC_VERSION__) || (__STDC_VERSION__ < 199901L) ) +# if SECP256K1_GNUC_PREREQ(3,0) +# define SECP256K1_RESTRICT __restrict__ +# elif (defined(_MSC_VER) && _MSC_VER >= 1400) +# define SECP256K1_RESTRICT __restrict +# else +# define SECP256K1_RESTRICT +# endif +# else +# define SECP256K1_RESTRICT restrict +# endif +#endif + +#if defined(_WIN32) +# define I64FORMAT "I64d" +# define I64uFORMAT "I64u" +#else +# define I64FORMAT "lld" +# define I64uFORMAT "llu" +#endif + +#if defined(HAVE___INT128) +# if defined(__GNUC__) +# define SECP256K1_GNUC_EXT __extension__ +# else +# define SECP256K1_GNUC_EXT +# endif +SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t; +#endif + +/* Zero memory if flag == 1. Flag must be 0 or 1. Constant time. */ +static SECP256K1_INLINE void memczero(void *s, size_t len, int flag) { + unsigned char *p = (unsigned char *)s; + /* Access flag with a volatile-qualified lvalue. + This prevents clang from figuring out (after inlining) that flag can + take only be 0 or 1, which leads to variable time code. */ + volatile int vflag = flag; + unsigned char mask = -(unsigned char) vflag; + while (len) { + *p &= ~mask; + p++; + len--; + } +} + +#endif /* SECP256K1_UTIL_H */ diff --git a/libsecp256k1/src/valgrind_ctime_test.c b/libsecp256k1/src/valgrind_ctime_test.c new file mode 100644 index 0000000..5d26244 --- /dev/null +++ b/libsecp256k1/src/valgrind_ctime_test.c @@ -0,0 +1,100 @@ +/********************************************************************** + * Copyright (c) 2020 Gregory Maxwell * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#include +#include "include/secp256k1.h" +#include "util.h" + +#if ENABLE_MODULE_ECDH +# include "include/secp256k1_ecdh.h" +#endif + +int main(void) { + secp256k1_context* ctx; + secp256k1_ecdsa_signature signature; + secp256k1_pubkey pubkey; + size_t siglen = 74; + size_t outputlen = 33; + int i; + int ret; + unsigned char msg[32]; + unsigned char key[32]; + unsigned char sig[74]; + unsigned char spubkey[33]; + + if (!RUNNING_ON_VALGRIND) { + fprintf(stderr, "This test can only usefully be run inside valgrind.\n"); + fprintf(stderr, "Usage: libtool --mode=execute valgrind ./valgrind_ctime_test\n"); + exit(1); + } + + /** In theory, testing with a single secret input should be sufficient: + * If control flow depended on secrets the tool would generate an error. + */ + for (i = 0; i < 32; i++) { + key[i] = i + 65; + } + for (i = 0; i < 32; i++) { + msg[i] = i + 1; + } + + ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_DECLASSIFY); + + /* Test keygen. */ + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_ec_pubkey_create(ctx, &pubkey, key); + VALGRIND_MAKE_MEM_DEFINED(&pubkey, sizeof(secp256k1_pubkey)); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret); + CHECK(secp256k1_ec_pubkey_serialize(ctx, spubkey, &outputlen, &pubkey, SECP256K1_EC_COMPRESSED) == 1); + + /* Test signing. */ + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_ecdsa_sign(ctx, &signature, msg, key, NULL, NULL); + VALGRIND_MAKE_MEM_DEFINED(&signature, sizeof(secp256k1_ecdsa_signature)); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret); + CHECK(secp256k1_ecdsa_signature_serialize_der(ctx, sig, &siglen, &signature)); + +#if ENABLE_MODULE_ECDH + /* Test ECDH. */ + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_ecdh(ctx, msg, &pubkey, key, NULL, NULL); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); +#endif + + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_ec_seckey_verify(ctx, key); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); + + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_ec_seckey_negate(ctx, key); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); + + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + VALGRIND_MAKE_MEM_UNDEFINED(msg, 32); + ret = secp256k1_ec_seckey_tweak_add(ctx, key, msg); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); + + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + VALGRIND_MAKE_MEM_UNDEFINED(msg, 32); + ret = secp256k1_ec_seckey_tweak_mul(ctx, key, msg); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret == 1); + + /* Test context randomisation. Do this last because it leaves the context tainted. */ + VALGRIND_MAKE_MEM_UNDEFINED(key, 32); + ret = secp256k1_context_randomize(ctx, key); + VALGRIND_MAKE_MEM_DEFINED(&ret, sizeof(ret)); + CHECK(ret); + + secp256k1_context_destroy(ctx); + return 0; +} diff --git a/panic_cb.go b/panic_cb.go new file mode 100644 index 0000000..6d59a1d --- /dev/null +++ b/panic_cb.go @@ -0,0 +1,21 @@ +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// Use of this source code is governed by a BSD-style license that can be found in +// the LICENSE file. + +package secp256k1 + +import "C" +import "unsafe" + +// Callbacks for converting libsecp256k1 internal faults into +// recoverable Go panics. + +//export secp256k1GoPanicIllegal +func secp256k1GoPanicIllegal(msg *C.char, data unsafe.Pointer) { + panic("illegal argument: " + C.GoString(msg)) +} + +//export secp256k1GoPanicError +func secp256k1GoPanicError(msg *C.char, data unsafe.Pointer) { + panic("internal error: " + C.GoString(msg)) +} diff --git a/secp256.go b/secp256.go new file mode 100644 index 0000000..76e72fd --- /dev/null +++ b/secp256.go @@ -0,0 +1,222 @@ +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// Use of this source code is governed by a BSD-style license that can be found in +// the LICENSE file. + +// Package secp256k1 wraps the bitcoin secp256k1 C library. +package secp256k1 + +/* +#cgo CFLAGS: -I./libsecp256k1 +#cgo CFLAGS: -I./libsecp256k1/src/ + +#ifdef __SIZEOF_INT128__ +# define HAVE___INT128 +# define USE_FIELD_5X52 +# define USE_SCALAR_4X64 +#else +# define USE_FIELD_10X26 +# define USE_SCALAR_8X32 +#endif + +#define USE_ENDOMORPHISM +#define USE_NUM_NONE +#define USE_FIELD_INV_BUILTIN +#define USE_SCALAR_INV_BUILTIN +#if defined(__x86_64__) +#define USE_FIELD_5X52 +#define USE_SCALAR_4X64 +#define HAVE___INT128 +#else +#define USE_FIELD_10X26 +#define USE_SCALAR_8X32 +#endif +#define ECMULT_WINDOW_SIZE 15 +#define ECMULT_GEN_PREC_BITS 4 +#define USE_ENDOMORPHISM +#define NDEBUG +#include "./libsecp256k1/src/secp256k1.c" +#include "./libsecp256k1/src/modules/recovery/main_impl.h" +#include "ext.h" + +typedef void (*callbackFunc) (const char* msg, void* data); +extern void secp256k1GoPanicIllegal(const char* msg, void* data); +extern void secp256k1GoPanicError(const char* msg, void* data); +*/ +import "C" + +import ( + "errors" + "math/big" + "runtime" + "unsafe" +) + +type Context struct { + context *C.secp256k1_context +} + +var ( + context *C.secp256k1_context + contextsForThreads []*C.secp256k1_context + DefaultContext *Context // to avoid allocating structures every time on `RecoverPubkey` w/o context +) + +func init() { + context = initContext() + DefaultContext = &Context{context} + for i := 0; i < runtime.NumCPU(); i++ { + contextsForThreads = append(contextsForThreads, initContext()) + } +} + +func initContext() *C.secp256k1_context { + // around 20 ms on a modern CPU. + ctx := C.secp256k1_context_create_sign_verify() + C.secp256k1_context_set_illegal_callback(ctx, C.callbackFunc(C.secp256k1GoPanicIllegal), nil) + C.secp256k1_context_set_error_callback(ctx, C.callbackFunc(C.secp256k1GoPanicError), nil) + return ctx +} + +func ContextForThread(threadNo int) *Context { + return &Context{contextsForThreads[threadNo]} +} + +func NumOfContexts() int { + return len(contextsForThreads) +} + +func NewContext() *Context { + ctx := initContext() + return &Context{ctx} +} + +var ( + ErrInvalidMsgLen = errors.New("invalid message length, need 32 bytes") + ErrInvalidSignatureLen = errors.New("invalid signature length") + ErrInvalidRecoveryID = errors.New("invalid signature recovery id") + ErrInvalidKey = errors.New("invalid private key") + ErrInvalidPubkey = errors.New("invalid public key") + ErrSignFailed = errors.New("signing failed") + ErrRecoverFailed = errors.New("recovery failed") +) + +// Sign creates a recoverable ECDSA signature. +// The produced signature is in the 65-byte [R || S || V] format where V is 0 or 1. +// +// The caller is responsible for ensuring that msg cannot be chosen +// directly by an attacker. It is usually preferable to use a cryptographic +// hash function on any input before handing it to this function. +func Sign(msg []byte, seckey []byte) ([]byte, error) { + if len(msg) != 32 { + return nil, ErrInvalidMsgLen + } + if len(seckey) != 32 { + return nil, ErrInvalidKey + } + seckeydata := (*C.uchar)(unsafe.Pointer(&seckey[0])) + if C.secp256k1_ec_seckey_verify(context, seckeydata) != 1 { + return nil, ErrInvalidKey + } + + var ( + msgdata = (*C.uchar)(unsafe.Pointer(&msg[0])) + noncefunc = C.secp256k1_nonce_function_rfc6979 + sigstruct C.secp256k1_ecdsa_recoverable_signature + ) + if C.secp256k1_ecdsa_sign_recoverable(context, &sigstruct, msgdata, seckeydata, noncefunc, nil) == 0 { + return nil, ErrSignFailed + } + + var ( + sig = make([]byte, 65) + sigdata = (*C.uchar)(unsafe.Pointer(&sig[0])) + recid C.int + ) + C.secp256k1_ecdsa_recoverable_signature_serialize_compact(context, sigdata, &recid, &sigstruct) + sig[64] = byte(recid) // add back recid to get 65 bytes sig + return sig, nil +} + +// RecoverPubkey returns the public key of the signer. +// msg must be the 32-byte hash of the message to be signed. +// sig must be a 65-byte compact ECDSA signature containing the +// recovery id as the last element. +func RecoverPubkey(msg []byte, sig []byte) ([]byte, error) { + return RecoverPubkeyWithContext(DefaultContext, msg, sig) +} + +func RecoverPubkeyWithContext(context *Context, msg []byte, sig []byte) ([]byte, error) { + if len(msg) != 32 { + return nil, ErrInvalidMsgLen + } + if err := checkSignature(sig); err != nil { + return nil, err + } + + var ( + pubkey = make([]byte, 65) + sigdata = (*C.uchar)(unsafe.Pointer(&sig[0])) + msgdata = (*C.uchar)(unsafe.Pointer(&msg[0])) + ) + if C.secp256k1_ext_ecdsa_recover(context.context, (*C.uchar)(unsafe.Pointer(&pubkey[0])), sigdata, msgdata) == 0 { + return nil, ErrRecoverFailed + } + return pubkey, nil +} + +// VerifySignature checks that the given pubkey created signature over message. +// The signature should be in [R || S] format. +func VerifySignature(pubkey, msg, signature []byte) bool { + if len(msg) != 32 || len(signature) != 64 || len(pubkey) == 0 { + return false + } + sigdata := (*C.uchar)(unsafe.Pointer(&signature[0])) + msgdata := (*C.uchar)(unsafe.Pointer(&msg[0])) + keydata := (*C.uchar)(unsafe.Pointer(&pubkey[0])) + return C.secp256k1_ext_ecdsa_verify(context, sigdata, msgdata, keydata, C.size_t(len(pubkey))) != 0 +} + +// DecompressPubkey parses a public key in the 33-byte compressed format. +// It returns non-nil coordinates if the public key is valid. +func DecompressPubkey(pubkey []byte) (x, y *big.Int) { + if len(pubkey) != 33 { + return nil, nil + } + var ( + pubkeydata = (*C.uchar)(unsafe.Pointer(&pubkey[0])) + pubkeylen = C.size_t(len(pubkey)) + out = make([]byte, 65) + outdata = (*C.uchar)(unsafe.Pointer(&out[0])) + outlen = C.size_t(len(out)) + ) + if C.secp256k1_ext_reencode_pubkey(context, outdata, outlen, pubkeydata, pubkeylen) == 0 { + return nil, nil + } + return new(big.Int).SetBytes(out[1:33]), new(big.Int).SetBytes(out[33:]) +} + +// CompressPubkey encodes a public key to 33-byte compressed format. +func CompressPubkey(x, y *big.Int) []byte { + var ( + pubkey = S256().Marshal(x, y) + pubkeydata = (*C.uchar)(unsafe.Pointer(&pubkey[0])) + pubkeylen = C.size_t(len(pubkey)) + out = make([]byte, 33) + outdata = (*C.uchar)(unsafe.Pointer(&out[0])) + outlen = C.size_t(len(out)) + ) + if C.secp256k1_ext_reencode_pubkey(context, outdata, outlen, pubkeydata, pubkeylen) == 0 { + panic("libsecp256k1 error") + } + return out +} + +func checkSignature(sig []byte) error { + if len(sig) != 65 { + return ErrInvalidSignatureLen + } + if sig[64] >= 4 { + return ErrInvalidRecoveryID + } + return nil +} diff --git a/secp256_test.go b/secp256_test.go new file mode 100644 index 0000000..ef2a3a3 --- /dev/null +++ b/secp256_test.go @@ -0,0 +1,238 @@ +// Copyright 2015 Jeffrey Wilcke, Felix Lange, Gustav Simonsson. All rights reserved. +// Use of this source code is governed by a BSD-style license that can be found in +// the LICENSE file. + +package secp256k1 + +import ( + "bytes" + "crypto/ecdsa" + "crypto/elliptic" + "crypto/rand" + "encoding/hex" + "io" + "testing" +) + +const TestCount = 1000 + +func generateKeyPair() (pubkey, privkey []byte) { + key, err := ecdsa.GenerateKey(S256(), rand.Reader) + if err != nil { + panic(err) + } + pubkey = elliptic.Marshal(S256(), key.X, key.Y) + + privkey = make([]byte, 32) + blob := key.D.Bytes() + copy(privkey[32-len(blob):], blob) + + return pubkey, privkey +} + +func csprngEntropy(n int) []byte { + buf := make([]byte, n) + if _, err := io.ReadFull(rand.Reader, buf); err != nil { + panic("reading from crypto/rand failed: " + err.Error()) + } + return buf +} + +func randSig() []byte { + sig := csprngEntropy(65) + sig[32] &= 0x70 + sig[64] %= 4 + return sig +} + +// tests for malleability +// highest bit of signature ECDSA s value must be 0, in the 33th byte +func compactSigCheck(t *testing.T, sig []byte) { + var b = int(sig[32]) + if b < 0 { + t.Errorf("highest bit is negative: %d", b) + } + if ((b >> 7) == 1) != ((b & 0x80) == 0x80) { + t.Errorf("highest bit: %d bit >> 7: %d", b, b>>7) + } + if (b & 0x80) == 0x80 { + t.Errorf("highest bit: %d bit & 0x80: %d", b, b&0x80) + } +} + +func TestSignatureValidity(t *testing.T) { + pubkey, seckey := generateKeyPair() + msg := csprngEntropy(32) + sig, err := Sign(msg, seckey) + if err != nil { + t.Errorf("signature error: %s", err) + } + compactSigCheck(t, sig) + if len(pubkey) != 65 { + t.Errorf("pubkey length mismatch: want: 65 have: %d", len(pubkey)) + } + if len(seckey) != 32 { + t.Errorf("seckey length mismatch: want: 32 have: %d", len(seckey)) + } + if len(sig) != 65 { + t.Errorf("sig length mismatch: want: 65 have: %d", len(sig)) + } + recid := int(sig[64]) + if recid > 4 || recid < 0 { + t.Errorf("sig recid mismatch: want: within 0 to 4 have: %d", int(sig[64])) + } +} + +func TestInvalidRecoveryID(t *testing.T) { + _, seckey := generateKeyPair() + msg := csprngEntropy(32) + sig, _ := Sign(msg, seckey) + sig[64] = 99 + _, err := RecoverPubkey(msg, sig) + if err != ErrInvalidRecoveryID { + t.Fatalf("got %q, want %q", err, ErrInvalidRecoveryID) + } +} + +func TestSignAndRecover(t *testing.T) { + pubkey1, seckey := generateKeyPair() + msg := csprngEntropy(32) + sig, err := Sign(msg, seckey) + if err != nil { + t.Errorf("signature error: %s", err) + } + pubkey2, err := RecoverPubkey(msg, sig) + if err != nil { + t.Errorf("recover error: %s", err) + } + if !bytes.Equal(pubkey1, pubkey2) { + t.Errorf("pubkey mismatch: want: %x have: %x", pubkey1, pubkey2) + } +} + +func TestSignDeterministic(t *testing.T) { + _, seckey := generateKeyPair() + msg := make([]byte, 32) + copy(msg, "hi there") + + sig1, err := Sign(msg, seckey) + if err != nil { + t.Fatal(err) + } + sig2, err := Sign(msg, seckey) + if err != nil { + t.Fatal(err) + } + if !bytes.Equal(sig1, sig2) { + t.Fatal("signatures not equal") + } +} + +func TestRandomMessagesWithSameKey(t *testing.T) { + pubkey, seckey := generateKeyPair() + keys := func() ([]byte, []byte) { + return pubkey, seckey + } + signAndRecoverWithRandomMessages(t, keys) +} + +func TestRandomMessagesWithRandomKeys(t *testing.T) { + keys := func() ([]byte, []byte) { + pubkey, seckey := generateKeyPair() + return pubkey, seckey + } + signAndRecoverWithRandomMessages(t, keys) +} + +func signAndRecoverWithRandomMessages(t *testing.T, keys func() ([]byte, []byte)) { + for i := 0; i < TestCount; i++ { + pubkey1, seckey := keys() + msg := csprngEntropy(32) + sig, err := Sign(msg, seckey) + if err != nil { + t.Fatalf("signature error: %s", err) + } + if sig == nil { + t.Fatal("signature is nil") + } + compactSigCheck(t, sig) + + // TODO: why do we flip around the recovery id? + sig[len(sig)-1] %= 4 + + pubkey2, err := RecoverPubkey(msg, sig) + if err != nil { + t.Fatalf("recover error: %s", err) + } + if pubkey2 == nil { + t.Error("pubkey is nil") + } + if !bytes.Equal(pubkey1, pubkey2) { + t.Fatalf("pubkey mismatch: want: %x have: %x", pubkey1, pubkey2) + } + } +} + +func TestRecoveryOfRandomSignature(t *testing.T) { + pubkey1, _ := generateKeyPair() + msg := csprngEntropy(32) + + for i := 0; i < TestCount; i++ { + // recovery can sometimes work, but if so should always give wrong pubkey + pubkey2, _ := RecoverPubkey(msg, randSig()) + if bytes.Equal(pubkey1, pubkey2) { + t.Fatalf("iteration: %d: pubkey mismatch: do NOT want %x: ", i, pubkey2) + } + } +} + +func TestRandomMessagesAgainstValidSig(t *testing.T) { + pubkey1, seckey := generateKeyPair() + msg := csprngEntropy(32) + sig, _ := Sign(msg, seckey) + + for i := 0; i < TestCount; i++ { + msg = csprngEntropy(32) + pubkey2, _ := RecoverPubkey(msg, sig) + // recovery can sometimes work, but if so should always give wrong pubkey + if bytes.Equal(pubkey1, pubkey2) { + t.Fatalf("iteration: %d: pubkey mismatch: do NOT want %x: ", i, pubkey2) + } + } +} + +// Useful when the underlying libsecp256k1 API changes to quickly +// check only recover function without use of signature function +func TestRecoverSanity(t *testing.T) { + msg, _ := hex.DecodeString("ce0677bb30baa8cf067c88db9811f4333d131bf8bcf12fe7065d211dce971008") + sig, _ := hex.DecodeString("90f27b8b488db00b00606796d2987f6a5f59ae62ea05effe84fef5b8b0e549984a691139ad57a3f0b906637673aa2f63d1f55cb1a69199d4009eea23ceaddc9301") + pubkey1, _ := hex.DecodeString("04e32df42865e97135acfb65f3bae71bdc86f4d49150ad6a440b6f15878109880a0a2b2667f7e725ceea70c673093bf67663e0312623c8e091b13cf2c0f11ef652") + pubkey2, err := RecoverPubkey(msg, sig) + if err != nil { + t.Fatalf("recover error: %s", err) + } + if !bytes.Equal(pubkey1, pubkey2) { + t.Errorf("pubkey mismatch: want: %x have: %x", pubkey1, pubkey2) + } +} + +func BenchmarkSign(b *testing.B) { + _, seckey := generateKeyPair() + msg := csprngEntropy(32) + b.ResetTimer() + + for i := 0; i < b.N; i++ { + Sign(msg, seckey) + } +} + +func BenchmarkRecover(b *testing.B) { + msg := csprngEntropy(32) + _, seckey := generateKeyPair() + sig, _ := Sign(msg, seckey) + b.ResetTimer() + + for i := 0; i < b.N; i++ { + RecoverPubkey(msg, sig) + } +}