Initial commit

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.

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
+}