secret-sharing/src/poly: Restrict add/sub/mul assign std ops

The AddAssign, SubAssign, and MulAssign functions can now be used
only when the prime field supports zeroization. This ensures that
any leftover data from heap reallocation, when the right-hand-side
polynomial has more coefficients than the left-hand-side, is zeroized.

An alternative solution is to remove these functions, but this
could lead to performance drawbacks.

secret-sharing/src/poly/univariate.rs

@@ -238,7 +238,7 @@ where
 
 impl<F> AddAssign for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     #[inline]
     fn add_assign(&mut self, rhs: Polynomial<F>) {
@@ -248,9 +248,16 @@ where
 
 impl<F> AddAssign<&Polynomial<F>> for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     fn add_assign(&mut self, rhs: &Polynomial<F>) {
+        if self.a.capacity() < rhs.a.len() {
+            let mut a = Vec::with_capacity(rhs.a.len());
+            a.extend_from_slice(&self.a);
+            self.a.zeroize();
+            self.a = a;
+        }
+
         let min_len = min(self.a.len(), rhs.a.len());
 
         for i in 0..min_len {
@@ -321,7 +328,7 @@ where
 
 impl<F> SubAssign for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     #[inline]
     fn sub_assign(&mut self, rhs: Polynomial<F>) {
@@ -331,9 +338,16 @@ where
 
 impl<F> SubAssign<&Polynomial<F>> for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     fn sub_assign(&mut self, rhs: &Polynomial<F>) {
+        if self.a.capacity() < rhs.a.len() {
+            let mut a = Vec::with_capacity(rhs.a.len());
+            a.extend_from_slice(&self.a);
+            self.a.zeroize();
+            self.a = a;
+        }
+
         let min_len = min(self.a.len(), rhs.a.len());
 
         for i in 0..min_len {
@@ -510,7 +524,7 @@ where
 
 impl<F> Sum for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     fn sum<I: Iterator<Item = Polynomial<F>>>(iter: I) -> Polynomial<F> {
         let mut sum = Polynomial::zero(0);
@@ -521,7 +535,7 @@ where
 
 impl<'a, F> Sum<&'a Polynomial<F>> for Polynomial<F>
 where
-    F: PrimeField,
+    F: PrimeField + Zeroize,
 {
     fn sum<I: Iterator<Item = &'a Polynomial<F>>>(iter: I) -> Polynomial<F> {
         let mut sum = Polynomial::zero(0);