test: check field representations in used libraries

src/gadgets/nonnative/util.rs

@@ -245,7 +245,7 @@ fn write_be<F: PrimeField, W: Write>(f: &F, mut writer: W) -> io::Result<()> {
 /// Convert a field element to a natural number
 pub fn f_to_nat<Scalar: PrimeField>(f: &Scalar) -> BigInt {
   let mut s = Vec::new();
-  write_be(f, &mut s).unwrap(); // f.to_repr().write_be(&mut s).unwrap();
+  write_be(f, &mut s).unwrap();
   BigInt::from_bytes_le(Sign::Plus, f.to_repr().as_ref())
 }
 
@@ -254,3 +254,41 @@ pub fn f_to_nat<Scalar: PrimeField>(f: &Scalar) -> BigInt {
 pub fn nat_to_f<Scalar: PrimeField>(n: &BigInt) -> Option<Scalar> {
   Scalar::from_str_vartime(&format!("{n}"))
 }
+
+#[cfg(test)]
+mod tests {
+  use bitvec::field::BitField as _;
+  use ff::PrimeFieldBits;
+  use rand::SeedableRng;
+  use rand_chacha::ChaCha20Rng;
+
+  // the write_be function above assumes Field::to_repr() outputs a representation that's an instance
+  // of `AsRef<[u8]>` in lower endian. We test that here, as this is not what the I2OSP standard recommends
+  // and may change in some implementations.
+  fn test_repr_is_le_with<F: PrimeFieldBits>() {
+    let mut rng = ChaCha20Rng::from_seed([0u8; 32]);
+    for _i in 0..50 {
+      let f = F::random(&mut rng);
+      // This is guaranteed to be in LE
+      let le_bits = f.to_le_bits();
+      let leftmost_u64 = le_bits[..64].load_le::<u64>();
+
+      // This is not
+      let f_repr = f.to_repr();
+      let bytes: [u8; 8] = f_repr.as_ref()[..8].try_into().unwrap();
+      let u64_from_repr = u64::from_le_bytes(bytes);
+
+      assert_eq!(leftmost_u64, u64_from_repr);
+    }
+  }
+
+  #[test]
+  fn test_repr_is_le() {
+    test_repr_is_le_with::<pasta_curves::pallas::Scalar>();
+    test_repr_is_le_with::<pasta_curves::pallas::Base>();
+    test_repr_is_le_with::<crate::provider::bn256_grumpkin::bn256::Scalar>();
+    test_repr_is_le_with::<crate::provider::bn256_grumpkin::bn256::Base>();
+    test_repr_is_le_with::<crate::provider::secp_secq::secp256k1::Scalar>();
+    test_repr_is_le_with::<crate::provider::secp_secq::secp256k1::Base>();
+  }
+}