Add tests for the premise of the Schnorr contract to the Schnorr crate

networks/ethereum/schnorr/src/tests/premise.rs

@@ -0,0 +1,111 @@
+use rand_core::{RngCore, OsRng};
+
+use sha3::{Digest, Keccak256};
+use group::ff::{Field, PrimeField};
+use k256::{
+  elliptic_curve::{ops::Reduce, point::AffineCoordinates, sec1::ToEncodedPoint},
+  ecdsa::{
+    self, hazmat::SignPrimitive, signature::hazmat::PrehashVerifier, SigningKey, VerifyingKey,
+  },
+  U256, Scalar, ProjectivePoint,
+};
+
+use alloy_core::primitives::Address;
+
+use crate::{PublicKey, Signature};
+
+// The ecrecover opcode, yet with if the y is odd replacing v
+fn ecrecover(message: Scalar, odd_y: bool, r: Scalar, s: Scalar) -> Option<[u8; 20]> {
+  let sig = ecdsa::Signature::from_scalars(r, s).ok()?;
+  let message: [u8; 32] = message.to_repr().into();
+  alloy_core::primitives::Signature::from_signature_and_parity(
+    sig,
+    alloy_core::primitives::Parity::Parity(odd_y),
+  )
+  .ok()?
+  .recover_address_from_prehash(&alloy_core::primitives::B256::from(message))
+  .ok()
+  .map(Into::into)
+}
+
+// Test ecrecover behaves as expected
+#[test]
+fn test_ecrecover() {
+  let private = SigningKey::random(&mut OsRng);
+  let public = VerifyingKey::from(&private);
+
+  // Sign the signature
+  const MESSAGE: &[u8] = b"Hello, World!";
+  let (sig, recovery_id) = private
+    .as_nonzero_scalar()
+    .try_sign_prehashed(Scalar::random(&mut OsRng), &Keccak256::digest(MESSAGE))
+    .unwrap();
+
+  // Sanity check the signature verifies
+  #[allow(clippy::unit_cmp)] // Intended to assert this wasn't changed to Result<bool>
+  {
+    assert_eq!(public.verify_prehash(&Keccak256::digest(MESSAGE), &sig).unwrap(), ());
+  }
+
+  // Perform the ecrecover
+  assert_eq!(
+    ecrecover(
+      <Scalar as Reduce<U256>>::reduce_bytes(&Keccak256::digest(MESSAGE)),
+      u8::from(recovery_id.unwrap().is_y_odd()) == 1,
+      *sig.r(),
+      *sig.s()
+    )
+    .unwrap(),
+    Address::from_raw_public_key(&public.to_encoded_point(false).as_ref()[1 ..]),
+  );
+}
+
+// Test that we can recover the nonce from a Schnorr signature via a call to ecrecover, the premise
+// of efficiently verifying Schnorr signatures in an Ethereum contract
+#[test]
+fn nonce_recovery_via_ecrecover() {
+  let (key, public_key) = loop {
+    let key = Scalar::random(&mut OsRng);
+    if let Some(public_key) = PublicKey::new(ProjectivePoint::GENERATOR * key) {
+      break (key, public_key);
+    }
+  };
+
+  let nonce = Scalar::random(&mut OsRng);
+  let R = ProjectivePoint::GENERATOR * nonce;
+
+  let mut message = vec![0; 1 + usize::try_from(OsRng.next_u32() % 256).unwrap()];
+  OsRng.fill_bytes(&mut message);
+
+  let c = Signature::challenge(R, &public_key, &message);
+  let s = nonce + (c * key);
+
+  /*
+    An ECDSA signature is `(r, s)` with `s = (H(m) + rx) / k`, where:
+    - `m` is the message
+    - `r` is the x-coordinate of the nonce, reduced into a scalar
+    - `x` is the private key
+    - `k` is the nonce
+
+    We fix the recovery ID to be for the even key with an x-coordinate < the order. Accordingly,
+    `kG = Point::from(Even, r)`. This enables recovering the public key via
+    `((s Point::from(Even, r)) - H(m)G) / r`.
+
+    We want to calculate `R` from `(c, s)` where `s = r + cx`. That means we need to calculate
+    `sG - cX`.
+
+    We can calculate `sG - cX` with `((s Point::from(Even, r)) - H(m)G) / r` if:
+    - Latter `r` = `X.x`
+    - Latter `s` = `c`
+    - `H(m)` = former `s`
+    This gets us to `(cX - sG) / X.x`. If we additionally scale the latter's `s, H(m)` values (the
+    former's `c, s` values) by `X.x`, we get `cX - sG`. This just requires negating each to achieve
+    `sG - cX`.
+  */
+  let x_scalar = <Scalar as Reduce<U256>>::reduce_bytes(&public_key.point().to_affine().x());
+  let sa = -(s * x_scalar);
+  let ca = -(c * x_scalar);
+
+  let q = ecrecover(sa, false, x_scalar, ca).unwrap();
+  assert_eq!(q, Address::from_raw_public_key(&R.to_encoded_point(false).as_ref()[1 ..]));
+}