Implement P256 verification via RIP-7212 precompile with Solidity fallback

.changeset/odd-lobsters-wash.md

@@ -0,0 +1,5 @@
+---
+'openzeppelin-solidity': minor
+---
+
+`P256`: Library for verification and public key recovery of P256 (aka secp256r1) signatures.

contracts/mocks/Stateless.sol

@@ -25,6 +25,7 @@ import {ERC721Holder} from "../token/ERC721/utils/ERC721Holder.sol";
 import {Math} from "../utils/math/Math.sol";
 import {MerkleProof} from "../utils/cryptography/MerkleProof.sol";
 import {MessageHashUtils} from "../utils/cryptography/MessageHashUtils.sol";
+import {P256} from "../utils/cryptography/P256.sol";
 import {Panic} from "../utils/Panic.sol";
 import {Packing} from "../utils/Packing.sol";
 import {RSA} from "../utils/cryptography/RSA.sol";

contracts/utils/Errors.sol

@@ -23,4 +23,9 @@ library Errors {
      * @dev The deployment failed.
      */
     error FailedDeployment();
+
+    /**
+     * @dev A necessary precompile is missing.
+     */
+    error MissingPrecompile(address);
 }

contracts/utils/README.adoc

@@ -8,6 +8,8 @@ Miscellaneous contracts and libraries containing utility functions you can use t
  * {Math}, {SignedMath}: Implementation of various arithmetic functions.
  * {SafeCast}: Checked downcasting functions to avoid silent truncation.
  * {ECDSA}, {MessageHashUtils}: Libraries for interacting with ECDSA signatures.
+ * {P256}: Library for verifying and recovering public keys from secp256r1 signatures.
+ * {RSA}: Library with RSA PKCS#1 v1.5 signature verification utilities.
  * {SignatureChecker}: A library helper to support regular ECDSA from EOAs as well as ERC-1271 signatures for smart contracts.
  * {Hashes}: Commonly used hash functions.
  * {MerkleProof}: Functions for verifying https://en.wikipedia.org/wiki/Merkle_tree[Merkle Tree] proofs.

contracts/utils/cryptography/P256.sol

@@ -0,0 +1,313 @@
+// SPDX-License-Identifier: MIT
+pragma solidity ^0.8.20;
+
+import {Math} from "../math/Math.sol";
+import {Errors} from "../Errors.sol";
+
+/**
+ * @dev Implementation of secp256r1 verification and recovery functions.
+ *
+ * The secp256r1 curve (also known as P256) is a NIST standard curve with wide support in modern devices
+ * and cryptographic standards. Some notable examples include Apple's Secure Enclave and Android's Keystore
+ * as well as authentication protocols like FIDO2.
+ *
+ * Based on the original https://github.com/itsobvioustech/aa-passkeys-wallet/blob/main/src/Secp256r1.sol[implementation of itsobvioustech].
+ * Heavily inspired in https://github.com/maxrobot/elliptic-solidity/blob/master/contracts/Secp256r1.sol[maxrobot] and
+ * https://github.com/tdrerup/elliptic-curve-solidity/blob/master/contracts/curves/EllipticCurve.sol[tdrerup] implementations.
+ */
+library P256 {
+    struct JPoint {
+        uint256 x;
+        uint256 y;
+        uint256 z;
+    }
+
+    /// @dev Generator (x component)
+    uint256 internal constant GX = 0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296;
+    /// @dev Generator (y component)
+    uint256 internal constant GY = 0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5;
+    /// @dev P (size of the field)
+    uint256 internal constant P = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF;
+    /// @dev N (order of G)
+    uint256 internal constant N = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551;
+    /// @dev A parameter of the weierstrass equation
+    uint256 internal constant A = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC;
+    /// @dev B parameter of the weierstrass equation
+    uint256 internal constant B = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B;
+
+    /// @dev (P + 1) / 4. Useful to compute sqrt
+    uint256 private constant P1DIV4 = 0x3fffffffc0000000400000000000000000000000400000000000000000000000;
+
+    /// @dev N/2 for excluding higher order `s` values
+    uint256 private constant HALF_N = 0x7fffffff800000007fffffffffffffffde737d56d38bcf4279dce5617e3192a8;
+
+    /**
+     * @dev Verifies a secp256r1 signature using the RIP-7212 precompile and falls back to the Solidity implementation
+     * if the precompile is not available. This version should work on all chains, but requires the deployment of more
+     * bytecode.
+     *
+     * @param h - hashed message
+     * @param r - signature half R
+     * @param s - signature half S
+     * @param qx - public key coordinate X
+     * @param qy - public key coordinate Y
+     *
+     * IMPORTANT: This function disallows signatures where the `s` value is above `N/2` to prevent malleability.
+     * To flip the `s` value, compute `s = N - s`.
+     */
+    function verify(bytes32 h, bytes32 r, bytes32 s, bytes32 qx, bytes32 qy) internal view returns (bool) {
+        (bool valid, bool supported) = _tryVerifyNative(h, r, s, qx, qy);
+        return supported ? valid : verifySolidity(h, r, s, qx, qy);
+    }
+
+    /**
+     * @dev Same as {verify}, but it will revert if the required precompile is not available.
+     */
+    function verifyNative(bytes32 h, bytes32 r, bytes32 s, bytes32 qx, bytes32 qy) internal view returns (bool) {
+        (bool valid, bool supported) = _tryVerifyNative(h, r, s, qx, qy);
+        if (supported) {
+            return valid;
+        } else {
+            revert Errors.MissingPrecompile(address(0x100));
+        }
+    }
+
+    /**
+     * @dev Same as {verify}, but it will return false if the required precompile is not available.
+     */
+    function _tryVerifyNative(
+        bytes32 h,
+        bytes32 r,
+        bytes32 s,
+        bytes32 qx,
+        bytes32 qy
+    ) private view returns (bool valid, bool supported) {
+        if (!_isProperSignature(r, s) || !isValidPublicKey(qx, qy)) {
+            return (false, true); // signature is invalid, and its not because the precompile is missing
+        }
+
+        (bool success, bytes memory returndata) = address(0x100).staticcall(abi.encode(h, r, s, qx, qy));
+        return (success && returndata.length == 0x20) ? (abi.decode(returndata, (bool)), true) : (false, false);
+    }
+
+    /**
+     * @dev Same as {verify}, but only the Solidity implementation is used.
+     */
+    function verifySolidity(bytes32 h, bytes32 r, bytes32 s, bytes32 qx, bytes32 qy) internal view returns (bool) {
+        if (!_isProperSignature(r, s) || !isValidPublicKey(qx, qy)) {
+            return false;
+        }
+
+        JPoint[16] memory points = _preComputeJacobianPoints(uint256(qx), uint256(qy));
+        uint256 w = Math.invModPrime(uint256(s), N);
+        uint256 u1 = mulmod(uint256(h), w, N);
+        uint256 u2 = mulmod(uint256(r), w, N);
+        (uint256 x, ) = _jMultShamir(points, u1, u2);
+        return ((x % N) == uint256(r));
+    }
+
+    /**
+     * @dev Public key recovery
+     *
+     * @param h - hashed message
+     * @param v - signature recovery param
+     * @param r - signature half R
+     * @param s - signature half S
+     *
+     * IMPORTANT: This function disallows signatures where the `s` value is above `N/2` to prevent malleability.
+     * To flip the `s` value, compute `s = N - s` and `v = 1 - v` if (`v = 0 | 1`).
+     */
+    function recovery(bytes32 h, uint8 v, bytes32 r, bytes32 s) internal view returns (bytes32, bytes32) {
+        if (!_isProperSignature(r, s) || v > 1) {
+            return (0, 0);
+        }
+
+        uint256 rx = uint256(r);
+        uint256 ry2 = addmod(mulmod(addmod(mulmod(rx, rx, P), A, P), rx, P), B, P); // weierstrass equation y² = x³ + a.x + b
+        uint256 ry = Math.modExp(ry2, P1DIV4, P); // This formula for sqrt work because P ≡ 3 (mod 4)
+        if (mulmod(ry, ry, P) != ry2) return (0, 0); // Sanity check
+        if (ry % 2 != v % 2) ry = P - ry;
+
+        JPoint[16] memory points = _preComputeJacobianPoints(rx, ry);
+        uint256 w = Math.invModPrime(uint256(r), N);
+        uint256 u1 = mulmod(N - (uint256(h) % N), w, N);
+        uint256 u2 = mulmod(uint256(s), w, N);
+        (uint256 x, uint256 y) = _jMultShamir(points, u1, u2);
+        return (bytes32(x), bytes32(y));
+    }
+
+    /**
+     * @dev Checks if (x, y) are valid coordinates of a point on the curve.
+     * In particular this function checks that x <= P and y <= P.
+     */
+    function isValidPublicKey(bytes32 x, bytes32 y) internal pure returns (bool result) {
+        assembly ("memory-safe") {
+            let p := P
+            let lhs := mulmod(y, y, p) // y^2
+            let rhs := addmod(mulmod(addmod(mulmod(x, x, p), A, p), x, p), B, p) // ((x^2 + a) * x) + b = x^3 + ax + b
+            result := and(and(lt(x, p), lt(y, p)), eq(lhs, rhs)) // Should conform with the Weierstrass equation
+        }
+    }
+
+    /**
+     * @dev Checks if (r, s) is a proper signature.
+     * In particular, this checks that `s` is in the "lower-range", making the signature non-malleable.
+     */
+    function _isProperSignature(bytes32 r, bytes32 s) private pure returns (bool) {
+        return uint256(r) > 0 && uint256(r) < N && uint256(s) > 0 && uint256(s) <= HALF_N;
+    }
+
+    /**
+     * @dev Reduce from jacobian to affine coordinates
+     * @param jx - jacobian coordinate x
+     * @param jy - jacobian coordinate y
+     * @param jz - jacobian coordinate z
+     * @return ax - affine coordinate x
+     * @return ay - affine coordinate y
+     */
+    function _affineFromJacobian(uint256 jx, uint256 jy, uint256 jz) private view returns (uint256 ax, uint256 ay) {
+        if (jz == 0) return (0, 0);
+        uint256 zinv = Math.invModPrime(jz, P);
+        uint256 zzinv = mulmod(zinv, zinv, P);
+        uint256 zzzinv = mulmod(zzinv, zinv, P);
+        ax = mulmod(jx, zzinv, P);
+        ay = mulmod(jy, zzzinv, P);
+    }
+
+    /**
+     * @dev Point addition on the jacobian coordinates
+     * Reference: https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-1998-cmo-2
+     */
+    function _jAdd(
+        JPoint memory p1,
+        uint256 x2,
+        uint256 y2,
+        uint256 z2
+    ) private pure returns (uint256 rx, uint256 ry, uint256 rz) {
+        assembly ("memory-safe") {
+            let p := P
+            let z1 := mload(add(p1, 0x40))
+            let s1 := mulmod(mload(add(p1, 0x20)), mulmod(mulmod(z2, z2, p), z2, p), p) // s1 = y1*z2³
+            let s2 := mulmod(y2, mulmod(mulmod(z1, z1, p), z1, p), p) // s2 = y2*z1³
+            let r := addmod(s2, sub(p, s1), p) // r = s2-s1
+            let u1 := mulmod(mload(p1), mulmod(z2, z2, p), p) // u1 = x1*z2²
+            let u2 := mulmod(x2, mulmod(z1, z1, p), p) // u2 = x2*z1²
+            let h := addmod(u2, sub(p, u1), p) // h = u2-u1
+            let hh := mulmod(h, h, p) // h²
+
+            // x' = r²-h³-2*u1*h²
+            rx := addmod(
+                addmod(mulmod(r, r, p), sub(p, mulmod(h, hh, p)), p),
+                sub(p, mulmod(2, mulmod(u1, hh, p), p)),
+                p
+            )
+            // y' = r*(u1*h²-x')-s1*h³
+            ry := addmod(
+                mulmod(r, addmod(mulmod(u1, hh, p), sub(p, rx), p), p),
+                sub(p, mulmod(s1, mulmod(h, hh, p), p)),
+                p
+            )
+            // z' = h*z1*z2
+            rz := mulmod(h, mulmod(z1, z2, p), p)
+        }
+    }
+
+    /**
+     * @dev Point doubling on the jacobian coordinates
+     * Reference: https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-1998-cmo-2
+     */
+    function _jDouble(uint256 x, uint256 y, uint256 z) private pure returns (uint256 rx, uint256 ry, uint256 rz) {
+        assembly ("memory-safe") {
+            let p := P
+            let yy := mulmod(y, y, p)
+            let zz := mulmod(z, z, p)
+            let s := mulmod(4, mulmod(x, yy, p), p) // s = 4*x*y²
+            let m := addmod(mulmod(3, mulmod(x, x, p), p), mulmod(A, mulmod(zz, zz, p), p), p) // m = 3*x²+a*z⁴
+            let t := addmod(mulmod(m, m, p), sub(p, mulmod(2, s, p)), p) // t = m²-2*s
+
+            // x' = t
+            rx := t
+            // y' = m*(s-t)-8*y⁴
+            ry := addmod(mulmod(m, addmod(s, sub(p, t), p), p), sub(p, mulmod(8, mulmod(yy, yy, p), p)), p)
+            // z' = 2*y*z
+            rz := mulmod(2, mulmod(y, z, p), p)
+        }
+    }
+
+    /**
+     * @dev Compute P·u1 + Q·u2 using the precomputed points for P and Q (see {_preComputeJacobianPoints}).
+     *
+     * Uses Strauss Shamir trick for EC multiplication
+     * https://stackoverflow.com/questions/50993471/ec-scalar-multiplication-with-strauss-shamir-method
+     * we optimise on this a bit to do with 2 bits at a time rather than a single bit
+     * the individual points for a single pass are precomputed
+     * overall this reduces the number of additions while keeping the same number of doublings
+     */
+    function _jMultShamir(JPoint[16] memory points, uint256 u1, uint256 u2) private view returns (uint256, uint256) {
+        uint256 x = 0;
+        uint256 y = 0;
+        uint256 z = 0;
+        unchecked {
+            for (uint256 i = 0; i < 128; ++i) {
+                if (z > 0) {
+                    (x, y, z) = _jDouble(x, y, z);
+                    (x, y, z) = _jDouble(x, y, z);
+                }
+                // Read 2 bits of u1, and 2 bits of u2. Combining the two give a lookup index in the table.
+                uint256 pos = ((u1 >> 252) & 0xc) | ((u2 >> 254) & 0x3);
+                if (pos > 0) {
+                    if (z == 0) {
+                        (x, y, z) = (points[pos].x, points[pos].y, points[pos].z);
+                    } else {
+                        (x, y, z) = _jAdd(points[pos], x, y, z);
+                    }
+                }
+                u1 <<= 2;
+                u2 <<= 2;
+            }
+        }
+        return _affineFromJacobian(x, y, z);
+    }
+
+    /**
+     * @dev Precompute a matrice of useful jacobian points associated with a given P. This can be seen as a 4x4 matrix
+     * that contains combination of P and G (generator) up to 3 times each. See the table below:
+     *
+     * ┌────┬─────────────────────┐
+     * │  i │  0    1     2     3 │
+     * ├────┼─────────────────────┤
+     * │  0 │  0    p    2p    3p │
+     * │  4 │  g  g+p  g+2p  g+3p │
+     * │  8 │ 2g 2g+p 2g+2p 2g+3p │
+     * │ 12 │ 3g 3g+p 3g+2p 3g+3p │
+     * └────┴─────────────────────┘
+     */
+    function _preComputeJacobianPoints(uint256 px, uint256 py) private pure returns (JPoint[16] memory points) {
+        points[0x00] = JPoint(0, 0, 0); // 0,0
+        points[0x01] = JPoint(px, py, 1); // 1,0 (p)
+        points[0x04] = JPoint(GX, GY, 1); // 0,1 (g)
+        points[0x02] = _jDoublePoint(points[0x01]); // 2,0 (2p)
+        points[0x08] = _jDoublePoint(points[0x04]); // 0,2 (2g)
+        points[0x03] = _jAddPoint(points[0x01], points[0x02]); // 3,0 (3p)
+        points[0x05] = _jAddPoint(points[0x01], points[0x04]); // 1,1 (p+g)
+        points[0x06] = _jAddPoint(points[0x02], points[0x04]); // 2,1 (2p+g)
+        points[0x07] = _jAddPoint(points[0x03], points[0x04]); // 3,1 (3p+g)
+        points[0x09] = _jAddPoint(points[0x01], points[0x08]); // 1,2 (p+2g)
+        points[0x0a] = _jAddPoint(points[0x02], points[0x08]); // 2,2 (2p+2g)
+        points[0x0b] = _jAddPoint(points[0x03], points[0x08]); // 3,2 (3p+2g)
+        points[0x0c] = _jAddPoint(points[0x04], points[0x08]); // 0,3 (g+2g)
+        points[0x0d] = _jAddPoint(points[0x01], points[0x0c]); // 1,3 (p+3g)
+        points[0x0e] = _jAddPoint(points[0x02], points[0x0c]); // 2,3 (2p+3g)
+        points[0x0f] = _jAddPoint(points[0x03], points[0x0C]); // 3,3 (3p+3g)
+    }
+
+    function _jAddPoint(JPoint memory p1, JPoint memory p2) private pure returns (JPoint memory) {
+        (uint256 x, uint256 y, uint256 z) = _jAdd(p1, p2.x, p2.y, p2.z);
+        return JPoint(x, y, z);
+    }
+
+    function _jDoublePoint(JPoint memory p) private pure returns (JPoint memory) {
+        (uint256 x, uint256 y, uint256 z) = _jDouble(p.x, p.y, p.z);
+        return JPoint(x, y, z);
+    }
+}

contracts/utils/math/Math.sol

@@ -237,8 +237,8 @@ library Math {
      *
      * If the input value is not inversible, 0 is returned.
      *
-     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Ferma's little theorem and get the
-     * inverse using `Math.modExp(a, n - 2, n)`.
+     * NOTE: If you know for sure that n is (big) a prime, it may be cheaper to use Fermat's little theorem and get the
+     * inverse using `Math.modExp(a, n - 2, n)`. See {invModPrime}.
      */
     function invMod(uint256 a, uint256 n) internal pure returns (uint256) {
         unchecked {
@@ -288,6 +288,21 @@ library Math {
         }
     }
 
+    /**
+     * @dev Variant of {invMod}. More efficient, but only works if `p` is known to be a prime greater than `2`.
+     *
+     * From https://en.wikipedia.org/wiki/Fermat%27s_little_theorem[Fermat's little theorem], we know that if p is
+     * prime, then `a**(p-1) ≡ 1 mod p`. As a consequence, we have `a * a**(p-2) ≡ 1 mod p`, which means that
+     * `a**(p-2)` is the modular multiplicative inverse of a in Fp.
+     *
+     * NOTE: this function does NOT check that `p` is a prime greater than `2`.
+     */
+    function invModPrime(uint256 a, uint256 p) internal view returns (uint256) {
+        unchecked {
+            return Math.modExp(a, p - 2, p);
+        }
+    }
+
     /**
      * @dev Returns the modular exponentiation of the specified base, exponent and modulus (b ** e % m)
      *