Implement Secp256r1 / P256 verification in solidity

.changeset/odd-lobsters-wash.md

@@ -0,0 +1,5 @@
+---
+'openzeppelin-solidity': minor
+---
+
+`P256`: Add a library for verification/recovery of Secp256r1 (Aka P256) signatures.

.github/workflows/checks.yml

@@ -66,6 +66,8 @@ jobs:
         run: bash scripts/upgradeable/transpile.sh
       - name: Run tests
         run: npm run test
+        env:
+          UNLIMITED: true
       - name: Check linearisation of the inheritance graph
         run: npm run test:inheritance
       - name: Check storage layout

contracts/mocks/Stateless.sol

@@ -24,6 +24,7 @@ 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 {SafeCast} from "../utils/math/SafeCast.sol";
 import {SafeERC20} from "../token/ERC20/utils/SafeERC20.sol";
 import {ShortStrings} from "../utils/ShortStrings.sol";

contracts/utils/cryptography/P256.sol

@@ -0,0 +1,316 @@
+// SPDX-License-Identifier: GPL-3.0
+pragma solidity ^0.8.20;
+
+import {Math} from "../math/Math.sol";
+
+/**
+ * @dev Implementation of secp256r1 verification and recovery functions.
+ *
+ * Based on
+ * - https://github.com/itsobvioustech/A-passkeys-wallet/blob/main/src/Secp256r1.sol
+ * Which is heavily inspired from
+ * - https://github.com/maxrobot/elliptic-solidity/blob/master/contracts/Secp256r1.sol
+ * - https://github.com/tdrerup/elliptic-curve-solidity/blob/master/contracts/curves/EllipticCurve.sol
+ */
+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;
+
+    uint256 private constant P2 = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFD;
+    uint256 private constant N2 = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC63254F;
+    uint256 private constant P1DIV4 = 0x3fffffffc0000000400000000000000000000000400000000000000000000000;
+
+    /**
+     * @dev signature verification
+     * @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
+     */
+    function verify(uint256 h, uint256 r, uint256 s, uint256 qx, uint256 qy) internal view returns (bool) {
+        if (r == 0 || r >= N || s == 0 || s >= N || !isOnCurve(qx, qy)) return false;
+
+        JPoint[16] memory points = _preComputeJacobianPoints(qx, qy);
+        uint256 w = _invModN(s);
+        uint256 u1 = mulmod(h, w, N);
+        uint256 u2 = mulmod(r, w, N);
+        (uint256 x, ) = _jMultShamir(points, u1, u2);
+        return (x == r);
+    }
+
+    /**
+     * @dev public key recovery
+     * @param h - hashed message
+     * @param v - signature recovery param
+     * @param r - signature half R
+     * @param s - signature half S
+     */
+    function recovery(uint256 h, uint8 v, uint256 r, uint256 s) internal view returns (uint256, uint256) {
+        if (r == 0 || r >= N || s == 0 || s >= N || v > 1) return (0, 0);
+
+        uint256 rx = 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 = _invModN(r);
+        uint256 u1 = mulmod(N - (h % N), w, N);
+        uint256 u2 = mulmod(s, w, N);
+        (uint256 x, uint256 y) = _jMultShamir(points, u1, u2);
+        return (x, y);
+    }
+
+    /**
+     * @dev address recovery
+     * @param h - hashed message
+     * @param v - signature recovery param
+     * @param r - signature half R
+     * @param s - signature half S
+     */
+    function recoveryAddress(uint256 h, uint8 v, uint256 r, uint256 s) internal view returns (address) {
+        (uint256 qx, uint256 qy) = recovery(h, v, r, s);
+        return getAddress(qx, qy);
+    }
+
+    /**
+     * @dev derivate public key
+     * @param privateKey - private key
+     */
+    function getPublicKey(uint256 privateKey) internal view returns (uint256, uint256) {
+        (uint256 x, uint256 y, uint256 z) = _jMult(GX, GY, 1, privateKey);
+        return _affineFromJacobian(x, y, z);
+    }
+
+    /**
+     * @dev Hash public key into an address
+     * @param qx - public key coordinate X
+     * @param qy - public key coordinate Y
+     */
+    function getAddress(uint256 qx, uint256 qy) internal pure returns (address result) {
+        /// @solidity memory-safe-assembly
+        assembly {
+            mstore(0x00, qx)
+            mstore(0x20, qy)
+            result := keccak256(0x00, 0x40)
+        }
+    }
+
+    /**
+     * @dev check if a point is on the curve.
+     */
+    function isOnCurve(uint256 x, uint256 y) internal pure returns (bool result) {
+        /// @solidity memory-safe-assembly
+        assembly {
+            let p := P
+            let lhs := mulmod(y, y, p)
+            let rhs := addmod(mulmod(addmod(mulmod(x, x, p), A, p), x, p), B, p)
+            result := eq(lhs, rhs)
+        }
+    }
+
+    /**
+     * @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 = _invModP(jz);
+        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
+     * https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
+     */
+    function _jAdd(
+        uint256 x1,
+        uint256 y1,
+        uint256 z1,
+        uint256 x2,
+        uint256 y2,
+        uint256 z2
+    ) private pure returns (uint256 x3, uint256 y3, uint256 z3) {
+        if (z1 == 0) {
+            return (x2, y2, z2);
+        }
+        if (z2 == 0) {
+            return (x1, y1, z1);
+        }
+        /// @solidity memory-safe-assembly
+        assembly {
+            let p := P
+            let zz1 := mulmod(z1, z1, p) // zz1 = z1²
+            let zz2 := mulmod(z2, z2, p) // zz2 = z2²
+            let u1 := mulmod(x1, zz2, p) // u1 = x1*z2²
+            let u2 := mulmod(x2, zz1, p) // u2 = x2*z1²
+            let s1 := mulmod(y1, mulmod(zz2, z2, p), p) // s1 = y1*z2³
+            let s2 := mulmod(y2, mulmod(zz1, z1, p), p) // s2 = y2*z1³
+            let h := addmod(u2, sub(p, u1), p) // h = u2-u1
+            let hh := mulmod(h, h, p) // h²
+            let hhh := mulmod(h, hh, p) // h³
+            let r := addmod(s2, sub(p, s1), p) // r = s2-s1
+
+            // x' = r²-h³-2*u1*h²
+            x3 := addmod(addmod(mulmod(r, r, p), sub(p, hhh), p), sub(p, mulmod(2, mulmod(u1, hh, p), p)), p)
+            // y' = r*(u1*h²-x')-s1*h³
+            y3 := addmod(mulmod(r, addmod(mulmod(u1, hh, p), sub(p, x3), p), p), sub(p, mulmod(s1, hhh, p)), p)
+            // z' = h*z1*z2
+            z3 := mulmod(h, mulmod(z1, z2, p), p)
+        }
+    }
+
+    /**
+     * @dev Point doubling on the jacobian coordinates
+     * https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
+     */
+    function _jDouble(uint256 x, uint256 y, uint256 z) private pure returns (uint256 x2, uint256 y2, uint256 z2) {
+        /// @solidity memory-safe-assembly
+        assembly {
+            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
+
+            // x' = m²-2*s
+            x2 := addmod(mulmod(m, m, p), sub(p, mulmod(2, s, p)), p)
+            // y' = m*(s-x')-8*y⁴
+            y2 := addmod(mulmod(m, addmod(s, sub(p, x2), p), p), sub(p, mulmod(8, mulmod(yy, yy, p), p)), p)
+            // z' = 2*y*z
+            z2 := mulmod(2, mulmod(y, z, p), p)
+        }
+    }
+
+    /**
+     * @dev Point multiplication on the jacobian coordinates
+     */
+    function _jMult(
+        uint256 x,
+        uint256 y,
+        uint256 z,
+        uint256 k
+    ) private pure returns (uint256 x2, uint256 y2, uint256 z2) {
+        unchecked {
+            for (uint256 i = 0; i < 256; ++i) {
+                if (z > 0) {
+                    (x2, y2, z2) = _jDouble(x2, y2, z2);
+                }
+                if (k >> 255 > 0) {
+                    (x2, y2, z2) = _jAdd(x2, y2, z2, x, y, z);
+                }
+                k <<= 1;
+            }
+        }
+    }
+
+    /**
+     * @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) {
+                    (x, y, z) = _jAdd(x, y, z, points[pos].x, points[pos].y, points[pos].z);
+                }
+                u1 <<= 2;
+                u2 <<= 2;
+            }
+        }
+        return _affineFromJacobian(x, y, z);
+    }
+
+    /**
+     * @dev Precompute a matrice of useful jacobian points associated to a given P. This can be seen as a 4x4 matrix
+     * that contains combinaison of P and G (generator) up to 3 times each. See 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);
+        points[0x01] = JPoint(px, py, 1);
+        points[0x04] = JPoint(GX, GY, 1);
+        points[0x02] = _jDoublePoint(points[0x01]);
+        points[0x08] = _jDoublePoint(points[0x04]);
+        points[0x03] = _jAddPoint(points[0x01], points[0x02]);
+        points[0x05] = _jAddPoint(points[0x01], points[0x04]);
+        points[0x06] = _jAddPoint(points[0x02], points[0x04]);
+        points[0x07] = _jAddPoint(points[0x03], points[0x04]);
+        points[0x09] = _jAddPoint(points[0x01], points[0x08]);
+        points[0x0a] = _jAddPoint(points[0x02], points[0x08]);
+        points[0x0b] = _jAddPoint(points[0x03], points[0x08]);
+        points[0x0c] = _jAddPoint(points[0x04], points[0x08]);
+        points[0x0d] = _jAddPoint(points[0x01], points[0x0c]);
+        points[0x0e] = _jAddPoint(points[0x02], points[0x0c]);
+        points[0x0f] = _jAddPoint(points[0x03], points[0x0C]);
+    }
+
+    function _jAddPoint(JPoint memory p1, JPoint memory p2) private pure returns (JPoint memory) {
+        (uint256 x, uint256 y, uint256 z) = _jAdd(p1.x, p1.y, p1.z, 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);
+    }
+
+    /**
+     *@dev From Fermat's little theorem https://en.wikipedia.org/wiki/Fermat%27s_little_theorem:
+     * `a**(p-1) ≡ 1 mod p`. This means that `a**(p-2)` is an inverse of a in Fp.
+     */
+    function _invModN(uint256 value) private view returns (uint256) {
+        return Math.modExp(value, N2, N);
+    }
+
+    function _invModP(uint256 value) private view returns (uint256) {
+        return Math.modExp(value, P2, P);
+    }
+}