├── .gas-snapshot ├── .github └── workflows │ ├── checks.yml │ └── test.yml ├── .gitignore ├── .gitmodules ├── .prettierignore ├── LICENSE ├── README.md ├── foundry.toml ├── lib └── utils │ └── compile.py ├── remappings.txt ├── src └── P256Verifier.vy └── test └── P256Verifier.t.sol /.gas-snapshot: -------------------------------------------------------------------------------- 1 | P256Verifier:testBasic() (gas: 661274) 2 | P256Verifier:testOutOfBounds() (gas: 48773) 3 | P256Verifier:testWrongInputLength() (gas: 646613) 4 | P256Verifier:testWycheproof() (gas: 422731572) -------------------------------------------------------------------------------- /.github/workflows/checks.yml: -------------------------------------------------------------------------------- 1 | name: 👮‍♂️ Sanity checks 2 | 3 | on: [push, pull_request, workflow_dispatch] 4 | 5 | concurrency: 6 | group: ${{github.workflow}}-${{github.ref}} 7 | cancel-in-progress: true 8 | 9 | jobs: 10 | prettify: 11 | runs-on: ${{ matrix.os }} 12 | strategy: 13 | matrix: 14 | os: 15 | - ubuntu-latest 16 | node_version: 17 | - 22 18 | 19 | steps: 20 | - name: Checkout 21 | uses: actions/checkout@v4 22 | with: 23 | submodules: recursive 24 | 25 | - name: Use Node.js ${{ matrix.node_version }} 26 | uses: actions/setup-node@v4 27 | with: 28 | node-version: ${{ matrix.node_version }} 29 | 30 | - name: Run Prettier 31 | run: npx prettier -c '**/*.{md,yml,yaml}' 32 | 33 | - name: Install Foundry 34 | uses: foundry-rs/foundry-toolchain@v1 35 | with: 36 | version: nightly 37 | 38 | - name: Prettify Solidity files 39 | run: forge fmt --check 40 | env: 41 | FOUNDRY_DISABLE_NIGHTLY_WARNING: "1" 42 | 43 | codespell: 44 | runs-on: ${{ matrix.os }} 45 | strategy: 46 | matrix: 47 | os: 48 | - ubuntu-latest 49 | 50 | steps: 51 | - name: Checkout 52 | uses: actions/checkout@v4 53 | 54 | - name: Run codespell 55 | uses: codespell-project/actions-codespell@v2 56 | with: 57 | check_filenames: true 58 | skip: ./.git 59 | 60 | validate-links: 61 | runs-on: ${{ matrix.os }} 62 | strategy: 63 | matrix: 64 | os: 65 | - ubuntu-latest 66 | ruby_version: 67 | - 3.4 68 | 69 | steps: 70 | - name: Checkout 71 | uses: actions/checkout@v4 72 | 73 | - name: Set up Ruby 74 | uses: ruby/setup-ruby@v1 75 | with: 76 | ruby-version: ${{ matrix.ruby_version }} 77 | bundler-cache: true 78 | 79 | - name: Install awesome_bot 80 | run: gem install awesome_bot 81 | 82 | - name: Validate URLs 83 | run: awesome_bot ./*.md src/*.vy test/*.sol --allow-dupe --request-delay 0.4 --white-list https://stackoverflow.com,https://hyperelliptic.org 84 | -------------------------------------------------------------------------------- /.github/workflows/test.yml: -------------------------------------------------------------------------------- 1 | name: 🕵️‍♂️ Test smart contracts 2 | 3 | on: [push, pull_request, workflow_dispatch] 4 | 5 | concurrency: 6 | group: ${{github.workflow}}-${{github.ref}} 7 | cancel-in-progress: true 8 | 9 | jobs: 10 | tests: 11 | runs-on: ${{ matrix.os }} 12 | strategy: 13 | matrix: 14 | os: 15 | - ubuntu-latest 16 | architecture: 17 | - x64 18 | python_version: 19 | - 3.13 20 | 21 | steps: 22 | - name: Checkout 23 | uses: actions/checkout@v4 24 | with: 25 | submodules: recursive 26 | 27 | - name: Setup Python 28 | uses: actions/setup-python@v5 29 | with: 30 | python-version: ${{ matrix.python_version }} 31 | architecture: ${{ matrix.architecture }} 32 | 33 | - name: Install Vyper 34 | run: pip install vyper==0.3.10 35 | 36 | - name: Install Foundry 37 | uses: foundry-rs/foundry-toolchain@v1 38 | with: 39 | version: nightly 40 | 41 | - name: Foundry tests 42 | run: forge test 43 | env: 44 | FOUNDRY_PROFILE: ci 45 | FOUNDRY_DISABLE_NIGHTLY_WARNING: "1" 46 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Compiler files 2 | cache 3 | out 4 | 5 | # Python virtual environments 6 | env 7 | venv 8 | -------------------------------------------------------------------------------- /.gitmodules: -------------------------------------------------------------------------------- 1 | [submodule "lib/forge-std"] 2 | path = lib/forge-std 3 | url = https://github.com/foundry-rs/forge-std.git 4 | [submodule "lib/snekmate"] 5 | path = lib/snekmate 6 | url = https://github.com/pcaversaccio/snekmate.git 7 | [submodule "lib/p256-verifier"] 8 | path = lib/p256-verifier 9 | url = https://github.com/daimo-eth/p256-verifier.git 10 | -------------------------------------------------------------------------------- /.prettierignore: -------------------------------------------------------------------------------- 1 | lib 2 | cache 3 | out 4 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU AFFERO GENERAL PUBLIC LICENSE 2 | Version 3, 19 November 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU Affero General Public License is a free, copyleft license for 11 | software and other kinds of works, specifically designed to ensure 12 | cooperation with the community in the case of network server software. 13 | 14 | The licenses for most software and other practical works are designed 15 | to take away your freedom to share and change the works. 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It is safest 628 | to attach them to the start of each source file to most effectively 629 | state the exclusion of warranty; and each file should have at least 630 | the "copyright" line and a pointer to where the full notice is found. 631 | 632 | 633 | Copyright (C) 634 | 635 | This program is free software: you can redistribute it and/or modify 636 | it under the terms of the GNU Affero General Public License as published 637 | by the Free Software Foundation, either version 3 of the License, or 638 | (at your option) any later version. 639 | 640 | This program is distributed in the hope that it will be useful, 641 | but WITHOUT ANY WARRANTY; without even the implied warranty of 642 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 643 | GNU Affero General Public License for more details. 644 | 645 | You should have received a copy of the GNU Affero General Public License 646 | along with this program. If not, see . 647 | 648 | Also add information on how to contact you by electronic and paper mail. 649 | 650 | If your software can interact with users remotely through a computer 651 | network, you should also make sure that it provides a way for users to 652 | get its source. For example, if your program is a web application, its 653 | interface could display a "Source" link that leads users to an archive 654 | of the code. There are many ways you could offer source, and different 655 | solutions will be better for different programs; see section 13 for the 656 | specific requirements. 657 | 658 | You should also get your employer (if you work as a programmer) or school, 659 | if any, to sign a "copyright disclaimer" for the program, if necessary. 660 | For more information on this, and how to apply and follow the GNU AGPL, see 661 | . 662 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # `P256Verifier` 🐍Vyper Contract 2 | 3 | [![🕵️‍♂️ Test smart contracts](https://github.com/pcaversaccio/p256-verifier-vyper/actions/workflows/test.yml/badge.svg)](https://github.com/pcaversaccio/p256-verifier-vyper/actions/workflows/test.yml) 4 | [![License: AGPL-3.0-only](https://img.shields.io/badge/License-AGPL--3.0--only-blue)](https://www.gnu.org/licenses/agpl-3.0) 5 | 6 | 7 | 8 | > [!TIP] 9 | > A fully optimised and thoroughly tested `P256` verifier using the latest Vyper version `0.4.0` is implemented in 🐍 snekmate: https://github.com/pcaversaccio/snekmate/pull/243. 10 | 11 | `P256` (a.k.a. `secp256r1` elliptic curve) signature verification [🐍Vyper contract](./src/P256Verifier.vy). These functions can be used to verify a `P256` signature. The implementation is inspired by [dcposch](https://github.com/dcposch)'s and [nalinbhardwaj](https://github.com/nalinbhardwaj)'s implementation [here](https://github.com/daimo-eth/p256-verifier/blob/master/src/P256Verifier.sol). Also, for more technical details, please refer to [RIP-7212](https://github.com/ethereum/RIPs/blob/master/RIPS/rip-7212.md). 12 | 13 | > [!WARNING] 14 | > This is **experimental software** and is provided on an "as is" and "as available" basis. We **do not give any warranties** and **will not be liable for any losses** incurred through any use of this code base. 15 | 16 | ## Deployments 17 | 18 | - Sepolia: [`0xD99D0f622506C2521cceb80B78CAeBE1798C7Ed5`](https://sepolia.etherscan.io/address/0xD99D0f622506C2521cceb80B78CAeBE1798C7Ed5) 19 | - Holešky: [`0xD99D0f622506C2521cceb80B78CAeBE1798C7Ed5`](https://holesky.etherscan.io/address/0xD99D0f622506C2521cceb80B78CAeBE1798C7Ed5) 20 | 21 | ## Further References 22 | 23 | - Daimo's GitHub Repository: [daimo-eth/p256-verifier](https://github.com/daimo-eth/p256-verifier) 24 | - Daimo's Blog: [blog/p256verifier](https://daimo.com/blog/p256verifier) 25 | - Daimo's Website: [p256.eth.limo](https://p256.eth.limo) 26 | - Daimo's `P256Verifier` Deployment: [`0xc2b78104907F722DABAc4C69f826a522B2754De4`](https://etherscan.io/address/0xc2b78104907F722DABAc4C69f826a522B2754De4) 27 | -------------------------------------------------------------------------------- /foundry.toml: -------------------------------------------------------------------------------- 1 | ## defaults for all profiles 2 | [profile.default] 3 | src = "src" # the source directory 4 | test = "test" # the test directory 5 | out = "out" # the output directory (for artifacts) 6 | libs = ["lib"] # a list of library directories 7 | cache = true # whether to cache builds or not 8 | cache_path = "cache" # where the cache is stored if enabled 9 | ffi = true # whether to enable foreign function interface (ffi) cheatcodes or not 10 | verbosity = 3 # the verbosity of tests 11 | fs_permissions = [{ access = "read-write", path = "./" }] # set read-write access to project root 12 | solc_version = "0.8.30" # override for the solc version 13 | evm_version = "shanghai" # set the EVM target version 14 | optimizer = true # enable the solc optimiser 15 | optimizer_runs = 999_999 # the number of optimiser runs 16 | 17 | ## default overrides for the CI runs 18 | [profile.ci] 19 | force = true # always perform a clean build 20 | verbosity = 4 # increase the verbosity of tests 21 | -------------------------------------------------------------------------------- /lib/utils/compile.py: -------------------------------------------------------------------------------- 1 | import sys, subprocess, json 2 | 3 | 4 | # Check if `experimental_codegen` is enabled in the 5 | # Foundry profile. 6 | def is_experimental_codegen(): 7 | try: 8 | result = subprocess.run( 9 | ["forge", "config", "--json"], capture_output=True, text=True, check=True 10 | ) 11 | config = json.loads(result.stdout) 12 | return config.get("vyper", {}).get("experimental_codegen", False) == True 13 | except (subprocess.CalledProcessError, json.JSONDecodeError, KeyError): 14 | return False 15 | 16 | 17 | # Build the Vyper command. 18 | command = ( 19 | ["vyper", "--experimental-codegen"] if is_experimental_codegen() else ["vyper"] 20 | ) 21 | command += sys.argv[1:] 22 | 23 | result = subprocess.run(command, capture_output=True, text=True) 24 | if result.returncode != 0: 25 | raise Exception(f"Error compiling: {sys.argv[1]}") 26 | 27 | # Remove any leading and trailing whitespace characters 28 | # from the compilation result. 29 | sys.stdout.write(result.stdout.strip()) 30 | -------------------------------------------------------------------------------- /remappings.txt: -------------------------------------------------------------------------------- 1 | forge-std/=lib/forge-std/src/ 2 | vyper-deployer/=lib/snekmate/lib/utils/ 3 | -------------------------------------------------------------------------------- /src/P256Verifier.vy: -------------------------------------------------------------------------------- 1 | # pragma version ^0.3.10 2 | """ 3 | @title P256 Signature Verification Functions 4 | @custom:contract-name P256Verifier 5 | @license GNU Affero General Public License v3.0 only 6 | @author pcaversaccio 7 | @notice These functions can be used to verify a P256 (a.k.a. secp256r1 elliptic curve) signature. 8 | The implementation is inspired by dcposch's and nalinbhardwaj's implementation here: 9 | https://github.com/daimo-eth/p256-verifier/blob/master/src/P256Verifier.sol. Also, for more 10 | technical details, please refer to RIP-7212: https://github.com/ethereum/RIPs/blob/master/RIPS/rip-7212.md. 11 | """ 12 | 13 | 14 | # @notice Parameters for the secp256r1 elliptic curve. 15 | # @dev Curve prime field modulus. 16 | p: constant(uint256) = 115_792_089_210_356_248_762_697_446_949_407_573_530_086_143_415_290_314_195_533_631_308_867_097_853_951 17 | 18 | 19 | # @dev Short Weierstrass first coefficient. 20 | # @notice The assumption "a == -3 (mod p)" is used throughout the codebase. 21 | a: constant(uint256) = 115_792_089_210_356_248_762_697_446_949_407_573_530_086_143_415_290_314_195_533_631_308_867_097_853_948 22 | # @dev Short Weierstrass second coefficient. 23 | b: constant(uint256) = 41_058_363_725_152_142_129_326_129_780_047_268_409_114_441_015_993_725_554_835_256_314_039_467_401_291 24 | 25 | 26 | # @dev Generate point affine coordinates. 27 | GX: constant(uint256) = 48_439_561_293_906_451_759_052_585_252_797_914_202_762_949_526_041_747_995_844_080_717_082_404_635_286 28 | GY: constant(uint256) = 36_134_250_956_749_795_798_585_127_919_587_881_956_611_106_672_985_015_071_877_198_253_568_414_405_109 29 | 30 | 31 | # @dev Curve order (number of points). 32 | n: constant(uint256) = 115_792_089_210_356_248_762_697_446_949_407_573_529_996_955_224_135_760_342_422_259_061_068_512_044_369 33 | 34 | 35 | # @dev The "-2 mod p" constant is used to speed up inversion and doubling (avoid negation). 36 | minus_2modp: constant(uint256) = 115_792_089_210_356_248_762_697_446_949_407_573_530_086_143_415_290_314_195_533_631_308_867_097_853_949 37 | # @dev The "-2 mod n" constant is used to speed up inversion. 38 | minus_2modn: constant(uint256) = 115_792_089_210_356_248_762_697_446_949_407_573_529_996_955_224_135_760_342_422_259_061_068_512_044_367 39 | 40 | 41 | @external 42 | @payable 43 | def __init__(): 44 | """ 45 | @dev To omit the opcodes for checking the `msg.value` 46 | in the creation-time EVM bytecode, the constructor 47 | is declared as `payable`. 48 | """ 49 | pass 50 | 51 | 52 | @external 53 | def __default__() -> bytes32: 54 | """ 55 | @dev Note that if you call a precompile, the calldata does not contain 56 | any function signature. It's simply a byte array that gets parsed 57 | to extract the values. Technically, the function signature in this 58 | context is just the `to` address. 59 | @return bytes32 The 32-byte return value, which can be either `0x00...00` 60 | (invalid) or `0x00..01` (valid). 61 | """ 62 | if (len(msg.data) != 160): 63 | return empty(bytes32) 64 | 65 | # The signed data hash. 66 | hash: bytes32 = convert(slice(msg.data, empty(uint256), 32), bytes32) 67 | # The secp256r1 32-byte signature parameter `r`. 68 | r: uint256 = convert(slice(msg.data, 32, 32), uint256) 69 | # The secp256r1 32-byte signature parameter `s`. 70 | s: uint256 = convert(slice(msg.data, 64, 32), uint256) 71 | # The public key `x`. 72 | x: uint256 = convert(slice(msg.data, 96, 32), uint256) 73 | # The public key `y`. 74 | y: uint256 = convert(slice(msg.data, 128, 32), uint256) 75 | 76 | return convert(1, bytes32) if self._ecdsa_verify(hash, r, s, [x, y]) else convert(empty(uint256), bytes32) 77 | 78 | 79 | @internal 80 | @view 81 | def _ecdsa_verify(message_hash: bytes32, r: uint256, s: uint256, pub_key: uint256[2]) -> bool: 82 | """ 83 | @dev ECDSA verification given a signature and a public key. 84 | """ 85 | # Check if `r` and `s` are in the scalar field. 86 | if (r == empty(uint256) or r >= n or s == empty(uint256) or s >= n): 87 | return False 88 | 89 | if (not self._ec_aff_is_valid_pubkey(pub_key[0], pub_key[1])): 90 | return False 91 | 92 | s_inv: uint256 = self._n_mod_inv(s) 93 | 94 | # "(h * s^-1)" in scalar field. 95 | scalar_u: uint256 = uint256_mulmod(convert(message_hash, uint256), s_inv, n) 96 | # "(r * s^-1)" in scalar field. 97 | scalar_v: uint256 = uint256_mulmod(r, s_inv, n) 98 | 99 | r_x: uint256 = self._ec_zz_mulmuladd(pub_key[0], pub_key[1], scalar_u, scalar_v) 100 | return r_x % n == r 101 | 102 | 103 | @internal 104 | @pure 105 | def _ec_aff_is_valid_pubkey(x: uint256, y: uint256) -> bool: 106 | """ 107 | @dev Check if a point in affine coordinates is on the curve. Reject 0 point at infinity. 108 | """ 109 | if (x >= p or y >= p or (x == empty(uint256) and y == empty(uint256))): 110 | return False 111 | 112 | return self._ec_aff_satisfies_curve_eqn(x, y) 113 | 114 | 115 | @internal 116 | @pure 117 | def _ec_aff_satisfies_curve_eqn(x: uint256, y: uint256) -> bool: 118 | # y^2. 119 | lhs: uint256 = uint256_mulmod(y, y, p) 120 | # x^3 + a*x + b. 121 | rhs: uint256 = uint256_addmod(uint256_addmod(uint256_mulmod(uint256_mulmod(x, x, p), x, p), uint256_mulmod(a, x, p), p), b, p) 122 | return lhs == rhs 123 | 124 | 125 | @internal 126 | @view 127 | def _ec_zz_mulmuladd(QX: uint256, QY: uint256, scalar_u: uint256, scalar_v: uint256) -> uint256: 128 | """ 129 | @dev Compute of "uG + vQ" using Strauss-Shamir's trick. Strauss-Shamir is 130 | described well in https://stackoverflow.com/questions/50993471/ec-scalar-multiplication-with-strauss-shamir-method/50994362#50994362. 131 | """ 132 | zz: uint256 = 1 133 | zzz: uint256 = 1 134 | X: uint256 = empty(uint256) 135 | Y: uint256 = empty(uint256) 136 | HX: uint256 = empty(uint256) 137 | HY: uint256 = empty(uint256) 138 | 139 | if (scalar_u == empty(uint256) and scalar_v == empty(uint256)): 140 | return empty(uint256) 141 | 142 | # H = g + Q. 143 | (HX, HY) = self._ec_aff_add(GX, GY, QX, QY) 144 | 145 | index: int256 = 255 146 | bitpair: uint256 = empty(uint256) 147 | 148 | # Find the first bit index that is active in either `scalar_u` or `scalar_v`. 149 | for _ in range(255): 150 | bitpair = self._compute_bitpair(convert(index, uint256), scalar_u, scalar_v) 151 | # The following line cannot negatively overflow because we have limited the 152 | # for-loop by the constant value 255. The theoretically maximum achievable 153 | # value is therefore `-1`. 154 | index = unsafe_sub(index, 1) 155 | if (bitpair != empty(uint256)): 156 | break 157 | 158 | if (bitpair == 1): 159 | X = GX 160 | Y = GY 161 | elif (bitpair == 2): 162 | X = QX 163 | Y = QY 164 | elif (bitpair == 3): 165 | X = HX 166 | Y = HY 167 | 168 | TX: uint256 = empty(uint256) 169 | TY: uint256 = empty(uint256) 170 | 171 | for _ in range(255): 172 | if (index < empty(int256)): 173 | break 174 | 175 | (X, Y, zz, zzz) = self._ec_zz_double_zz(X, Y, zz, zzz) 176 | bitpair = self._compute_bitpair(convert(index, uint256), scalar_u, scalar_v) 177 | # The following line cannot negatively overflow because we have limited the 178 | # for-loop by the constant value 255. The theoretically maximum achievable 179 | # value is therefore `-1`. 180 | index = unsafe_sub(index, 1) 181 | 182 | if (bitpair == empty(uint256)): 183 | continue 184 | elif (bitpair == 1): 185 | TX = GX 186 | TY = GY 187 | elif (bitpair == 2): 188 | TX = QX 189 | TY = QY 190 | else: 191 | TX = HX 192 | TY = HY 193 | 194 | (X, Y, zz, zzz) = self._ec_zz_dadd_affine(X, Y, zz, zzz, TX, TY) 195 | 196 | # If `zz = 0`, `zzInv = 0`. 197 | zz_inv: uint256 = self._p_mod_inv(zz) 198 | # X/zz. 199 | return uint256_mulmod(X, zz_inv, p) 200 | 201 | 202 | @internal 203 | @pure 204 | def _compute_bitpair(index: uint256, scalar_u: uint256, scalar_v: uint256) -> uint256: 205 | """ 206 | @dev Compute the bits at `index` of `u` and `v` and return them as 2 bit 207 | concatenation. The bit at index 0 is on if the `index`th bit of `scalar_u` 208 | is on and the bit at index 1 is on if the `index`th bit of `scalar_v` is on. 209 | Examples: 210 | - compute_bitpair(0, 1, 1) == 3, 211 | - compute_bitpair(0, 1, 0) == 1, 212 | - compute_bitpair(0, 0, 1) == 2. 213 | """ 214 | return (((scalar_v >> index) & 1) << 1) + ((scalar_u >> index) & 1) 215 | 216 | 217 | @internal 218 | @view 219 | def _ec_aff_add(x1: uint256, y1: uint256, x2: uint256, y2: uint256) -> (uint256, uint256): 220 | """ 221 | @dev Add two elliptic curve points in affine coordinates. Assumes that the points 222 | are on the elliptic curve. 223 | """ 224 | zz1: uint256 = empty(uint256) 225 | zzz1: uint256 = empty(uint256) 226 | 227 | if (self._ec_aff_is_inf(x1, y1)): 228 | return (x2, y2) 229 | 230 | if (self._ec_aff_is_inf(x2, y2)): 231 | return (x1, y1) 232 | 233 | (x1, y1, zz1, zzz1) = self._ec_zz_dadd_affine(x1, y1, 1, 1, x2, y2) 234 | return self._ec_zz_set_aff(x1, y1, zz1, zzz1) 235 | 236 | 237 | @internal 238 | @pure 239 | def _ec_aff_is_inf(x: uint256, y: uint256) -> bool: 240 | """ 241 | @dev Check if a point is the infinity point in affine representation. Assumes that the 242 | point is on the elliptic curve or is the point at infinity. 243 | """ 244 | return (x == empty(uint256) and y == empty(uint256)) 245 | 246 | 247 | @internal 248 | @pure 249 | def _ec_zz_is_inf(zz: uint256, zzz: uint256) -> bool: 250 | """ 251 | @dev Check if a point is the infinity point in ZZ representation. Assumes point is on the 252 | elliptic curve or is the point at infinity. 253 | """ 254 | return (zz == empty(uint256) and zzz == empty(uint256)) 255 | 256 | 257 | @internal 258 | @view 259 | def _ec_zz_dadd_affine(x1: uint256, y1: uint256, zz1: uint256, zzz1: uint256, x2: uint256, y2: uint256) -> (uint256, uint256, uint256, uint256): 260 | """ 261 | @dev Add a ZZ point to an affine point and return as ZZ representation. Uses "madd-2008-s" and 262 | "mdbl-2008-s" internally: 263 | https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html#addition-madd-2008-s. Matches: 264 | https://github.com/supranational/blst/blob/9c87d4a09d6648e933c818118a4418349804ce7f/src/ec_ops.h#L705 265 | closely. Handles points at infinity gracefully. 266 | """ 267 | x3: uint256 = empty(uint256) 268 | y3: uint256 = empty(uint256) 269 | zz3: uint256 = empty(uint256) 270 | zzz3: uint256 = empty(uint256) 271 | 272 | # `(X2, Y2)` is point at infinity. 273 | if (self._ec_aff_is_inf(x2, y2)): 274 | if (self._ec_zz_is_inf(zz1, zzz1)): 275 | return self._ec_zz_point_at_inf() 276 | return (x1, y1, zz1, zzz1) 277 | # `(X1, Y1)` is point at infinity. 278 | elif (self._ec_zz_is_inf(zz1, zzz1)): 279 | return (x2, y2, 1, 1) 280 | 281 | # R = S2 - y1 = y2*zzz1 - y1. 282 | comp_r: uint256 = uint256_addmod(uint256_mulmod(y2, zzz1, p), p - y1, p) 283 | # P = U2 - x1 = x2*zz1 - x1. 284 | comp_p: uint256 = uint256_addmod(uint256_mulmod(x2, zz1, p), p - x1, p) 285 | 286 | # X1 != X2. 287 | if (comp_p != empty(uint256)): 288 | # PP = P^2. 289 | comp_pp: uint256 = uint256_mulmod(comp_p, comp_p, p) 290 | # PPP = P*PP. 291 | comp_ppp: uint256 = uint256_mulmod(comp_pp, comp_p, p) 292 | # ZZ3 = ZZ1*PP. 293 | zz3 = uint256_mulmod(zz1, comp_pp, p) 294 | # ZZZ3 = ZZZ1*PPP. 295 | zzz3 = uint256_mulmod(zzz1, comp_ppp, p) 296 | # Q = X1*PP. 297 | comp_q: uint256 = uint256_mulmod(x1, comp_pp, p) 298 | # R^2 - PPP - 2*Q 299 | x3 = uint256_addmod(uint256_addmod(uint256_mulmod(comp_r, comp_r, p), p - comp_ppp, p), uint256_mulmod(minus_2modp, comp_q, p), p) 300 | # Y3 = R*(Q-x3) - y1*PPP. 301 | return(x3, uint256_addmod(uint256_mulmod(uint256_addmod(comp_q, p - x3, p), comp_r, p), uint256_mulmod(p - y1, comp_ppp, p), p), zz3, zzz3) 302 | # X1 == X2 and Y1 == Y2. 303 | elif (comp_r == empty(uint256)): 304 | return self._ec_zz_double_affine(x2, y2) 305 | # X1 == X2 and Y1 == -Y2. 306 | else: 307 | return self._ec_zz_point_at_inf() 308 | 309 | return (x3, y3, zz3, zzz3) 310 | 311 | 312 | @internal 313 | @pure 314 | def _ec_zz_double_zz(x1: uint256, y1: uint256, zz1: uint256, zzz1: uint256) -> (uint256, uint256, uint256, uint256): 315 | """ 316 | @dev Double a ZZ point. Uses: http://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz.html#doubling-dbl-2008-s-1. 317 | Handles point at infinity gracefully. 318 | """ 319 | if (self._ec_zz_is_inf(zz1, zzz1)): 320 | return self._ec_zz_point_at_inf() 321 | 322 | # U = 2*Y1. 323 | comp_u: uint256 = uint256_mulmod(2, y1, p) 324 | # V = U^2. 325 | comp_v: uint256 = uint256_mulmod(comp_u, comp_u, p) 326 | # W = U*V. 327 | comp_w: uint256 = uint256_mulmod(comp_u, comp_v, p) 328 | # S = X1*V. 329 | comp_s: uint256 = uint256_mulmod(x1, comp_v, p) 330 | # M = 3*(X1)^2 + a*(zz1)^2. 331 | comp_m: uint256 = uint256_addmod(uint256_mulmod(3, uint256_mulmod(x1, x1, p), p), uint256_mulmod(a, uint256_mulmod(zz1, zz1, p), p), p) 332 | 333 | # M^2 + (-2)*S. 334 | x3: uint256 = uint256_addmod(uint256_mulmod(comp_m, comp_m, p), uint256_mulmod(minus_2modp, comp_s, p), p) 335 | # Y3 = M*(S+(-X3)) + (-W)*Y1, ZZ3 = V*ZZ1, ZZZ3 = W*ZZZ1. 336 | return (x3, uint256_addmod(uint256_mulmod(comp_m, uint256_addmod(comp_s, p - x3, p), p), uint256_mulmod(p - comp_w, y1, p), p), uint256_mulmod(comp_v, zz1, p), uint256_mulmod(comp_w, zzz1, p)) 337 | 338 | 339 | @internal 340 | @view 341 | def _ec_zz_double_affine(x1: uint256, y1: uint256) -> (uint256, uint256, uint256, uint256): 342 | """ 343 | @dev Double an affine point and return as a ZZ point. Uses: http://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz.html#doubling-mdbl-2008-s-1. 344 | Handles point at infinity gracefully. 345 | """ 346 | if (self._ec_aff_is_inf(x1, y1)): 347 | return self._ec_zz_point_at_inf() 348 | 349 | # U = 2*Y1. 350 | comp_u: uint256 = uint256_mulmod(2, y1, p) 351 | # V = U^2 = zz3. 352 | zz3: uint256 = uint256_mulmod(comp_u, comp_u, p) 353 | # W = U*V = zzz3. 354 | zzz3: uint256 = uint256_mulmod(comp_u, zz3, p) 355 | # S = X1*V. 356 | comp_s: uint256 = uint256_mulmod(x1, zz3, p) 357 | # M = 3*(X1)^2 + a. 358 | comp_m: uint256 = uint256_addmod(uint256_mulmod(3, uint256_mulmod(x1, x1, p), p), a, p) 359 | 360 | # M^2 + (-2)*S. 361 | x3: uint256 = uint256_addmod(uint256_mulmod(comp_m, comp_m, p), uint256_mulmod(minus_2modp, comp_s, p), p) 362 | # Y3 = M*(S+(-X3)) + (-W)*Y1. 363 | return (x3, uint256_addmod(uint256_mulmod(comp_m, uint256_addmod(comp_s, p - x3, p), p), uint256_mulmod(p - zzz3, y1, p), p), zz3, zzz3) 364 | 365 | 366 | @internal 367 | @view 368 | def _ec_zz_set_aff(x: uint256, y: uint256, zz: uint256, zzz: uint256) -> (uint256, uint256): 369 | """ 370 | @dev Convert from ZZ rep to affine representation. Assumes "(zz)^(3/2) == zzz (i.e. zz == z^2 and zzz == z^3)". 371 | See https://hyperelliptic.org/EFD/g1p/auto-shortw-xyzz-3.html. 372 | """ 373 | x1: uint256 = empty(uint256) 374 | y1: uint256 = empty(uint256) 375 | if (self._ec_zz_is_inf(zz, zzz)): 376 | return self._ec_affine_point_at_inf() 377 | 378 | # 1 / zzz. 379 | zzz_inv: uint256 = self._p_mod_inv(zzz) 380 | # 1 / z. 381 | z_inv: uint256 = uint256_mulmod(zz, zzz_inv, p) 382 | # 1 / zz. 383 | zz_inv: uint256 = uint256_mulmod(z_inv, z_inv, p) 384 | 385 | # X1 = X / zz, y = Y / zzz. 386 | return (uint256_mulmod(x, zz_inv, p), uint256_mulmod(y, zzz_inv, p)) 387 | 388 | 389 | @internal 390 | @pure 391 | def _ec_zz_point_at_inf() -> (uint256, uint256, uint256, uint256): 392 | """ 393 | @dev Point at infinity in ZZ representation. 394 | """ 395 | return (empty(uint256), empty(uint256), empty(uint256), empty(uint256)) 396 | 397 | 398 | @internal 399 | @pure 400 | def _ec_affine_point_at_inf() -> (uint256, uint256): 401 | """ 402 | @dev Point at infinity in affine representation. 403 | """ 404 | return (empty(uint256), empty(uint256)) 405 | 406 | 407 | @internal 408 | @view 409 | def _n_mod_inv(u: uint256) -> uint256: 410 | """ 411 | @dev "u^-1 mod n". 412 | """ 413 | return self._mod_inv(u, n, minus_2modn) 414 | 415 | 416 | @internal 417 | @view 418 | def _p_mod_inv(u: uint256) -> uint256: 419 | """ 420 | @dev "u"^-1 mod p". 421 | """ 422 | return self._mod_inv(u, p, minus_2modp) 423 | 424 | 425 | @internal 426 | @view 427 | def _mod_inv(u: uint256, f: uint256, minus_2modf: uint256) -> uint256: 428 | """ 429 | @dev "u^-1 mod f = u^(phi(f) - 1) mod f = u^(f-2) mod f" for prime f by Fermat's 430 | little theorem, compute "u^(f-2) mod f" using the `modexp` precompile. Assumes 431 | "f != 0". If `u` is 0, then "u^-1 mod f" is undefined mathematically, but this 432 | function returns 0. 433 | """ 434 | c: uint256 = 32 435 | modexp: address = 0x0000000000000000000000000000000000000005 436 | return_data: Bytes[32] = b"" 437 | success: bool = empty(bool) 438 | success, return_data = raw_call(modexp, _abi_encode(c, c, c, u, minus_2modf, f), max_outsize=32, is_static_call=True, revert_on_failure=False) 439 | assert success, "P256: modexp precompile call did not succeed" 440 | return _abi_decode(return_data, (uint256)) 441 | -------------------------------------------------------------------------------- /test/P256Verifier.t.sol: -------------------------------------------------------------------------------- 1 | // SPDX-License-Identifier: AGPL-3.0-only 2 | pragma solidity ^0.8.30; 3 | 4 | import {Test, console} from "forge-std/Test.sol"; 5 | import {stdJson} from "forge-std/StdJson.sol"; 6 | import {VyperDeployer} from "vyper-deployer/VyperDeployer.sol"; 7 | 8 | contract P256Verifier is Test { 9 | using stdJson for string; 10 | 11 | /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/ 12 | /* HELPER VARIABLES */ 13 | /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/ 14 | 15 | VyperDeployer private vyperDeployer = new VyperDeployer(); 16 | address private p256Verifier; 17 | 18 | /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/ 19 | /* HELPER FUNCTIONS */ 20 | /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/ 21 | 22 | /** 23 | * @dev Checks a single test vector: signature rs, pubkey Q = (x,y). 24 | */ 25 | function evaluate(bytes32 hash, uint256 r, uint256 s, uint256 x, uint256 y) 26 | private 27 | view 28 | returns (bool valid, uint256 gasUsed) 29 | { 30 | bytes memory input = abi.encodePacked(hash, r, s, x, y); 31 | 32 | uint256 gasBefore = gasleft(); 33 | (bool success, bytes memory res) = p256Verifier.staticcall(input); 34 | gasUsed = gasBefore - gasleft(); 35 | 36 | assertEq(success, true, "call failed"); 37 | assertEq(res.length, 32, "invalid result length"); 38 | uint256 result = abi.decode(res, (uint256)); 39 | assertTrue(result == 1 || result == 0, "invalid result"); 40 | 41 | return (result == 1, gasUsed); 42 | } 43 | 44 | /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/ 45 | /* SETUP */ 46 | /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/ 47 | 48 | function setUp() public { 49 | p256Verifier = vyperDeployer.deployContract("src/", "P256Verifier"); 50 | } 51 | 52 | /*´:°•.°+.*•´.*:˚.°*.˚•´.°:°•.°•.*•´.*:˚.°*.˚•´.°:°•.°+.*•´.*:*/ 53 | /* TESTS */ 54 | /*.•°:°.´+˚.*°.˚:*.´•*.+°.•°:´*.´•*.•°.•°:°.´:•˚°.*°.˚:*.´+°.•*/ 55 | 56 | /** 57 | * @dev Sanity check. Demonstrate input and output handling. 58 | */ 59 | function testBasic() public view { 60 | // Zero inputs. 61 | bytes32 hash = bytes32(0); 62 | (uint256 r, uint256 s, uint256 x, uint256 y) = (0, 0, 0, 0); 63 | (bool res, uint256 gasUsed) = evaluate(hash, r, s, x, y); 64 | console.log("Zero inputs, gasUsed ", gasUsed); 65 | assertEq(res, false); 66 | 67 | // First valid Wycheproof vector. 68 | hash = 0xbb5a52f42f9c9261ed4361f59422a1e30036e7c32b270c8807a419feca605023; 69 | r = 19738613187745101558623338726804762177711919211234071563652772152683725073944; 70 | s = 34753961278895633991577816754222591531863837041401341770838584739693604822390; 71 | x = 18614955573315897657680976650685450080931919913269223958732452353593824192568; 72 | y = 90223116347859880166570198725387569567414254547569925327988539833150573990206; 73 | (res, gasUsed) = evaluate(hash, r, s, x, y); 74 | console.log("Valid signature, gasUsed ", gasUsed); 75 | assertEq(res, true); 76 | 77 | // Same as above, but off by 1. 78 | (res, gasUsed) = evaluate(hash, r, s, x + 1, y); 79 | console.log("Invalid signature, gasUsed ", gasUsed); 80 | assertEq(res, false); 81 | } 82 | 83 | /** 84 | * @dev This is the most comprehensive test, covering many edge cases. See vector 85 | * generation and validation in Daimo's test-vectors directory: https://github.com/daimo-eth/p256-verifier/tree/master/test-vectors. 86 | */ 87 | function testWycheproof() public view { 88 | string memory file = "./lib/p256-verifier/test-vectors/vectors_wycheproof.jsonl"; 89 | while (true) { 90 | string memory vector = vm.readLine(file); 91 | if (bytes(vector).length == 0) { 92 | break; 93 | } 94 | 95 | uint256 x = uint256(vector.readBytes32(".x")); 96 | uint256 y = uint256(vector.readBytes32(".y")); 97 | uint256 r = uint256(vector.readBytes32(".r")); 98 | uint256 s = uint256(vector.readBytes32(".s")); 99 | bytes32 hash = vector.readBytes32(".hash"); 100 | bool expected = vector.readBool(".valid"); 101 | string memory comment = vector.readString(".comment"); 102 | 103 | (bool result,) = evaluate(hash, r, s, x, y); 104 | 105 | string memory err = string( 106 | abi.encodePacked("exp ", expected ? "1" : "0", ", we return ", result ? "1" : "0", ": ", comment) 107 | ); 108 | assertTrue(result == expected, err); 109 | } 110 | } 111 | 112 | function testWrongInputLength() public { 113 | // First valid Wycheproof vector. 114 | bytes32 hash = 0xbb5a52f42f9c9261ed4361f59422a1e30036e7c32b270c8807a419feca605023; 115 | uint256 r = 19738613187745101558623338726804762177711919211234071563652772152683725073944; 116 | uint256 s = 34753961278895633991577816754222591531863837041401341770838584739693604822390; 117 | uint256 x = 18614955573315897657680976650685450080931919913269223958732452353593824192568; 118 | uint256 y = 90223116347859880166570198725387569567414254547569925327988539833150573990206; 119 | bytes memory input = abi.encodePacked(hash, r, s, x, y); 120 | (bool success, bytes memory result) = p256Verifier.call(input); 121 | bytes32 res = abi.decode(result, (bytes32)); 122 | assertTrue(success && res == bytes32(uint256(1)), "expected valid"); 123 | 124 | // Append a trailing byte. 125 | input = abi.encodePacked(input, uint8(0)); 126 | (success, result) = p256Verifier.call(input); 127 | res = abi.decode(result, (bytes32)); 128 | assertTrue(success && res == bytes32(uint256(0)), "expected invalid"); 129 | } 130 | 131 | function testOutOfBounds() public view { 132 | // Curve prime field modulus. 133 | uint256 p = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF; 134 | 135 | bytes32 hash = bytes32(0); 136 | (uint256 r, uint256 s, uint256 x, uint256 y) = (1, 1, 1, 1); 137 | 138 | // In-bounds dummy key (1, 1). 139 | // Calls modexp, which takes gas. 140 | (bool result, uint256 gasUsed) = evaluate(hash, r, s, x, y); 141 | console.log("gasUsed ", gasUsed); 142 | assertEq(result, false); 143 | assertGt(gasUsed, 2500); 144 | 145 | // Out-of-bounds public key. Fails fast, takes less gas. 146 | (x, y) = (0, 1); 147 | (result, gasUsed) = evaluate(hash, r, s, x, y); 148 | console.log("gasUsed ", gasUsed); 149 | assertEq(result, false); 150 | assertLt(gasUsed, 2500); 151 | 152 | (x, y) = (1, 0); 153 | (result, gasUsed) = evaluate(hash, r, s, x, y); 154 | console.log("gasUsed ", gasUsed); 155 | assertEq(result, false); 156 | assertLt(gasUsed, 2500); 157 | 158 | (x, y) = (1, p); 159 | (result, gasUsed) = evaluate(hash, r, s, x, y); 160 | console.log("gasUsed ", gasUsed); 161 | assertEq(result, false); 162 | assertLt(gasUsed, 2500); 163 | 164 | (x, y) = (p, 1); 165 | (result, gasUsed) = evaluate(hash, r, s, x, y); 166 | console.log("gasUsed ", gasUsed); 167 | assertEq(result, false); 168 | assertLt(gasUsed, 2500); 169 | 170 | // p-1 is in-bounds but point is not on curve. 171 | (x, y) = (p - 1, 1); 172 | (result, gasUsed) = evaluate(hash, r, s, x, y); 173 | console.log("gasUsed ", gasUsed); 174 | assertEq(result, false); 175 | } 176 | } 177 | --------------------------------------------------------------------------------