// https://tornado.ws Verifier.sol generated by trusted setup ceremony. /* * d888888P dP a88888b. dP * 88 88 d8' `88 88 * 88 .d8888b. 88d888b. 88d888b. .d8888b. .d888b88 .d8888b. 88 .d8888b. .d8888b. 88d888b. * 88 88' `88 88' `88 88' `88 88' `88 88' `88 88' `88 88 88' `88 Y8ooooo. 88' `88 * 88 88. .88 88 88 88 88. .88 88. .88 88. .88 dP Y8. .88 88. .88 88 88 88 * dP `88888P' dP dP dP `88888P8 `88888P8 `88888P' 88 Y88888P' `88888P8 `88888P' dP dP * ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo */ // SPDX-License-Identifier: MIT // Copyright 2017 Christian Reitwiessner // Permission is hereby granted, free of charge, to any person obtaining a copy // of this software and associated documentation files (the "Software"), to // deal in the Software without restriction, including without limitation the // rights to use, copy, modify, merge, publish, distribute, sublicense, and/or // sell copies of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // The above copyright notice and this permission notice shall be included in // all copies or substantial portions of the Software. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING // FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS // IN THE SOFTWARE. // 2019 OKIMS pragma solidity ^0.8.20; library Pairing { uint256 constant PRIME_Q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; struct G1Point { uint256 X; uint256 Y; } // Encoding of field elements is: X[0] * z + X[1] struct G2Point { uint256[2] X; uint256[2] Y; } /* * @return The negation of p, i.e. p.plus(p.negate()) should be zero. */ function negate(G1Point memory p) internal pure returns (G1Point memory) { // The prime q in the base field F_q for G1 if (p.X == 0 && p.Y == 0) { return G1Point(0, 0); } else { return G1Point(p.X, PRIME_Q - (p.Y % PRIME_Q)); } } /* * @return r the sum of two points of G1 */ function plus( G1Point memory p1, G1Point memory p2 ) internal view returns (G1Point memory r) { uint256[4] memory input; input[0] = p1.X; input[1] = p1.Y; input[2] = p2.X; input[3] = p2.Y; bool success; // solium-disable-next-line security/no-inline-assembly assembly { success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60) // Use "invalid" to make gas estimation work switch success case 0 { invalid() } } require(success, "pairing-add-failed"); } /* * @return r the product of a point on G1 and a scalar, i.e. * p == p.scalar_mul(1) and p.plus(p) == p.scalar_mul(2) for all * points p. */ function scalar_mul(G1Point memory p, uint256 s) internal view returns (G1Point memory r) { uint256[3] memory input; input[0] = p.X; input[1] = p.Y; input[2] = s; bool success; // solium-disable-next-line security/no-inline-assembly assembly { success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60) // Use "invalid" to make gas estimation work switch success case 0 { invalid() } } require(success, "pairing-mul-failed"); } /* @return The result of computing the pairing check * e(p1[0], p2[0]) * .... * e(p1[n], p2[n]) == 1 * For example, * pairing([P1(), P1().negate()], [P2(), P2()]) should return true. */ function pairing( G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2, G1Point memory c1, G2Point memory c2, G1Point memory d1, G2Point memory d2 ) internal view returns (bool) { G1Point[4] memory p1 = [a1, b1, c1, d1]; G2Point[4] memory p2 = [a2, b2, c2, d2]; uint256 inputSize = 24; uint256[] memory input = new uint256[](inputSize); for (uint256 i = 0; i < 4; i++) { uint256 j = i * 6; input[j + 0] = p1[i].X; input[j + 1] = p1[i].Y; input[j + 2] = p2[i].X[0]; input[j + 3] = p2[i].X[1]; input[j + 4] = p2[i].Y[0]; input[j + 5] = p2[i].Y[1]; } uint256[1] memory out; bool success; // solium-disable-next-line security/no-inline-assembly assembly { success := staticcall(sub(gas(), 2000), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20) // Use "invalid" to make gas estimation work switch success case 0 { invalid() } } require(success, "pairing-opcode-failed"); return out[0] != 0; } } contract Verifier { uint256 constant SNARK_SCALAR_FIELD = 21888242871839275222246405745257275088548364400416034343698204186575808495617; uint256 constant PRIME_Q = 21888242871839275222246405745257275088696311157297823662689037894645226208583; using Pairing for *; struct VerifyingKey { Pairing.G1Point alfa1; Pairing.G2Point beta2; Pairing.G2Point gamma2; Pairing.G2Point delta2; Pairing.G1Point[7] IC; } struct Proof { Pairing.G1Point A; Pairing.G2Point B; Pairing.G1Point C; } function verifyingKey() internal pure returns (VerifyingKey memory vk) { vk.alfa1 = Pairing.G1Point(uint256(20692898189092739278193869274495556617788530808486270118371701516666252877969), uint256(11713062878292653967971378194351968039596396853904572879488166084231740557279)); vk.beta2 = Pairing.G2Point([uint256(12168528810181263706895252315640534818222943348193302139358377162645029937006), uint256(281120578337195720357474965979947690431622127986816839208576358024608803542)], [uint256(16129176515713072042442734839012966563817890688785805090011011570989315559913), uint256(9011703453772030375124466642203641636825223906145908770308724549646909480510)]); vk.gamma2 = Pairing.G2Point([uint256(11559732032986387107991004021392285783925812861821192530917403151452391805634), uint256(10857046999023057135944570762232829481370756359578518086990519993285655852781)], [uint256(4082367875863433681332203403145435568316851327593401208105741076214120093531), uint256(8495653923123431417604973247489272438418190587263600148770280649306958101930)]); vk.delta2 = Pairing.G2Point([uint256(21280594949518992153305586783242820682644996932183186320680800072133486887432), uint256(150879136433974552800030963899771162647715069685890547489132178314736470662)], [uint256(1081836006956609894549771334721413187913047383331561601606260283167615953295), uint256(11434086686358152335540554643130007307617078324975981257823476472104616196090)]); vk.IC[0] = Pairing.G1Point(uint256(16225148364316337376768119297456868908427925829817748684139175309620217098814), uint256(5167268689450204162046084442581051565997733233062478317813755636162413164690)); vk.IC[1] = Pairing.G1Point(uint256(12882377842072682264979317445365303375159828272423495088911985689463022094260), uint256(19488215856665173565526758360510125932214252767275816329232454875804474844786)); vk.IC[2] = Pairing.G1Point(uint256(13083492661683431044045992285476184182144099829507350352128615182516530014777), uint256(602051281796153692392523702676782023472744522032670801091617246498551238913)); vk.IC[3] = Pairing.G1Point(uint256(9732465972180335629969421513785602934706096902316483580882842789662669212890), uint256(2776526698606888434074200384264824461688198384989521091253289776235602495678)); vk.IC[4] = Pairing.G1Point(uint256(8586364274534577154894611080234048648883781955345622578531233113180532234842), uint256(21276134929883121123323359450658320820075698490666870487450985603988214349407)); vk.IC[5] = Pairing.G1Point(uint256(4910628533171597675018724709631788948355422829499855033965018665300386637884), uint256(20532468890024084510431799098097081600480376127870299142189696620752500664302)); vk.IC[6] = Pairing.G1Point(uint256(15335858102289947642505450692012116222827233918185150176888641903531542034017), uint256(5311597067667671581646709998171703828965875677637292315055030353779531404812)); } /* * @returns Whether the proof is valid given the hardcoded verifying key * above and the public inputs */ function verifyProof( bytes memory proof, uint256[6] memory input ) public view returns (bool) { uint256[8] memory p = abi.decode(proof, (uint256[8])); // Make sure that each element in the proof is less than the prime q for (uint8 i = 0; i < p.length; i++) { require(p[i] < PRIME_Q, "verifier-proof-element-gte-prime-q"); } Proof memory _proof; _proof.A = Pairing.G1Point(p[0], p[1]); _proof.B = Pairing.G2Point([p[2], p[3]], [p[4], p[5]]); _proof.C = Pairing.G1Point(p[6], p[7]); VerifyingKey memory vk = verifyingKey(); // Compute the linear combination vk_x Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0); vk_x = Pairing.plus(vk_x, vk.IC[0]); // Make sure that every input is less than the snark scalar field for (uint256 i = 0; i < input.length; i++) { require(input[i] < SNARK_SCALAR_FIELD, "verifier-gte-snark-scalar-field"); vk_x = Pairing.plus(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i])); } return Pairing.pairing( Pairing.negate(_proof.A), _proof.B, vk.alfa1, vk.beta2, vk_x, vk.gamma2, _proof.C, vk.delta2 ); } }