From dee2f66a8f7f9509d1feaf89caf5bdea9570db75 Mon Sep 17 00:00:00 2001 From: "jiaji.wei" Date: Thu, 11 Apr 2024 15:33:44 +0800 Subject: [PATCH 1/2] [feat] add mock mode and admin role --- .../verifiers/FflonkVerifierWithMock.sol | 2183 +++++++++++++++++ tools/deployVerifier/deployVerifier.ts | 2 +- 2 files changed, 2184 insertions(+), 1 deletion(-) create mode 100644 contracts/verifiers/FflonkVerifierWithMock.sol diff --git a/contracts/verifiers/FflonkVerifierWithMock.sol b/contracts/verifiers/FflonkVerifierWithMock.sol new file mode 100644 index 000000000..49ca8fea6 --- /dev/null +++ b/contracts/verifiers/FflonkVerifierWithMock.sol @@ -0,0 +1,2183 @@ +// SPDX-License-Identifier: GPL-3.0 +/* + Copyright 2021 0KIMS association. + + This file is generated with [snarkJS](https://github.com/iden3/snarkjs). + + snarkJS is a free software: you can redistribute it and/or modify it + under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + snarkJS is distributed in the hope that it will be useful, but WITHOUT + ANY WARRANTY; without even the implied warranty of MERCHANTABILITY + or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public + License for more details. + + You should have received a copy of the GNU General Public License + along with snarkJS. If not, see . +*/ + +pragma solidity >=0.7.0 <0.9.0; + +contract FflonkVerifierWithMock { + uint32 constant n = 16777216; // Domain size + + // Verification Key data + uint256 constant k1 = 2; // Plonk k1 multiplicative factor to force distinct cosets of H + uint256 constant k2 = 3; // Plonk k2 multiplicative factor to force distinct cosets of H + + // OMEGAS + // Omega, Omega^{1/3} + uint256 constant w1 = + 5709868443893258075976348696661355716898495876243883251619397131511003808859; + uint256 constant wr = + 18200100796661656210024324131237448517259556535315737226009542456080026430510; + // Omega_3, Omega_3^2 + uint256 constant w3 = + 21888242871839275217838484774961031246154997185409878258781734729429964517155; + uint256 constant w3_2 = + 4407920970296243842393367215006156084916469457145843978461; + // Omega_4, Omega_4^2, Omega_4^3 + uint256 constant w4 = + 21888242871839275217838484774961031246007050428528088939761107053157389710902; + uint256 constant w4_2 = + 21888242871839275222246405745257275088548364400416034343698204186575808495616; + uint256 constant w4_3 = + 4407920970296243842541313971887945403937097133418418784715; + // Omega_8, Omega_8^2, Omega_8^3, Omega_8^4, Omega_8^5, Omega_8^6, Omega_8^7 + uint256 constant w8_1 = + 19540430494807482326159819597004422086093766032135589407132600596362845576832; + uint256 constant w8_2 = + 21888242871839275217838484774961031246007050428528088939761107053157389710902; + uint256 constant w8_3 = + 13274704216607947843011480449124596415239537050559949017414504948711435969894; + uint256 constant w8_4 = + 21888242871839275222246405745257275088548364400416034343698204186575808495616; + uint256 constant w8_5 = + 2347812377031792896086586148252853002454598368280444936565603590212962918785; + uint256 constant w8_6 = + 4407920970296243842541313971887945403937097133418418784715; + uint256 constant w8_7 = + 8613538655231327379234925296132678673308827349856085326283699237864372525723; + + // Verifier preprocessed input C_0(x)·[1]_1 + uint256 constant C0x = + 19531210301294568511992648735135291982401633864004026433715722115099857739632; + uint256 constant C0y = + 16913517370715546973488219367119174715262034757907912789481968159710930517904; + + // Verifier preprocessed input x·[1]_2 + uint256 constant X2x1 = + 21831381940315734285607113342023901060522397560371972897001948545212302161822; + uint256 constant X2x2 = + 17231025384763736816414546592865244497437017442647097510447326538965263639101; + uint256 constant X2y1 = + 2388026358213174446665280700919698872609886601280537296205114254867301080648; + uint256 constant X2y2 = + 11507326595632554467052522095592665270651932854513688777769618397986436103170; + + // Scalar field size + uint256 constant q = + 21888242871839275222246405745257275088548364400416034343698204186575808495617; + // Base field size + uint256 constant qf = + 21888242871839275222246405745257275088696311157297823662689037894645226208583; + // [1]_1 + uint256 constant G1x = 1; + uint256 constant G1y = 2; + // [1]_2 + uint256 constant G2x1 = + 10857046999023057135944570762232829481370756359578518086990519993285655852781; + uint256 constant G2x2 = + 11559732032986387107991004021392285783925812861821192530917403151452391805634; + uint256 constant G2y1 = + 8495653923123431417604973247489272438418190587263600148770280649306958101930; + uint256 constant G2y2 = + 4082367875863433681332203403145435568316851327593401208105741076214120093531; + + // Proof calldata + // Byte offset of every parameter of the calldata + // Polynomial commitments + uint16 constant pC1 = 4 + 0; // [C1]_1 + uint16 constant pC2 = 4 + 32 * 2; // [C2]_1 + uint16 constant pW1 = 4 + 32 * 4; // [W]_1 + uint16 constant pW2 = 4 + 32 * 6; // [W']_1 + // Opening evaluations + uint16 constant pEval_ql = 4 + 32 * 8; // q_L(xi) + uint16 constant pEval_qr = 4 + 32 * 9; // q_R(xi) + uint16 constant pEval_qm = 4 + 32 * 10; // q_M(xi) + uint16 constant pEval_qo = 4 + 32 * 11; // q_O(xi) + uint16 constant pEval_qc = 4 + 32 * 12; // q_C(xi) + uint16 constant pEval_s1 = 4 + 32 * 13; // S_{sigma_1}(xi) + uint16 constant pEval_s2 = 4 + 32 * 14; // S_{sigma_2}(xi) + uint16 constant pEval_s3 = 4 + 32 * 15; // S_{sigma_3}(xi) + uint16 constant pEval_a = 4 + 32 * 16; // a(xi) + uint16 constant pEval_b = 4 + 32 * 17; // b(xi) + uint16 constant pEval_c = 4 + 32 * 18; // c(xi) + uint16 constant pEval_z = 4 + 32 * 19; // z(xi) + uint16 constant pEval_zw = 4 + 32 * 20; // z_omega(xi) + uint16 constant pEval_t1w = 4 + 32 * 21; // T_1(xi omega) + uint16 constant pEval_t2w = 4 + 32 * 22; // T_2(xi omega) + uint16 constant pEval_inv = 4 + 32 * 23; // inv(batch) sent by the prover to avoid any inverse calculation to save gas, + // we check the correctness of the inv(batch) by computing batch + // and checking inv(batch) * batch == 1 + + // Memory data + // Challenges + uint16 constant pAlpha = 0; // alpha challenge + uint16 constant pBeta = 32; // beta challenge + uint16 constant pGamma = 64; // gamma challenge + uint16 constant pY = 96; // y challenge + uint16 constant pXiSeed = 128; // xi seed, from this value we compute xi = xiSeed^24 + uint16 constant pXiSeed2 = 160; // (xi seed)^2 + uint16 constant pXi = 192; // xi challenge + + // Roots + // S_0 = roots_8(xi) = { h_0, h_0w_8, h_0w_8^2, h_0w_8^3, h_0w_8^4, h_0w_8^5, h_0w_8^6, h_0w_8^7 } + uint16 constant pH0w8_0 = 224; + uint16 constant pH0w8_1 = 256; + uint16 constant pH0w8_2 = 288; + uint16 constant pH0w8_3 = 320; + uint16 constant pH0w8_4 = 352; + uint16 constant pH0w8_5 = 384; + uint16 constant pH0w8_6 = 416; + uint16 constant pH0w8_7 = 448; + + // S_1 = roots_4(xi) = { h_1, h_1w_4, h_1w_4^2, h_1w_4^3 } + uint16 constant pH1w4_0 = 480; + uint16 constant pH1w4_1 = 512; + uint16 constant pH1w4_2 = 544; + uint16 constant pH1w4_3 = 576; + + // S_2 = roots_3(xi) U roots_3(xi omega) + // roots_3(xi) = { h_2, h_2w_3, h_2w_3^2 } + uint16 constant pH2w3_0 = 608; + uint16 constant pH2w3_1 = 640; + uint16 constant pH2w3_2 = 672; + // roots_3(xi omega) = { h_3, h_3w_3, h_3w_3^2 } + uint16 constant pH3w3_0 = 704; + uint16 constant pH3w3_1 = 736; + uint16 constant pH3w3_2 = 768; + + uint16 constant pPi = 800; // PI(xi) + uint16 constant pR0 = 832; // r0(y) + uint16 constant pR1 = 864; // r1(y) + uint16 constant pR2 = 896; // r2(y) + + uint16 constant pF = 928; // [F]_1, 64 bytes + uint16 constant pE = 992; // [E]_1, 64 bytes + uint16 constant pJ = 1056; // [J]_1, 64 bytes + + uint16 constant pZh = 1184; // Z_H(xi) + // From this point we write all the variables that must be computed using the Montgomery batch inversion + uint16 constant pZhInv = 1216; // 1/Z_H(xi) + uint16 constant pDenH1 = 1248; // 1/( (y-h_1w_4) (y-h_1w_4^2) (y-h_1w_4^3) (y-h_1w_4^4) ) + uint16 constant pDenH2 = 1280; // 1/( (y-h_2w_3) (y-h_2w_3^2) (y-h_2w_3^3) (y-h_3w_3) (y-h_3w_3^2) (y-h_3w_3^3) ) + uint16 constant pLiS0Inv = 1312; // Reserve 8 * 32 bytes to compute r_0(X) + uint16 constant pLiS1Inv = 1568; // Reserve 4 * 32 bytes to compute r_1(X) + uint16 constant pLiS2Inv = 1696; // Reserve 6 * 32 bytes to compute r_2(X) + // Lagrange evaluations + + uint16 constant pEval_l1 = 1888; + + uint16 constant lastMem = 1920; + + address public amdin; + + bool public mockMode = false; + + constructor() { + amdin = msg.sender; + } + + modifier onlyAdmin() { + require(msg.sender == amdin, "Only admin can call this function"); + _; + } + + function activateMockMode() public onlyAdmin { + mockMode = true; + } + + function deactivateMockMode() public onlyAdmin { + mockMode = false; + } + + function verifyProof( + bytes32[24] calldata proof, + uint256[1] calldata pubSignals + ) public view returns (bool) { + if (mockMode) { + return true; + } + + assembly { + // Computes the inverse of an array of values + // See https://vitalik.ca/general/2018/07/21/starks_part_3.html in section where explain fields operations + // To save the inverse to be computed on chain the prover sends the inverse as an evaluation in commits.eval_inv + function inverseArray(pMem) { + let pAux := mload(0x40) // Point to the next free position + let acc := mload(add(pMem, pZhInv)) // Read the first element + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pDenH1)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pDenH2)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q) + mstore(pAux, acc) + + pAux := add(pAux, 32) + acc := mulmod(acc, mload(add(pMem, pEval_l1)), q) + mstore(pAux, acc) + + let inv := calldataload(pEval_inv) + + // Before using the inverse sent by the prover the verifier checks inv(batch) * batch === 1 + if iszero(eq(1, mulmod(acc, inv, q))) { + mstore(0, 0) + return(0, 0x20) + } + + acc := inv + + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pEval_l1)), q) + mstore(add(pMem, pEval_l1), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 160))), q) + mstore(add(pMem, add(pLiS2Inv, 160)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 128))), q) + mstore(add(pMem, add(pLiS2Inv, 128)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 96))), q) + mstore(add(pMem, add(pLiS2Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 64))), q) + mstore(add(pMem, add(pLiS2Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS2Inv, 32))), q) + mstore(add(pMem, add(pLiS2Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS2Inv)), q) + mstore(add(pMem, pLiS2Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 96))), q) + mstore(add(pMem, add(pLiS1Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 64))), q) + mstore(add(pMem, add(pLiS1Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS1Inv, 32))), q) + mstore(add(pMem, add(pLiS1Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS1Inv)), q) + mstore(add(pMem, pLiS1Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 224))), q) + mstore(add(pMem, add(pLiS0Inv, 224)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 192))), q) + mstore(add(pMem, add(pLiS0Inv, 192)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 160))), q) + mstore(add(pMem, add(pLiS0Inv, 160)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 128))), q) + mstore(add(pMem, add(pLiS0Inv, 128)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 96))), q) + mstore(add(pMem, add(pLiS0Inv, 96)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 64))), q) + mstore(add(pMem, add(pLiS0Inv, 64)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, add(pLiS0Inv, 32))), q) + mstore(add(pMem, add(pLiS0Inv, 32)), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pLiS0Inv)), q) + mstore(add(pMem, pLiS0Inv), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pDenH2)), q) + mstore(add(pMem, pDenH2), inv) + pAux := sub(pAux, 32) + inv := mulmod(acc, mload(pAux), q) + acc := mulmod(acc, mload(add(pMem, pDenH1)), q) + mstore(add(pMem, pDenH1), inv) + + mstore(add(pMem, pZhInv), acc) + } + + function checkField(v) { + if iszero(lt(v, q)) { + mstore(0, 0) + return(0, 0x20) + } + } + + function checkPointBelongsToBN128Curve(p) { + let x := calldataload(p) + let y := calldataload(add(p, 32)) + + // Check that the point is on the curve + // y^2 = x^3 + 3 + let x3_3 := addmod(mulmod(x, mulmod(x, x, qf), qf), 3, qf) + let y2 := mulmod(y, y, qf) + + if iszero(eq(x3_3, y2)) { + mstore(0, 0) + return(0, 0x20) + } + } + + // Validate all the evaluations sent by the prover ∈ F + function checkInput() { + // Check proof commitments fullfill bn128 curve equation Y^2 = X^3 + 3 + checkPointBelongsToBN128Curve(pC1) + checkPointBelongsToBN128Curve(pC2) + checkPointBelongsToBN128Curve(pW1) + checkPointBelongsToBN128Curve(pW2) + + checkField(calldataload(pEval_ql)) + checkField(calldataload(pEval_qr)) + checkField(calldataload(pEval_qm)) + checkField(calldataload(pEval_qo)) + checkField(calldataload(pEval_qc)) + checkField(calldataload(pEval_s1)) + checkField(calldataload(pEval_s2)) + checkField(calldataload(pEval_s3)) + checkField(calldataload(pEval_a)) + checkField(calldataload(pEval_b)) + checkField(calldataload(pEval_c)) + checkField(calldataload(pEval_z)) + checkField(calldataload(pEval_zw)) + checkField(calldataload(pEval_t1w)) + checkField(calldataload(pEval_t2w)) + checkField(calldataload(pEval_inv)) + + // Points are checked in the point operations precompiled smart contracts + } + + function computeChallenges(pMem, pPublic) { + // Compute challenge.beta & challenge.gamma + mstore(add(pMem, 1920), C0x) + mstore(add(pMem, 1952), C0y) + + mstore(add(pMem, 1984), calldataload(pPublic)) + + mstore(add(pMem, 2016), calldataload(pC1)) + mstore(add(pMem, 2048), calldataload(add(pC1, 32))) + + mstore( + add(pMem, pBeta), + mod(keccak256(add(pMem, lastMem), 160), q) + ) + mstore( + add(pMem, pGamma), + mod(keccak256(add(pMem, pBeta), 32), q) + ) + + // Get xiSeed & xiSeed2 + mstore(add(pMem, lastMem), mload(add(pMem, pGamma))) + mstore(add(pMem, 1952), calldataload(pC2)) + mstore(add(pMem, 1984), calldataload(add(pC2, 32))) + let xiSeed := mod(keccak256(add(pMem, lastMem), 96), q) + + mstore(add(pMem, pXiSeed), xiSeed) + mstore(add(pMem, pXiSeed2), mulmod(xiSeed, xiSeed, q)) + + // Compute roots.S0.h0w8 + mstore( + add(pMem, pH0w8_0), + mulmod( + mload(add(pMem, pXiSeed2)), + mload(add(pMem, pXiSeed)), + q + ) + ) + mstore( + add(pMem, pH0w8_1), + mulmod(mload(add(pMem, pH0w8_0)), w8_1, q) + ) + mstore( + add(pMem, pH0w8_2), + mulmod(mload(add(pMem, pH0w8_0)), w8_2, q) + ) + mstore( + add(pMem, pH0w8_3), + mulmod(mload(add(pMem, pH0w8_0)), w8_3, q) + ) + mstore( + add(pMem, pH0w8_4), + mulmod(mload(add(pMem, pH0w8_0)), w8_4, q) + ) + mstore( + add(pMem, pH0w8_5), + mulmod(mload(add(pMem, pH0w8_0)), w8_5, q) + ) + mstore( + add(pMem, pH0w8_6), + mulmod(mload(add(pMem, pH0w8_0)), w8_6, q) + ) + mstore( + add(pMem, pH0w8_7), + mulmod(mload(add(pMem, pH0w8_0)), w8_7, q) + ) + + // Compute roots.S1.h1w4 + mstore( + add(pMem, pH1w4_0), + mulmod( + mload(add(pMem, pH0w8_0)), + mload(add(pMem, pH0w8_0)), + q + ) + ) + mstore( + add(pMem, pH1w4_1), + mulmod(mload(add(pMem, pH1w4_0)), w4, q) + ) + mstore( + add(pMem, pH1w4_2), + mulmod(mload(add(pMem, pH1w4_0)), w4_2, q) + ) + mstore( + add(pMem, pH1w4_3), + mulmod(mload(add(pMem, pH1w4_0)), w4_3, q) + ) + + // Compute roots.S2.h2w3 + mstore( + add(pMem, pH2w3_0), + mulmod( + mload(add(pMem, pH1w4_0)), + mload(add(pMem, pXiSeed2)), + q + ) + ) + mstore( + add(pMem, pH2w3_1), + mulmod(mload(add(pMem, pH2w3_0)), w3, q) + ) + mstore( + add(pMem, pH2w3_2), + mulmod(mload(add(pMem, pH2w3_0)), w3_2, q) + ) + + // Compute roots.S2.h2w3 + mstore( + add(pMem, pH3w3_0), + mulmod(mload(add(pMem, pH2w3_0)), wr, q) + ) + mstore( + add(pMem, pH3w3_1), + mulmod(mload(add(pMem, pH3w3_0)), w3, q) + ) + mstore( + add(pMem, pH3w3_2), + mulmod(mload(add(pMem, pH3w3_0)), w3_2, q) + ) + + let xin := mulmod( + mulmod( + mload(add(pMem, pH2w3_0)), + mload(add(pMem, pH2w3_0)), + q + ), + mload(add(pMem, pH2w3_0)), + q + ) + mstore(add(pMem, pXi), xin) + + // Compute xi^n + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mulmod(xin, xin, q) + + xin := mod(add(sub(xin, 1), q), q) + mstore(add(pMem, pZh), xin) + mstore(add(pMem, pZhInv), xin) // We will invert later together with lagrange pols + + // Compute challenge.alpha + mstore(add(pMem, lastMem), xiSeed) + + calldatacopy(add(pMem, 1952), pEval_ql, 480) + mstore( + add(pMem, pAlpha), + mod(keccak256(add(pMem, lastMem), 512), q) + ) + + // Compute challenge.y + mstore(add(pMem, lastMem), mload(add(pMem, pAlpha))) + mstore(add(pMem, 1952), calldataload(pW1)) + mstore(add(pMem, 1984), calldataload(add(pW1, 32))) + mstore(add(pMem, pY), mod(keccak256(add(pMem, lastMem), 96), q)) + } + + function computeLiS0(pMem) { + let root0 := mload(add(pMem, pH0w8_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(8, den1, q) + + let den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 0), 8), 32))) + ) + let den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(0, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 0)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 1), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(1, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 32)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 2), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(2, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 64)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 3), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(3, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 96)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 4), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(4, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 128)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 5), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(5, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 160)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 6), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(6, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 192)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH0w8_0, mul(mod(mul(7, 7), 8), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH0w8_0, mul(7, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS0Inv, 224)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + } + + function computeLiS1(pMem) { + let root0 := mload(add(pMem, pH1w4_0)) + let y := mload(add(pMem, pY)) + let den1 := 1 + den1 := mulmod(den1, root0, q) + den1 := mulmod(den1, root0, q) + + den1 := mulmod(4, den1, q) + + let den2 := mload( + add(pMem, add(pH1w4_0, mul(mod(mul(3, 0), 4), 32))) + ) + let den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(0, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS1Inv, 0)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH1w4_0, mul(mod(mul(3, 1), 4), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(1, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS1Inv, 32)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH1w4_0, mul(mod(mul(3, 2), 4), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(2, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS1Inv, 64)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH1w4_0, mul(mod(mul(3, 3), 4), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH1w4_0, mul(3, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS1Inv, 96)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + } + + function computeLiS2(pMem) { + let y := mload(add(pMem, pY)) + + let den1 := mulmod( + mulmod(3, mload(add(pMem, pH2w3_0)), q), + addmod( + mload(add(pMem, pXi)), + mod(sub(q, mulmod(mload(add(pMem, pXi)), w1, q)), q), + q + ), + q + ) + + let den2 := mload( + add(pMem, add(pH2w3_0, mul(mod(mul(2, 0), 3), 32))) + ) + let den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(0, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 0)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH2w3_0, mul(mod(mul(2, 1), 3), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(1, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 32)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH2w3_0, mul(mod(mul(2, 2), 3), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH2w3_0, mul(2, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 64)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den1 := mulmod( + mulmod(3, mload(add(pMem, pH3w3_0)), q), + addmod( + mulmod(mload(add(pMem, pXi)), w1, q), + mod(sub(q, mload(add(pMem, pXi))), q), + q + ), + q + ) + + den2 := mload( + add(pMem, add(pH3w3_0, mul(mod(mul(2, 0), 3), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(0, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 96)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH3w3_0, mul(mod(mul(2, 1), 3), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(1, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 128)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + + den2 := mload( + add(pMem, add(pH3w3_0, mul(mod(mul(2, 2), 3), 32))) + ) + den3 := addmod( + y, + mod(sub(q, mload(add(pMem, add(pH3w3_0, mul(2, 32))))), q), + q + ) + + mstore( + add(pMem, add(pLiS2Inv, 160)), + mulmod(den1, mulmod(den2, den3, q), q) + ) + } + + // Prepare all the denominators that must be inverted, placed them in consecutive memory addresses + function computeInversions(pMem) { + // 1/ZH(xi) used in steps 8 and 9 of the verifier to multiply by 1/Z_H(xi) + // Value computed during computeChallenges function and stores in pMem+pZhInv + + // 1/((y - h1) (y - h1w4) (y - h1w4_2) (y - h1w4_3)) + // used in steps 10 and 11 of the verifier + let y := mload(add(pMem, pY)) + let w := addmod(y, mod(sub(q, mload(add(pMem, pH1w4_0))), q), q) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH1w4_1))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH1w4_2))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH1w4_3))), q), q), + q + ) + mstore(add(pMem, pDenH1), w) + + // 1/((y - h2) (y - h2w3) (y - h2w3_2) (y - h3) (y - h3w3) (y - h3w3_2)) + w := addmod(y, mod(sub(q, mload(add(pMem, pH2w3_0))), q), q) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH2w3_1))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH2w3_2))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH3w3_0))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH3w3_1))), q), q), + q + ) + w := mulmod( + w, + addmod(y, mod(sub(q, mload(add(pMem, pH3w3_2))), q), q), + q + ) + mstore(add(pMem, pDenH2), w) + + // Denominator needed in the verifier when computing L_i^{S0}(X) + computeLiS0(pMem) + + // Denominator needed in the verifier when computing L_i^{S1}(X) + computeLiS1(pMem) + + // Denominator needed in the verifier when computing L_i^{S2}(X) + computeLiS2(pMem) + + // L_i where i from 1 to num public inputs, needed in step 6 and 7 of the verifier to compute L_1(xi) and PI(xi) + w := 1 + let xi := mload(add(pMem, pXi)) + + mstore( + add(pMem, pEval_l1), + mulmod(n, mod(add(sub(xi, w), q), q), q) + ) + + // Execute Montgomery batched inversions of the previous prepared values + inverseArray(pMem) + } + + // Compute Lagrange polynomial evaluation L_i(xi) + function computeLagrange(pMem) { + let zh := mload(add(pMem, pZh)) + let w := 1 + + mstore( + add(pMem, pEval_l1), + mulmod(mload(add(pMem, pEval_l1)), zh, q) + ) + } + + // Compute public input polynomial evaluation PI(xi) + function computePi(pMem, pPub) { + let pi := 0 + pi := mod( + add( + sub( + pi, + mulmod( + mload(add(pMem, pEval_l1)), + calldataload(pPub), + q + ) + ), + q + ), + q + ) + + mstore(add(pMem, pPi), pi) + } + + // Compute r0(y) by interpolating the polynomial r0(X) using 8 points (x,y) + // where x = {h9, h0w8, h0w8^2, h0w8^3, h0w8^4, h0w8^5, h0w8^6, h0w8^7} + // and y = {C0(h0), C0(h0w8), C0(h0w8^2), C0(h0w8^3), C0(h0w8^4), C0(h0w8^5), C0(h0w8^6), C0(h0w8^7)} + // and computing C0(xi) + function computeR0(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + + let res + let h0w80 + let c0Value + let h0w8i + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_0)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 0))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_1)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 32))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_2)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 64))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_3)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 96))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_4)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 128))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_5)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 160))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_6)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 192))), q), + q + ), + q + ) + + // Compute c0Value = ql + (h0w8i) qr + (h0w8i)^2 qo + (h0w8i)^3 qm + (h0w8i)^4 qc + + // + (h0w8i)^5 S1 + (h0w8i)^6 S2 + (h0w8i)^7 S3 + h0w80 := mload(add(pMem, pH0w8_7)) + c0Value := addmod( + calldataload(pEval_ql), + mulmod(calldataload(pEval_qr), h0w80, q), + q + ) + h0w8i := mulmod(h0w80, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qo), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qm), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_qc), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s1), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s2), h0w8i, q), + q + ) + h0w8i := mulmod(h0w8i, h0w80, q) + c0Value := addmod( + c0Value, + mulmod(calldataload(pEval_s3), h0w8i, q), + q + ) + + res := addmod( + res, + mulmod( + c0Value, + mulmod(num, mload(add(pMem, add(pLiS0Inv, 224))), q), + q + ), + q + ) + + mstore(add(pMem, pR0), res) + } + + // Compute r1(y) by interpolating the polynomial r1(X) using 4 points (x,y) + // where x = {h1, h1w4, h1w4^2, h1w4^3} + // and y = {C1(h1), C1(h1w4), C1(h1w4^2), C1(h1w4^3)} + // and computing T0(xi) + function computeR1(pMem) { + let num := 1 + let y := mload(add(pMem, pY)) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + num := mulmod(num, y, q) + + num := addmod(num, mod(sub(q, mload(add(pMem, pXi))), q), q) + + let t0 + let evalA := calldataload(pEval_a) + let evalB := calldataload(pEval_b) + let evalC := calldataload(pEval_c) + + t0 := mulmod(calldataload(pEval_ql), evalA, q) + t0 := addmod(t0, mulmod(calldataload(pEval_qr), evalB, q), q) + t0 := addmod( + t0, + mulmod(calldataload(pEval_qm), mulmod(evalA, evalB, q), q), + q + ) + t0 := addmod(t0, mulmod(calldataload(pEval_qo), evalC, q), q) + t0 := addmod(t0, calldataload(pEval_qc), q) + t0 := addmod(t0, mload(add(pMem, pPi)), q) + t0 := mulmod(t0, mload(add(pMem, pZhInv)), q) + + let res + let c1Value + let h1w4 + let square + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_0)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod( + c1Value, + mulmod(mulmod(square, h1w4, q), t0, q), + q + ) + + res := addmod( + res, + mulmod( + c1Value, + mulmod( + num, + mload(add(pMem, add(pLiS1Inv, mul(0, 32)))), + q + ), + q + ), + q + ) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_1)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod( + c1Value, + mulmod(mulmod(square, h1w4, q), t0, q), + q + ) + + res := addmod( + res, + mulmod( + c1Value, + mulmod( + num, + mload(add(pMem, add(pLiS1Inv, mul(1, 32)))), + q + ), + q + ), + q + ) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_2)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod( + c1Value, + mulmod(mulmod(square, h1w4, q), t0, q), + q + ) + + res := addmod( + res, + mulmod( + c1Value, + mulmod( + num, + mload(add(pMem, add(pLiS1Inv, mul(2, 32)))), + q + ), + q + ), + q + ) + + c1Value := evalA + h1w4 := mload(add(pMem, pH1w4_3)) + + c1Value := addmod(c1Value, mulmod(h1w4, evalB, q), q) + square := mulmod(h1w4, h1w4, q) + c1Value := addmod(c1Value, mulmod(square, evalC, q), q) + c1Value := addmod( + c1Value, + mulmod(mulmod(square, h1w4, q), t0, q), + q + ) + + res := addmod( + res, + mulmod( + c1Value, + mulmod( + num, + mload(add(pMem, add(pLiS1Inv, mul(3, 32)))), + q + ), + q + ), + q + ) + + mstore(add(pMem, pR1), res) + } + + // Compute r2(y) by interpolating the polynomial r2(X) using 6 points (x,y) + // where x = {[h2, h2w3, h2w3^2], [h3, h3w3, h3w3^2]} + // and y = {[C2(h2), C2(h2w3), C2(h2w3^2)], [C2(h3), C2(h3w3), C2(h3w3^2)]} + // and computing T1(xi) and T2(xi) + function computeR2(pMem) { + let y := mload(add(pMem, pY)) + let num := 1 + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + num := mulmod(y, num, q) + + let num2 := 1 + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod(y, num2, q) + num2 := mulmod( + num2, + addmod( + mulmod(mload(add(pMem, pXi)), w1, q), + mload(add(pMem, pXi)), + q + ), + q + ) + + num := addmod(num, mod(sub(q, num2), q), q) + + num2 := mulmod( + mulmod(mload(add(pMem, pXi)), w1, q), + mload(add(pMem, pXi)), + q + ) + + num := addmod(num, num2, q) + + let t1 + let t2 + let betaXi := mulmod( + mload(add(pMem, pBeta)), + mload(add(pMem, pXi)), + q + ) + let gamma := mload(add(pMem, pGamma)) + + t2 := addmod(calldataload(pEval_a), addmod(betaXi, gamma, q), q) + t2 := mulmod( + t2, + addmod( + calldataload(pEval_b), + addmod(mulmod(betaXi, k1, q), gamma, q), + q + ), + q + ) + t2 := mulmod( + t2, + addmod( + calldataload(pEval_c), + addmod(mulmod(betaXi, k2, q), gamma, q), + q + ), + q + ) + t2 := mulmod(t2, calldataload(pEval_z), q) + + //Let's use t1 as a temporal variable to save one local + t1 := addmod( + calldataload(pEval_a), + addmod( + mulmod( + mload(add(pMem, pBeta)), + calldataload(pEval_s1), + q + ), + gamma, + q + ), + q + ) + t1 := mulmod( + t1, + addmod( + calldataload(pEval_b), + addmod( + mulmod( + mload(add(pMem, pBeta)), + calldataload(pEval_s2), + q + ), + gamma, + q + ), + q + ), + q + ) + t1 := mulmod( + t1, + addmod( + calldataload(pEval_c), + addmod( + mulmod( + mload(add(pMem, pBeta)), + calldataload(pEval_s3), + q + ), + gamma, + q + ), + q + ), + q + ) + t1 := mulmod(t1, calldataload(pEval_zw), q) + + t2 := addmod(t2, mod(sub(q, t1), q), q) + t2 := mulmod(t2, mload(add(pMem, pZhInv)), q) + + // Compute T1(xi) + t1 := sub(calldataload(pEval_z), 1) + t1 := mulmod(t1, mload(add(pMem, pEval_l1)), q) + t1 := mulmod(t1, mload(add(pMem, pZhInv)), q) + + // Let's use local variable gamma to save the result + gamma := 0 + + let hw + let c2Value + + hw := mload(add(pMem, pH2w3_0)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(0, 32)))), + q + ), + q + ), + q + ) + + hw := mload(add(pMem, pH2w3_1)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(1, 32)))), + q + ), + q + ), + q + ) + + hw := mload(add(pMem, pH2w3_2)) + c2Value := addmod(calldataload(pEval_z), mulmod(hw, t1, q), q) + c2Value := addmod(c2Value, mulmod(mulmod(hw, hw, q), t2, q), q) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(2, 32)))), + q + ), + q + ), + q + ) + + hw := mload(add(pMem, pH3w3_0)) + c2Value := addmod( + calldataload(pEval_zw), + mulmod(hw, calldataload(pEval_t1w), q), + q + ) + c2Value := addmod( + c2Value, + mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), + q + ) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(3, 32)))), + q + ), + q + ), + q + ) + + hw := mload(add(pMem, pH3w3_1)) + c2Value := addmod( + calldataload(pEval_zw), + mulmod(hw, calldataload(pEval_t1w), q), + q + ) + c2Value := addmod( + c2Value, + mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), + q + ) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(4, 32)))), + q + ), + q + ), + q + ) + + hw := mload(add(pMem, pH3w3_2)) + c2Value := addmod( + calldataload(pEval_zw), + mulmod(hw, calldataload(pEval_t1w), q), + q + ) + c2Value := addmod( + c2Value, + mulmod(mulmod(hw, hw, q), calldataload(pEval_t2w), q), + q + ) + gamma := addmod( + gamma, + mulmod( + c2Value, + mulmod( + num, + mload(add(pMem, add(pLiS2Inv, mul(5, 32)))), + q + ), + q + ), + q + ) + + mstore(add(pMem, pR2), gamma) + } + + // G1 function to accumulate a G1 value to an address + function g1_acc(pR, pP) { + let mIn := mload(0x40) + mstore(mIn, mload(pR)) + mstore(add(mIn, 32), mload(add(pR, 32))) + mstore(add(mIn, 64), mload(pP)) + mstore(add(mIn, 96), mload(add(pP, 32))) + + let success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } + } + + // G1 function to multiply a G1 value to value in an address + function g1_mulAcc(pR, pP, s) { + let success + let mIn := mload(0x40) + mstore(mIn, calldataload(pP)) + mstore(add(mIn, 32), calldataload(add(pP, 32))) + mstore(add(mIn, 64), s) + + success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } + + mstore(add(mIn, 64), mload(pR)) + mstore(add(mIn, 96), mload(add(pR, 32))) + + success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } + } + + // G1 function to multiply a G1 value(x,y) to value in an address + function g1_mulAccC(pR, x, y, s) { + let success + let mIn := mload(0x40) + mstore(mIn, x) + mstore(add(mIn, 32), y) + mstore(add(mIn, 64), s) + + success := staticcall(sub(gas(), 2000), 7, mIn, 96, mIn, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } + + mstore(add(mIn, 64), mload(pR)) + mstore(add(mIn, 96), mload(add(pR, 32))) + + success := staticcall(sub(gas(), 2000), 6, mIn, 128, pR, 64) + + if iszero(success) { + mstore(0, 0) + return(0, 0x20) + } + } + + function computeFEJ(pMem) { + // Prepare shared numerator between F, E and J to reuse it + let y := mload(add(pMem, pY)) + let numerator := addmod( + y, + mod(sub(q, mload(add(pMem, pH0w8_0))), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_1))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_2))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_3))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_4))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_5))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_6))), q), q), + q + ) + numerator := mulmod( + numerator, + addmod(y, mod(sub(q, mload(add(pMem, pH0w8_7))), q), q), + q + ) + + // Prepare shared quotient between F and E to reuse it + let quotient1 := mulmod( + mload(add(pMem, pAlpha)), + mulmod(numerator, mload(add(pMem, pDenH1)), q), + q + ) + let quotient2 := mulmod( + mulmod( + mload(add(pMem, pAlpha)), + mload(add(pMem, pAlpha)), + q + ), + mulmod(numerator, mload(add(pMem, pDenH2)), q), + q + ) + + // Compute full batched polynomial commitment [F]_1 + mstore(add(pMem, pF), C0x) + mstore(add(pMem, add(pF, 32)), C0y) + g1_mulAcc(add(pMem, pF), pC1, quotient1) + g1_mulAcc(add(pMem, pF), pC2, quotient2) + + // Compute group-encoded batch evaluation [E]_1 + g1_mulAccC( + add(pMem, pE), + G1x, + G1y, + addmod( + mload(add(pMem, pR0)), + addmod( + mulmod(quotient1, mload(add(pMem, pR1)), q), + mulmod(quotient2, mload(add(pMem, pR2)), q), + q + ), + q + ) + ) + + // Compute the full difference [J]_1 + g1_mulAcc(add(pMem, pJ), pW1, numerator) + } + + // Validate all evaluations with a pairing checking that e([F]_1 - [E]_1 - [J]_1 + y[W2]_1, [1]_2) == e([W']_1, [x]_2) + function checkPairing(pMem) -> isOk { + let mIn := mload(0x40) + + // First pairing value + // Compute -E + mstore( + add(add(pMem, pE), 32), + mod(sub(qf, mload(add(add(pMem, pE), 32))), qf) + ) + // Compute -J + mstore( + add(add(pMem, pJ), 32), + mod(sub(qf, mload(add(add(pMem, pJ), 32))), qf) + ) + // F = F - E - J + y·W2 + g1_acc(add(pMem, pF), add(pMem, pE)) + g1_acc(add(pMem, pF), add(pMem, pJ)) + g1_mulAcc(add(pMem, pF), pW2, mload(add(pMem, pY))) + + mstore(mIn, mload(add(pMem, pF))) + mstore(add(mIn, 32), mload(add(add(pMem, pF), 32))) + + // Second pairing value + mstore(add(mIn, 64), G2x2) + mstore(add(mIn, 96), G2x1) + mstore(add(mIn, 128), G2y2) + mstore(add(mIn, 160), G2y1) + + // Third pairing value + // Compute -W2 + mstore(add(mIn, 192), calldataload(pW2)) + let s := calldataload(add(pW2, 32)) + s := mod(sub(qf, s), qf) + mstore(add(mIn, 224), s) + + // Fourth pairing value + mstore(add(mIn, 256), X2x2) + mstore(add(mIn, 288), X2x1) + mstore(add(mIn, 320), X2y2) + mstore(add(mIn, 352), X2y1) + + let success := staticcall( + sub(gas(), 2000), + 8, + mIn, + 384, + mIn, + 0x20 + ) + + isOk := and(success, mload(mIn)) + } + + let pMem := mload(0x40) + mstore(0x40, add(pMem, lastMem)) + + // Validate that all evaluations ∈ F + checkInput() + + // Compute the challenges: beta, gamma, xi, alpha and y ∈ F, h1w4/h2w3/h3w3 roots, xiN and zh(xi) + computeChallenges(pMem, pubSignals) + + // To divide prime fields the Extended Euclidean Algorithm for computing modular inverses is needed. + // The Montgomery batch inversion algorithm allow us to compute n inverses reducing to a single one inversion. + // More info: https://vitalik.ca/general/2018/07/21/starks_part_3.html + // To avoid this single inverse computation on-chain, it has been computed in proving time and send it to the verifier. + // Therefore, the verifier: + // 1) Prepare all the denominators to inverse + // 2) Check the inverse sent by the prover it is what it should be + // 3) Compute the others inverses using the Montgomery Batched Algorithm using the inverse sent to avoid the inversion operation it does. + computeInversions(pMem) + + // Compute Lagrange polynomial evaluations Li(xi) + computeLagrange(pMem) + + // Compute public input polynomial evaluation PI(xi) = \sum_i^l -public_input_i·L_i(xi) + computePi(pMem, pubSignals) + + // Computes r1(y) and r2(y) + computeR0(pMem) + computeR1(pMem) + computeR2(pMem) + + // Compute full batched polynomial commitment [F]_1, group-encoded batch evaluation [E]_1 and the full difference [J]_1 + computeFEJ(pMem) + + // Validate all evaluations + let isValid := checkPairing(pMem) + + mstore(0, isValid) + return(0, 0x20) + } + } +} diff --git a/tools/deployVerifier/deployVerifier.ts b/tools/deployVerifier/deployVerifier.ts index 9a58d68a0..960a819eb 100644 --- a/tools/deployVerifier/deployVerifier.ts +++ b/tools/deployVerifier/deployVerifier.ts @@ -67,7 +67,7 @@ async function main() { verifierContract = await VerifierRollup.deploy(); await verifierContract.waitForDeployment(); } else { - const VerifierRollupHelperFactory = await ethers.getContractFactory("VerifierRollupHelperMock", deployer); + const VerifierRollupHelperFactory = await ethers.getContractFactory("FflonkVerifierWithMock", deployer); verifierContract = await VerifierRollupHelperFactory.deploy(); await verifierContract.waitForDeployment(); } From 388ea132d925d59ca983c15f908b4ee35cad9853 Mon Sep 17 00:00:00 2001 From: "jiaji.wei" Date: Thu, 11 Apr 2024 15:39:38 +0800 Subject: [PATCH 2/2] [feat] add setAdmin func --- contracts/verifiers/FflonkVerifierWithMock.sol | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/contracts/verifiers/FflonkVerifierWithMock.sol b/contracts/verifiers/FflonkVerifierWithMock.sol index 49ca8fea6..c5cf9ce7e 100644 --- a/contracts/verifiers/FflonkVerifierWithMock.sol +++ b/contracts/verifiers/FflonkVerifierWithMock.sol @@ -204,6 +204,11 @@ contract FflonkVerifierWithMock { mockMode = false; } + function setAdmin(address _admin) public onlyAdmin { + require(_admin != address(0), "Admin address cannot be 0"); + amdin = _admin; + } + function verifyProof( bytes32[24] calldata proof, uint256[1] calldata pubSignals