From 449e387d71914522852ea1f1b1467c1c25a3c476 Mon Sep 17 00:00:00 2001 From: mattstam Date: Wed, 9 Oct 2024 15:45:59 -0700 Subject: [PATCH] fmt --- contracts/src/v3.0.0-rc1/PlonkVerifier.sol | 2659 +++++++++-------- contracts/src/v3.0.0-rc1/SP1VerifierPlonk.sol | 4 +- 2 files changed, 1352 insertions(+), 1311 deletions(-) diff --git a/contracts/src/v3.0.0-rc1/PlonkVerifier.sol b/contracts/src/v3.0.0-rc1/PlonkVerifier.sol index db312df..d5a0c41 100644 --- a/contracts/src/v3.0.0-rc1/PlonkVerifier.sol +++ b/contracts/src/v3.0.0-rc1/PlonkVerifier.sol @@ -19,1314 +19,1357 @@ pragma solidity ^0.8.20; contract PlonkVerifier { - - uint256 private constant R_MOD = 21888242871839275222246405745257275088548364400416034343698204186575808495617; - uint256 private constant R_MOD_MINUS_ONE = 21888242871839275222246405745257275088548364400416034343698204186575808495616; - uint256 private constant P_MOD = 21888242871839275222246405745257275088696311157297823662689037894645226208583; - - uint256 private constant G2_SRS_0_X_0 = 11559732032986387107991004021392285783925812861821192530917403151452391805634; - uint256 private constant G2_SRS_0_X_1 = 10857046999023057135944570762232829481370756359578518086990519993285655852781; - uint256 private constant G2_SRS_0_Y_0 = 4082367875863433681332203403145435568316851327593401208105741076214120093531; - uint256 private constant G2_SRS_0_Y_1 = 8495653923123431417604973247489272438418190587263600148770280649306958101930; - - uint256 private constant G2_SRS_1_X_0 = 15805639136721018565402881920352193254830339253282065586954346329754995870280; - uint256 private constant G2_SRS_1_X_1 = 19089565590083334368588890253123139704298730990782503769911324779715431555531; - uint256 private constant G2_SRS_1_Y_0 = 9779648407879205346559610309258181044130619080926897934572699915909528404984; - uint256 private constant G2_SRS_1_Y_1 = 6779728121489434657638426458390319301070371227460768374343986326751507916979; - - uint256 private constant G1_SRS_X = 14312776538779914388377568895031746459131577658076416373430523308756343304251; - uint256 private constant G1_SRS_Y = 11763105256161367503191792604679297387056316997144156930871823008787082098465; - - // ----------------------- vk --------------------- - uint256 private constant VK_NB_PUBLIC_INPUTS = 2; - uint256 private constant VK_DOMAIN_SIZE = 16777216; - uint256 private constant VK_INV_DOMAIN_SIZE = 21888241567198334088790460357988866238279339518792980768180410072331574733841; - uint256 private constant VK_OMEGA = 5709868443893258075976348696661355716898495876243883251619397131511003808859; - uint256 private constant VK_QL_COM_X = 3290060728869345335154114718977447053330166483334167631366198142610428232620; - uint256 private constant VK_QL_COM_Y = 19162119719409246272115813094185025995857052458470900198554531144420657384429; - uint256 private constant VK_QR_COM_X = 20593285675028444864919533759061889592214551177771462207774701990433512561961; - uint256 private constant VK_QR_COM_Y = 2037190768409221720866644069987363251819987312430306430360685249062434970888; - uint256 private constant VK_QM_COM_X = 3243698466425196128341517132303061662197275421453284874501006751806324568406; - uint256 private constant VK_QM_COM_Y = 1522093955203686116281629526048034563543666750312611984631281801989604375093; - uint256 private constant VK_QO_COM_X = 18116824637133877774109916770339012329893346672063455581152619443461705941258; - uint256 private constant VK_QO_COM_Y = 12065546623891456568116583509565259597148533132778310848302637027619241642160; - uint256 private constant VK_QK_COM_X = 13141440805370550747455201471324318730010929401231584161046984899369324303111; - uint256 private constant VK_QK_COM_Y = 12213720583880706739223964024508346683319146975553789702175775841006924916084; - - uint256 private constant VK_S1_COM_X = 12793975975635479749073429864966625606798501224471844064009199522695564922740; - uint256 private constant VK_S1_COM_Y = 8132923293671412095334718058521033016410241972572274691532700944443498103422; - - uint256 private constant VK_S2_COM_X = 21657378963874914616650592302460330003572962134736577570012568301070663363623; - uint256 private constant VK_S2_COM_Y = 1718513843029691644222560949246389014329795284083891303459043520417235854191; - - uint256 private constant VK_S3_COM_X = 20415325187354694665500244845769422238048526183908185443188703734475579190071; - uint256 private constant VK_S3_COM_Y = 18073955099179029460825044425464668031894304571793555401967621518843518905026; - - uint256 private constant VK_COSET_SHIFT = 5; - - - uint256 private constant VK_QCP_0_X = 12741358679119216268442671261008764468184354452248089481320165441775601729818; - uint256 private constant VK_QCP_0_Y = 9936318890363003735758197368031202024870521212376882419342977488108314073196; - - - uint256 private constant VK_INDEX_COMMIT_API_0 = 10703054; - uint256 private constant VK_NB_CUSTOM_GATES = 1; - - // ------------------------------------------------ - - // offset proof - - uint256 private constant PROOF_L_COM_X = 0x0; - uint256 private constant PROOF_L_COM_Y = 0x20; - uint256 private constant PROOF_R_COM_X = 0x40; - uint256 private constant PROOF_R_COM_Y = 0x60; - uint256 private constant PROOF_O_COM_X = 0x80; - uint256 private constant PROOF_O_COM_Y = 0xa0; - - // h = h_0 + x^{n+2}h_1 + x^{2(n+2)}h_2 - uint256 private constant PROOF_H_0_X = 0xc0; - uint256 private constant PROOF_H_0_Y = 0xe0; - uint256 private constant PROOF_H_1_X = 0x100; - uint256 private constant PROOF_H_1_Y = 0x120; - uint256 private constant PROOF_H_2_X = 0x140; - uint256 private constant PROOF_H_2_Y = 0x160; - - // wire values at zeta - uint256 private constant PROOF_L_AT_ZETA = 0x180; - uint256 private constant PROOF_R_AT_ZETA = 0x1a0; - uint256 private constant PROOF_O_AT_ZETA = 0x1c0; - - // S1(zeta),S2(zeta) - uint256 private constant PROOF_S1_AT_ZETA = 0x1e0; // Sσ1(zeta) - uint256 private constant PROOF_S2_AT_ZETA = 0x200; // Sσ2(zeta) - - // [Z] - uint256 private constant PROOF_GRAND_PRODUCT_COMMITMENT_X = 0x220; - uint256 private constant PROOF_GRAND_PRODUCT_COMMITMENT_Y = 0x240; - - uint256 private constant PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA = 0x260; // z(w*zeta) - - // Folded proof for the opening of linearised poly, l, r, o, s_1, s_2, qcp - uint256 private constant PROOF_BATCH_OPENING_AT_ZETA_X = 0x280; - uint256 private constant PROOF_BATCH_OPENING_AT_ZETA_Y = 0x2a0; - - uint256 private constant PROOF_OPENING_AT_ZETA_OMEGA_X = 0x2c0; - uint256 private constant PROOF_OPENING_AT_ZETA_OMEGA_Y = 0x2e0; - - uint256 private constant PROOF_OPENING_QCP_AT_ZETA = 0x300; - uint256 private constant PROOF_BSB_COMMITMENTS = 0x320; - - // -> next part of proof is - // [ openings_selector_commits || commitments_wires_commit_api] - - // -------- offset state - - // challenges to check the claimed quotient - - uint256 private constant STATE_ALPHA = 0x0; - uint256 private constant STATE_BETA = 0x20; - uint256 private constant STATE_GAMMA = 0x40; - uint256 private constant STATE_ZETA = 0x60; - uint256 private constant STATE_ALPHA_SQUARE_LAGRANGE_0 = 0x80; - uint256 private constant STATE_FOLDED_H_X = 0xa0; - uint256 private constant STATE_FOLDED_H_Y = 0xc0; - uint256 private constant STATE_LINEARISED_POLYNOMIAL_X = 0xe0; - uint256 private constant STATE_LINEARISED_POLYNOMIAL_Y = 0x100; - uint256 private constant STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA = 0x120; - uint256 private constant STATE_FOLDED_CLAIMED_VALUES = 0x140; // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp - uint256 private constant STATE_FOLDED_DIGESTS_X = 0x160; // folded digests of H, linearised poly, l, r, o, s_1, s_2, qcp - uint256 private constant STATE_FOLDED_DIGESTS_Y = 0x180; - uint256 private constant STATE_PI = 0x1a0; - uint256 private constant STATE_ZETA_POWER_N_MINUS_ONE = 0x1c0; - uint256 private constant STATE_GAMMA_KZG = 0x1e0; - uint256 private constant STATE_SUCCESS = 0x200; - uint256 private constant STATE_CHECK_VAR = 0x220; // /!\ this slot is used for debugging only - uint256 private constant STATE_LAST_MEM = 0x240; - - // -------- utils (for Fiat Shamir) - uint256 private constant FS_ALPHA = 0x616C706861; // "alpha" - uint256 private constant FS_BETA = 0x62657461; // "beta" - uint256 private constant FS_GAMMA = 0x67616d6d61; // "gamma" - uint256 private constant FS_ZETA = 0x7a657461; // "zeta" - uint256 private constant FS_GAMMA_KZG = 0x67616d6d61; // "gamma" - - // -------- errors - uint256 private constant ERROR_STRING_ID = 0x08c379a000000000000000000000000000000000000000000000000000000000; // selector for function Error(string) - - - // -------- utils (for hash_fr) - uint256 private constant HASH_FR_BB = 340282366920938463463374607431768211456; // 2**128 - uint256 private constant HASH_FR_ZERO_UINT256 = 0; - uint8 private constant HASH_FR_LEN_IN_BYTES = 48; - uint8 private constant HASH_FR_SIZE_DOMAIN = 11; - uint8 private constant HASH_FR_ONE = 1; - uint8 private constant HASH_FR_TWO = 2; - - - // -------- precompiles - uint8 private constant MOD_EXP = 0x5; - uint8 private constant EC_ADD = 0x6; - uint8 private constant EC_MUL = 0x7; - uint8 private constant EC_PAIR = 0x8; - - /// Verify a Plonk proof. - /// Reverts if the proof or the public inputs are malformed. - /// @param proof serialised plonk proof (using gnark's MarshalSolidity) - /// @param public_inputs (must be reduced) - /// @return success true if the proof passes false otherwise - function Verify(bytes calldata proof, uint256[] calldata public_inputs) - public view returns(bool success) { - - assembly { - - let mem := mload(0x40) - let freeMem := add(mem, STATE_LAST_MEM) - - // sanity checks - check_number_of_public_inputs(public_inputs.length) - check_inputs_size(public_inputs.length, public_inputs.offset) - check_proof_size(proof.length) - check_proof_openings_size(proof.offset) - - // compute the challenges - let prev_challenge_non_reduced - prev_challenge_non_reduced := derive_gamma(proof.offset, public_inputs.length, public_inputs.offset) - prev_challenge_non_reduced := derive_beta(prev_challenge_non_reduced) - prev_challenge_non_reduced := derive_alpha(proof.offset, prev_challenge_non_reduced) - derive_zeta(proof.offset, prev_challenge_non_reduced) - - // evaluation of Z=Xⁿ-1 at ζ, we save this value - let zeta := mload(add(mem, STATE_ZETA)) - let zeta_power_n_minus_one := addmod(pow(zeta, VK_DOMAIN_SIZE, freeMem), sub(R_MOD, 1), R_MOD) - mstore(add(mem, STATE_ZETA_POWER_N_MINUS_ONE), zeta_power_n_minus_one) - - // public inputs contribution - let l_pi := sum_pi_wo_api_commit(public_inputs.offset, public_inputs.length, freeMem) - let l_pi_commit := sum_pi_commit(proof.offset, public_inputs.length, freeMem) - l_pi := addmod(l_pi_commit, l_pi, R_MOD) - mstore(add(mem, STATE_PI), l_pi) - - compute_alpha_square_lagrange_0() - verify_opening_linearised_polynomial(proof.offset) - fold_h(proof.offset) - compute_commitment_linearised_polynomial(proof.offset) - compute_gamma_kzg(proof.offset) - fold_state(proof.offset) - batch_verify_multi_points(proof.offset) - - success := mload(add(mem, STATE_SUCCESS)) - - // Beginning errors ------------------------------------------------- - - function error_nb_public_inputs() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x1d) - mstore(add(ptError, 0x44), "wrong number of public inputs") - revert(ptError, 0x64) - } - - /// Called when an operation on Bn254 fails - /// @dev for instance when calling EcMul on a point not on Bn254. - function error_ec_op() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x12) - mstore(add(ptError, 0x44), "error ec operation") - revert(ptError, 0x64) - } - - /// Called when one of the public inputs is not reduced. - function error_inputs_size() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x18) - mstore(add(ptError, 0x44), "inputs are bigger than r") - revert(ptError, 0x64) - } - - /// Called when the size proof is not as expected - /// @dev to avoid overflow attack for instance - function error_proof_size() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x10) - mstore(add(ptError, 0x44), "wrong proof size") - revert(ptError, 0x64) - } - - /// Called when one the openings is bigger than r - /// The openings are the claimed evalutions of a polynomial - /// in a Kzg proof. - function error_proof_openings_size() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x16) - mstore(add(ptError, 0x44), "openings bigger than r") - revert(ptError, 0x64) - } - - function error_pairing() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0xd) - mstore(add(ptError, 0x44), "error pairing") - revert(ptError, 0x64) - } - - function error_verify() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0xc) - mstore(add(ptError, 0x44), "error verify") - revert(ptError, 0x64) - } - - function error_random_generation() { - let ptError := mload(0x40) - mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) - mstore(add(ptError, 0x4), 0x20) - mstore(add(ptError, 0x24), 0x14) - mstore(add(ptError, 0x44), "error random gen kzg") - revert(ptError, 0x64) - } - // end errors ------------------------------------------------- - - // Beginning checks ------------------------------------------------- - - /// @param s actual number of public inputs - function check_number_of_public_inputs(s) { - if iszero(eq(s, VK_NB_PUBLIC_INPUTS)) { - error_nb_public_inputs() - } - } - - /// Checks that the public inputs are < R_MOD. - /// @param s number of public inputs - /// @param p pointer to the public inputs array - function check_inputs_size(s, p) { - for {let i} lt(i, s) {i:=add(i,1)} - { - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_inputs_size() - } - p := add(p, 0x20) - } - } - - /// Checks if the proof is of the correct size - /// @param actual_proof_size size of the proof (not the expected size) - function check_proof_size(actual_proof_size) { - let expected_proof_size := add(0x300, mul(VK_NB_CUSTOM_GATES,0x60)) - if iszero(eq(actual_proof_size, expected_proof_size)) { - error_proof_size() - } - } - - /// Checks if the multiple openings of the polynomials are < R_MOD. - /// @param aproof pointer to the beginning of the proof - /// @dev the 'a' prepending proof is to have a local name - function check_proof_openings_size(aproof) { - - // PROOF_L_AT_ZETA - let p := add(aproof, PROOF_L_AT_ZETA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_R_AT_ZETA - p := add(aproof, PROOF_R_AT_ZETA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_O_AT_ZETA - p := add(aproof, PROOF_O_AT_ZETA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_S1_AT_ZETA - p := add(aproof, PROOF_S1_AT_ZETA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_S2_AT_ZETA - p := add(aproof, PROOF_S2_AT_ZETA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA - p := add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA) - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - - // PROOF_OPENING_QCP_AT_ZETA - - p := add(aproof, PROOF_OPENING_QCP_AT_ZETA) - for {let i:=0} lt(i, VK_NB_CUSTOM_GATES) {i:=add(i,1)} - { - if gt(calldataload(p), R_MOD_MINUS_ONE) { - error_proof_openings_size() - } - p := add(p, 0x20) - } - - } - // end checks ------------------------------------------------- - - // Beginning challenges ------------------------------------------------- - - /// Derive gamma as Sha256() - /// @param aproof pointer to the proof - /// @param nb_pi number of public inputs - /// @param pi pointer to the array of public inputs - /// @return the challenge gamma, not reduced - /// @notice The transcript is the concatenation (in this order) of: - /// * the word "gamma" in ascii, equal to [0x67,0x61,0x6d, 0x6d, 0x61] and encoded as a uint256. - /// * the commitments to the permutation polynomials S1, S2, S3, where we concatenate the coordinates of those points - /// * the commitments of Ql, Qr, Qm, Qo, Qk - /// * the public inputs - /// * the commitments of the wires related to the custom gates (commitments_wires_commit_api) - /// * commitments to L, R, O (proof__com_) - /// The data described above is written starting at mPtr. "gamma" lies on 5 bytes, - /// and is encoded as a uint256 number n. In basis b = 256, the number looks like this - /// [0 0 0 .. 0x67 0x61 0x6d, 0x6d, 0x61]. The first non zero entry is at position 27=0x1b - /// Gamma reduced (the actual challenge) is stored at add(state, state_gamma) - function derive_gamma(aproof, nb_pi, pi)->gamma_not_reduced { - - let state := mload(0x40) - let mPtr := add(state, STATE_LAST_MEM) - - // gamma - // gamma in ascii is [0x67,0x61,0x6d, 0x6d, 0x61] - // (same for alpha, beta, zeta) - mstore(mPtr, FS_GAMMA) // "gamma" - - mstore(add(mPtr, 0x20), VK_S1_COM_X) - mstore(add(mPtr, 0x40), VK_S1_COM_Y) - mstore(add(mPtr, 0x60), VK_S2_COM_X) - mstore(add(mPtr, 0x80), VK_S2_COM_Y) - mstore(add(mPtr, 0xa0), VK_S3_COM_X) - mstore(add(mPtr, 0xc0), VK_S3_COM_Y) - mstore(add(mPtr, 0xe0), VK_QL_COM_X) - mstore(add(mPtr, 0x100), VK_QL_COM_Y) - mstore(add(mPtr, 0x120), VK_QR_COM_X) - mstore(add(mPtr, 0x140), VK_QR_COM_Y) - mstore(add(mPtr, 0x160), VK_QM_COM_X) - mstore(add(mPtr, 0x180), VK_QM_COM_Y) - mstore(add(mPtr, 0x1a0), VK_QO_COM_X) - mstore(add(mPtr, 0x1c0), VK_QO_COM_Y) - mstore(add(mPtr, 0x1e0), VK_QK_COM_X) - mstore(add(mPtr, 0x200), VK_QK_COM_Y) - - mstore(add(mPtr, 0x220), VK_QCP_0_X) - mstore(add(mPtr, 0x240), VK_QCP_0_Y) - - // public inputs - let _mPtr := add(mPtr, 0x260) - let size_pi_in_bytes := mul(nb_pi, 0x20) - calldatacopy(_mPtr, pi, size_pi_in_bytes) - _mPtr := add(_mPtr, size_pi_in_bytes) - - // commitments to l, r, o - let size_commitments_lro_in_bytes := 0xc0 - calldatacopy(_mPtr, aproof, size_commitments_lro_in_bytes) - _mPtr := add(_mPtr, size_commitments_lro_in_bytes) - - // total size is : - // sizegamma(=0x5) + 11*64(=0x2c0) - // + nb_public_inputs*0x20 - // + nb_custom gates*0x40 - let size := add(0x2c5, size_pi_in_bytes) - - size := add(size, mul(VK_NB_CUSTOM_GATES, 0x40)) - let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1b), size, mPtr, 0x20) //0x1b -> 000.."gamma" - if iszero(l_success) { - error_verify() - } - gamma_not_reduced := mload(mPtr) - mstore(add(state, STATE_GAMMA), mod(gamma_not_reduced, R_MOD)) - } - - /// derive beta as Sha256 - /// @param gamma_not_reduced the previous challenge (gamma) not reduced - /// @return beta_not_reduced the next challenge, beta, not reduced - /// @notice the transcript consists of the previous challenge only. - /// The reduced version of beta is stored at add(state, state_beta) - function derive_beta(gamma_not_reduced)->beta_not_reduced{ - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - - // beta - mstore(mPtr, FS_BETA) // "beta" - mstore(add(mPtr, 0x20), gamma_not_reduced) - let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1c), 0x24, mPtr, 0x20) //0x1b -> 000.."gamma" - if iszero(l_success) { - error_verify() - } - beta_not_reduced := mload(mPtr) - mstore(add(state, STATE_BETA), mod(beta_not_reduced, R_MOD)) - } - - /// derive alpha as sha256 - /// @param aproof pointer to the proof object - /// @param beta_not_reduced the previous challenge (beta) not reduced - /// @return alpha_not_reduced the next challenge, alpha, not reduced - /// @notice the transcript consists of the previous challenge (beta) - /// not reduced, the commitments to the wires associated to the QCP_i, - /// and the commitment to the grand product polynomial - function derive_alpha(aproof, beta_not_reduced)->alpha_not_reduced { - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - let full_size := 0x65 // size("alpha") + 0x20 (previous challenge) - - // alpha - mstore(mPtr, FS_ALPHA) // "alpha" - let _mPtr := add(mPtr, 0x20) - mstore(_mPtr, beta_not_reduced) - _mPtr := add(_mPtr, 0x20) - - // Bsb22Commitments - let proof_bsb_commitments := add(aproof, PROOF_BSB_COMMITMENTS) - let size_bsb_commitments := mul(0x40, VK_NB_CUSTOM_GATES) - calldatacopy(_mPtr, proof_bsb_commitments, size_bsb_commitments) - _mPtr := add(_mPtr, size_bsb_commitments) - full_size := add(full_size, size_bsb_commitments) - - // [Z], the commitment to the grand product polynomial - calldatacopy(_mPtr, add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X), 0x40) - let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1b), full_size, mPtr, 0x20) - if iszero(l_success) { - error_verify() - } - - alpha_not_reduced := mload(mPtr) - mstore(add(state, STATE_ALPHA), mod(alpha_not_reduced, R_MOD)) - } - - /// derive zeta as sha256 - /// @param aproof pointer to the proof object - /// @param alpha_not_reduced the previous challenge (alpha) not reduced - /// The transcript consists of the previous challenge and the commitment to - /// the quotient polynomial h. - function derive_zeta(aproof, alpha_not_reduced) { - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - - // zeta - mstore(mPtr, FS_ZETA) // "zeta" - mstore(add(mPtr, 0x20), alpha_not_reduced) - calldatacopy(add(mPtr, 0x40), add(aproof, PROOF_H_0_X), 0xc0) - let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1c), 0xe4, mPtr, 0x20) - if iszero(l_success) { - error_verify() - } - let zeta_not_reduced := mload(mPtr) - mstore(add(state, STATE_ZETA), mod(zeta_not_reduced, R_MOD)) - } - // END challenges ------------------------------------------------- - - // BEGINNING compute_pi ------------------------------------------------- - - /// sum_pi_wo_api_commit computes the public inputs contributions, - /// except for the public inputs coming from the custom gate - /// @param ins pointer to the public inputs - /// @param n number of public inputs - /// @param mPtr free memory - /// @return pi_wo_commit public inputs contribution (except the public inputs coming from the custom gate) - function sum_pi_wo_api_commit(ins, n, mPtr)->pi_wo_commit { - - let state := mload(0x40) - let z := mload(add(state, STATE_ZETA)) - let zpnmo := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) - - let li := mPtr - batch_compute_lagranges_at_z(z, zpnmo, n, li) - - let tmp := 0 - for {let i:=0} lt(i,n) {i:=add(i,1)} - { - tmp := mulmod(mload(li), calldataload(ins), R_MOD) - pi_wo_commit := addmod(pi_wo_commit, tmp, R_MOD) - li := add(li, 0x20) - ins := add(ins, 0x20) - } - - } - - /// batch_compute_lagranges_at_z computes [L_0(z), .., L_{n-1}(z)] - /// @param z point at which the Lagranges are evaluated - /// @param zpnmo ζⁿ-1 - /// @param n number of public inputs (number of Lagranges to compute) - /// @param mPtr pointer to which the results are stored - function batch_compute_lagranges_at_z(z, zpnmo, n, mPtr) { - - let zn := mulmod(zpnmo, VK_INV_DOMAIN_SIZE, R_MOD) // 1/n * (ζⁿ - 1) - - let _w := 1 - let _mPtr := mPtr - for {let i:=0} lt(i,n) {i:=add(i,1)} - { - mstore(_mPtr, addmod(z,sub(R_MOD, _w), R_MOD)) - _w := mulmod(_w, VK_OMEGA, R_MOD) - _mPtr := add(_mPtr, 0x20) - } - batch_invert(mPtr, n, _mPtr) - _mPtr := mPtr - _w := 1 - for {let i:=0} lt(i,n) {i:=add(i,1)} - { - mstore(_mPtr, mulmod(mulmod(mload(_mPtr), zn , R_MOD), _w, R_MOD)) - _mPtr := add(_mPtr, 0x20) - _w := mulmod(_w, VK_OMEGA, R_MOD) - } - } - - /// @notice Montgomery trick for batch inversion mod R_MOD - /// @param ins pointer to the data to batch invert - /// @param number of elements to batch invert - /// @param mPtr free memory - function batch_invert(ins, nb_ins, mPtr) { - mstore(mPtr, 1) - let offset := 0 - for {let i:=0} lt(i, nb_ins) {i:=add(i,1)} - { - let prev := mload(add(mPtr, offset)) - let cur := mload(add(ins, offset)) - cur := mulmod(prev, cur, R_MOD) - offset := add(offset, 0x20) - mstore(add(mPtr, offset), cur) - } - ins := add(ins, sub(offset, 0x20)) - mPtr := add(mPtr, offset) - let inv := pow(mload(mPtr), sub(R_MOD,2), add(mPtr, 0x20)) - for {let i:=0} lt(i, nb_ins) {i:=add(i,1)} - { - mPtr := sub(mPtr, 0x20) - let tmp := mload(ins) - let cur := mulmod(inv, mload(mPtr), R_MOD) - mstore(ins, cur) - inv := mulmod(inv, tmp, R_MOD) - ins := sub(ins, 0x20) - } - } - - - /// Public inputs (the ones coming from the custom gate) contribution - /// @param aproof pointer to the proof - /// @param nb_public_inputs number of public inputs - /// @param mPtr pointer to free memory - /// @return pi_commit custom gate public inputs contribution - function sum_pi_commit(aproof, nb_public_inputs, mPtr)->pi_commit { - - let state := mload(0x40) - let z := mload(add(state, STATE_ZETA)) - let zpnmo := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) - - let p := add(aproof, PROOF_BSB_COMMITMENTS) - - let h_fr, ith_lagrange - - - h_fr := hash_fr(calldataload(p), calldataload(add(p, 0x20)), mPtr) - ith_lagrange := compute_ith_lagrange_at_z(z, zpnmo, add(nb_public_inputs, VK_INDEX_COMMIT_API_0), mPtr) - pi_commit := addmod(pi_commit, mulmod(h_fr, ith_lagrange, R_MOD), R_MOD) - p := add(p, 0x40) - - - } - - /// Computes L_i(zeta) = ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where: - /// @param z zeta - /// @param zpmno ζⁿ-1 - /// @param i i-th lagrange - /// @param mPtr free memory - /// @return res = ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) - function compute_ith_lagrange_at_z(z, zpnmo, i, mPtr)->res { - - let w := pow(VK_OMEGA, i, mPtr) // w**i - i := addmod(z, sub(R_MOD, w), R_MOD) // z-w**i - w := mulmod(w, VK_INV_DOMAIN_SIZE, R_MOD) // w**i/n - i := pow(i, sub(R_MOD,2), mPtr) // (z-w**i)**-1 - w := mulmod(w, i, R_MOD) // w**i/n*(z-w)**-1 - res := mulmod(w, zpnmo, R_MOD) - - } - - /// @dev https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2 - /// @param x x coordinate of a point on Bn254(𝔽_p) - /// @param y y coordinate of a point on Bn254(𝔽_p) - /// @param mPtr free memory - /// @return res an element mod R_MOD - function hash_fr(x, y, mPtr)->res { - - // [0x00, .. , 0x00 || x, y, || 0, 48, 0, dst, HASH_FR_SIZE_DOMAIN] - // <- 64 bytes -> <-64b -> <- 1 bytes each -> - - // [0x00, .., 0x00] 64 bytes of zero - mstore(mPtr, HASH_FR_ZERO_UINT256) - mstore(add(mPtr, 0x20), HASH_FR_ZERO_UINT256) - - // msg = x || y , both on 32 bytes - mstore(add(mPtr, 0x40), x) - mstore(add(mPtr, 0x60), y) - - // 0 || 48 || 0 all on 1 byte - mstore8(add(mPtr, 0x80), 0) - mstore8(add(mPtr, 0x81), HASH_FR_LEN_IN_BYTES) - mstore8(add(mPtr, 0x82), 0) - - // "BSB22-Plonk" = [42, 53, 42, 32, 32, 2d, 50, 6c, 6f, 6e, 6b,] - mstore8(add(mPtr, 0x83), 0x42) - mstore8(add(mPtr, 0x84), 0x53) - mstore8(add(mPtr, 0x85), 0x42) - mstore8(add(mPtr, 0x86), 0x32) - mstore8(add(mPtr, 0x87), 0x32) - mstore8(add(mPtr, 0x88), 0x2d) - mstore8(add(mPtr, 0x89), 0x50) - mstore8(add(mPtr, 0x8a), 0x6c) - mstore8(add(mPtr, 0x8b), 0x6f) - mstore8(add(mPtr, 0x8c), 0x6e) - mstore8(add(mPtr, 0x8d), 0x6b) - - // size domain - mstore8(add(mPtr, 0x8e), HASH_FR_SIZE_DOMAIN) - - let l_success := staticcall(gas(), 0x2, mPtr, 0x8f, mPtr, 0x20) - if iszero(l_success) { - error_verify() - } - - let b0 := mload(mPtr) - - // [b0 || one || dst || HASH_FR_SIZE_DOMAIN] - // <-64bytes -> <- 1 byte each -> - mstore8(add(mPtr, 0x20), HASH_FR_ONE) // 1 - - mstore8(add(mPtr, 0x21), 0x42) // dst - mstore8(add(mPtr, 0x22), 0x53) - mstore8(add(mPtr, 0x23), 0x42) - mstore8(add(mPtr, 0x24), 0x32) - mstore8(add(mPtr, 0x25), 0x32) - mstore8(add(mPtr, 0x26), 0x2d) - mstore8(add(mPtr, 0x27), 0x50) - mstore8(add(mPtr, 0x28), 0x6c) - mstore8(add(mPtr, 0x29), 0x6f) - mstore8(add(mPtr, 0x2a), 0x6e) - mstore8(add(mPtr, 0x2b), 0x6b) - - mstore8(add(mPtr, 0x2c), HASH_FR_SIZE_DOMAIN) // size domain - l_success := staticcall(gas(), 0x2, mPtr, 0x2d, mPtr, 0x20) - if iszero(l_success) { - error_verify() - } - - // b1 is located at mPtr. We store b2 at add(mPtr, 0x20) - - // [b0^b1 || two || dst || HASH_FR_SIZE_DOMAIN] - // <-64bytes -> <- 1 byte each -> - mstore(add(mPtr, 0x20), xor(mload(mPtr), b0)) - mstore8(add(mPtr, 0x40), HASH_FR_TWO) - - mstore8(add(mPtr, 0x41), 0x42) // dst - mstore8(add(mPtr, 0x42), 0x53) - mstore8(add(mPtr, 0x43), 0x42) - mstore8(add(mPtr, 0x44), 0x32) - mstore8(add(mPtr, 0x45), 0x32) - mstore8(add(mPtr, 0x46), 0x2d) - mstore8(add(mPtr, 0x47), 0x50) - mstore8(add(mPtr, 0x48), 0x6c) - mstore8(add(mPtr, 0x49), 0x6f) - mstore8(add(mPtr, 0x4a), 0x6e) - mstore8(add(mPtr, 0x4b), 0x6b) - - mstore8(add(mPtr, 0x4c), HASH_FR_SIZE_DOMAIN) // size domain - - let offset := add(mPtr, 0x20) - l_success := staticcall(gas(), 0x2, offset, 0x2d, offset, 0x20) - if iszero(l_success) { - error_verify() - } - - // at this point we have mPtr = [ b1 || b2] where b1 is on 32byes and b2 in 16bytes. - // we interpret it as a big integer mod r in big endian (similar to regular decimal notation) - // the result is then 2**(8*16)*mPtr[32:] + mPtr[32:48] - res := mulmod(mload(mPtr), HASH_FR_BB, R_MOD) // <- res = 2**128 * mPtr[:32] - let b1 := shr(128, mload(add(mPtr, 0x20))) // b1 <- [0, 0, .., 0 || b2[:16] ] - res := addmod(res, b1, R_MOD) - - } - - // END compute_pi ------------------------------------------------- - - /// @notice compute α² * 1/n * (ζ{n}-1)/(ζ - 1) where - /// * α = challenge derived in derive_gamma_beta_alpha_zeta - /// * n = vk_domain_size - /// * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*) - /// * ζ = zeta (challenge derived with Fiat Shamir) - function compute_alpha_square_lagrange_0() { - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - - let res := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) - let den := addmod(mload(add(state, STATE_ZETA)), sub(R_MOD, 1), R_MOD) - den := pow(den, sub(R_MOD, 2), mPtr) - den := mulmod(den, VK_INV_DOMAIN_SIZE, R_MOD) - res := mulmod(den, res, R_MOD) - - let l_alpha := mload(add(state, STATE_ALPHA)) - res := mulmod(res, l_alpha, R_MOD) - res := mulmod(res, l_alpha, R_MOD) - mstore(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0), res) - } - - /// @notice follows alg. p.13 of https://eprint.iacr.org/2019/953.pdf - /// with t₁ = t₂ = 1, and the proofs are ([digest] + [quotient] +purported evaluation): - /// * [state_folded_state_digests], [proof_batch_opening_at_zeta_x], state_folded_evals - /// * [proof_grand_product_commitment], [proof_opening_at_zeta_omega_x], [proof_grand_product_at_zeta_omega] - /// @param aproof pointer to the proof - function batch_verify_multi_points(aproof) { - let state := mload(0x40) - let mPtr := add(state, STATE_LAST_MEM) - - // derive a random number. As there is no random generator, we - // do an FS like challenge derivation, depending on both digests and - // ζ to ensure that the prover cannot control the random numger. - // Note: adding the other point ζω is not needed, as ω is known beforehand. - mstore(mPtr, mload(add(state, STATE_FOLDED_DIGESTS_X))) - mstore(add(mPtr, 0x20), mload(add(state, STATE_FOLDED_DIGESTS_Y))) - mstore(add(mPtr, 0x40), calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X))) - mstore(add(mPtr, 0x60), calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_Y))) - mstore(add(mPtr, 0x80), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X))) - mstore(add(mPtr, 0xa0), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_Y))) - mstore(add(mPtr, 0xc0), calldataload(add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X))) - mstore(add(mPtr, 0xe0), calldataload(add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_Y))) - mstore(add(mPtr, 0x100), mload(add(state, STATE_ZETA))) - mstore(add(mPtr, 0x120), mload(add(state, STATE_GAMMA_KZG))) - let random := staticcall(gas(), 0x2, mPtr, 0x140, mPtr, 0x20) - if iszero(random){ - error_random_generation() - } - random := mod(mload(mPtr), R_MOD) // use the same variable as we are one variable away from getting stack-too-deep error... - - let folded_quotients := mPtr - mPtr := add(folded_quotients, 0x40) - mstore(folded_quotients, calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X))) - mstore(add(folded_quotients, 0x20), calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_Y))) - point_acc_mul_calldata(folded_quotients, add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X), random, mPtr) - - let folded_digests := add(state, STATE_FOLDED_DIGESTS_X) - point_acc_mul_calldata(folded_digests, add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X), random, mPtr) - - let folded_evals := add(state, STATE_FOLDED_CLAIMED_VALUES) - fr_acc_mul_calldata(folded_evals, add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA), random) - - let folded_evals_commit := mPtr - mPtr := add(folded_evals_commit, 0x40) - mstore(folded_evals_commit, G1_SRS_X) - mstore(add(folded_evals_commit, 0x20), G1_SRS_Y) - mstore(add(folded_evals_commit, 0x40), mload(folded_evals)) - let check_staticcall := staticcall(gas(), 7, folded_evals_commit, 0x60, folded_evals_commit, 0x40) - if iszero(check_staticcall) { - error_verify() - } - - let folded_evals_commit_y := add(folded_evals_commit, 0x20) - mstore(folded_evals_commit_y, sub(P_MOD, mload(folded_evals_commit_y))) - point_add(folded_digests, folded_digests, folded_evals_commit, mPtr) - - let folded_points_quotients := mPtr - mPtr := add(mPtr, 0x40) - point_mul_calldata( - folded_points_quotients, - add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X), - mload(add(state, STATE_ZETA)), - mPtr - ) - let zeta_omega := mulmod(mload(add(state, STATE_ZETA)), VK_OMEGA, R_MOD) - random := mulmod(random, zeta_omega, R_MOD) - point_acc_mul_calldata(folded_points_quotients, add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X), random, mPtr) - - point_add(folded_digests, folded_digests, folded_points_quotients, mPtr) - - let folded_quotients_y := add(folded_quotients, 0x20) - mstore(folded_quotients_y, sub(P_MOD, mload(folded_quotients_y))) - - mstore(mPtr, mload(folded_digests)) - mstore(add(mPtr, 0x20), mload(add(folded_digests, 0x20))) - mstore(add(mPtr, 0x40), G2_SRS_0_X_0) // the 4 lines are the canonical G2 point on BN254 - mstore(add(mPtr, 0x60), G2_SRS_0_X_1) - mstore(add(mPtr, 0x80), G2_SRS_0_Y_0) - mstore(add(mPtr, 0xa0), G2_SRS_0_Y_1) - mstore(add(mPtr, 0xc0), mload(folded_quotients)) - mstore(add(mPtr, 0xe0), mload(add(folded_quotients, 0x20))) - mstore(add(mPtr, 0x100), G2_SRS_1_X_0) - mstore(add(mPtr, 0x120), G2_SRS_1_X_1) - mstore(add(mPtr, 0x140), G2_SRS_1_Y_0) - mstore(add(mPtr, 0x160), G2_SRS_1_Y_1) - check_pairing_kzg(mPtr) - } - - /// @notice check_pairing_kzg checks the result of the final pairing product of the batched - /// kzg verification. The purpose of this function is to avoid exhausting the stack - /// in the function batch_verify_multi_points. - /// @param mPtr pointer storing the tuple of pairs - function check_pairing_kzg(mPtr) { - let state := mload(0x40) - - let l_success := staticcall(gas(), 8, mPtr, 0x180, 0x00, 0x20) - if iszero(l_success) { - error_pairing() - } - let res_pairing := mload(0x00) - mstore(add(state, STATE_SUCCESS), res_pairing) - } - - /// @notice Fold the opening proofs at ζ: - /// * at state+state_folded_digest we store: [Linearised_polynomial]+γ[L] + γ²[R] + γ³[O] + γ⁴[S₁] +γ⁵[S₂] + ∑ᵢγ⁵⁺ⁱ[Pi_{i}] - /// * at state+state_folded_claimed_values we store: H(ζ) + γLinearised_polynomial(ζ)+γ²L(ζ) + γ³R(ζ)+ γ⁴O(ζ) + γ⁵S₁(ζ) +γ⁶S₂(ζ) + ∑ᵢγ⁶⁺ⁱPi_{i}(ζ) - /// @param aproof pointer to the proof - /// acc_gamma stores the γⁱ - function fold_state(aproof) { - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - let mPtr20 := add(mPtr, 0x20) - let mPtr40 := add(mPtr, 0x40) - - let l_gamma_kzg := mload(add(state, STATE_GAMMA_KZG)) - let acc_gamma := l_gamma_kzg - let state_folded_digests := add(state, STATE_FOLDED_DIGESTS_X) - - mstore(add(state, STATE_FOLDED_DIGESTS_X), mload(add(state, STATE_LINEARISED_POLYNOMIAL_X))) - mstore(add(state, STATE_FOLDED_DIGESTS_Y), mload(add(state, STATE_LINEARISED_POLYNOMIAL_Y))) - mstore(add(state, STATE_FOLDED_CLAIMED_VALUES), mload(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA))) - - point_acc_mul_calldata(add(state, STATE_FOLDED_DIGESTS_X), add(aproof, PROOF_L_COM_X), acc_gamma, mPtr) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_L_AT_ZETA), acc_gamma) - - acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) - point_acc_mul_calldata(state_folded_digests, add(aproof, PROOF_R_COM_X), acc_gamma, mPtr) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_R_AT_ZETA), acc_gamma) - - acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) - point_acc_mul_calldata(state_folded_digests, add(aproof, PROOF_O_COM_X), acc_gamma, mPtr) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_O_AT_ZETA), acc_gamma) - - acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) - mstore(mPtr, VK_S1_COM_X) - mstore(mPtr20, VK_S1_COM_Y) - point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_S1_AT_ZETA), acc_gamma) - - acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) - mstore(mPtr, VK_S2_COM_X) - mstore(mPtr20, VK_S2_COM_Y) - point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_S2_AT_ZETA), acc_gamma) - let poqaz := add(aproof, PROOF_OPENING_QCP_AT_ZETA) - - acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) - mstore(mPtr, VK_QCP_0_X) - mstore(mPtr20, VK_QCP_0_Y) - point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) - fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), poqaz, acc_gamma) - poqaz := add(poqaz, 0x20) - - } - - /// @notice generate the challenge (using Fiat Shamir) to fold the opening proofs - /// at ζ. - /// The process for deriving γ is the same as in derive_gamma but this time the inputs are - /// in this order (the [] means it's a commitment): - /// * ζ - /// * [Linearised polynomial] - /// * [L], [R], [O] - /// * [S₁] [S₂] - /// * [Pi_{i}] (wires associated to custom gates) - /// Then there are the purported evaluations of the previous committed polynomials: - /// * Linearised_polynomial(ζ) - /// * L(ζ), R(ζ), O(ζ), S₁(ζ), S₂(ζ) - /// * Pi_{i}(ζ) - /// * Z(ζω) - /// @param aproof pointer to the proof - function compute_gamma_kzg(aproof) { - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - mstore(mPtr, FS_GAMMA_KZG) // "gamma" - mstore(add(mPtr, 0x20), mload(add(state, STATE_ZETA))) - mstore(add(mPtr,0x40), mload(add(state, STATE_LINEARISED_POLYNOMIAL_X))) - mstore(add(mPtr,0x60), mload(add(state, STATE_LINEARISED_POLYNOMIAL_Y))) - calldatacopy(add(mPtr, 0x80), add(aproof, PROOF_L_COM_X), 0xc0) - mstore(add(mPtr,0x140), VK_S1_COM_X) - mstore(add(mPtr,0x160), VK_S1_COM_Y) - mstore(add(mPtr,0x180), VK_S2_COM_X) - mstore(add(mPtr,0x1a0), VK_S2_COM_Y) - - let offset := 0x1c0 - - mstore(add(mPtr,offset), VK_QCP_0_X) - mstore(add(mPtr,add(offset, 0x20)), VK_QCP_0_Y) - offset := add(offset, 0x40) - mstore(add(mPtr, offset), mload(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA))) - mstore(add(mPtr, add(offset, 0x20)), calldataload(add(aproof, PROOF_L_AT_ZETA))) - mstore(add(mPtr, add(offset, 0x40)), calldataload(add(aproof, PROOF_R_AT_ZETA))) - mstore(add(mPtr, add(offset, 0x60)), calldataload(add(aproof, PROOF_O_AT_ZETA))) - mstore(add(mPtr, add(offset, 0x80)), calldataload(add(aproof, PROOF_S1_AT_ZETA))) - mstore(add(mPtr, add(offset, 0xa0)), calldataload(add(aproof, PROOF_S2_AT_ZETA))) - - let _mPtr := add(mPtr, add(offset, 0xc0)) - - - let _poqaz := add(aproof, PROOF_OPENING_QCP_AT_ZETA) - calldatacopy(_mPtr, _poqaz, mul(VK_NB_CUSTOM_GATES, 0x20)) - _mPtr := add(_mPtr, mul(VK_NB_CUSTOM_GATES, 0x20)) - - - mstore(_mPtr, calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA))) - - let start_input := 0x1b // 00.."gamma" - let size_input := add(0x14, mul(VK_NB_CUSTOM_GATES,3)) // number of 32bytes elmts = 0x17 (zeta+3*6 for the digests+openings) + 3*VK_NB_CUSTOM_GATES (for the commitments of the selectors) + 1 (opening of Z at ζω) - size_input := add(0x5, mul(size_input, 0x20)) // size in bytes: 15*32 bytes + 5 bytes for gamma - let check_staticcall := staticcall(gas(), 0x2, add(mPtr,start_input), size_input, add(state, STATE_GAMMA_KZG), 0x20) - if iszero(check_staticcall) { - error_verify() - } - mstore(add(state, STATE_GAMMA_KZG), mod(mload(add(state, STATE_GAMMA_KZG)), R_MOD)) - } - - function compute_commitment_linearised_polynomial_ec(aproof, s1, s2) { - - let state := mload(0x40) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - - mstore(mPtr, VK_QL_COM_X) - mstore(add(mPtr, 0x20), VK_QL_COM_Y) - point_mul( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - mPtr, - calldataload(add(aproof, PROOF_L_AT_ZETA)), - add(mPtr, 0x40) - ) - - mstore(mPtr, VK_QR_COM_X) - mstore(add(mPtr, 0x20), VK_QR_COM_Y) - point_acc_mul( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - mPtr, - calldataload(add(aproof, PROOF_R_AT_ZETA)), - add(mPtr, 0x40) - ) - - let rl := mulmod(calldataload(add(aproof, PROOF_L_AT_ZETA)), calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) - mstore(mPtr, VK_QM_COM_X) - mstore(add(mPtr, 0x20), VK_QM_COM_Y) - point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, rl, add(mPtr, 0x40)) - - mstore(mPtr, VK_QO_COM_X) - mstore(add(mPtr, 0x20), VK_QO_COM_Y) - point_acc_mul( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - mPtr, - calldataload(add(aproof, PROOF_O_AT_ZETA)), - add(mPtr, 0x40) - ) - - mstore(mPtr, VK_QK_COM_X) - mstore(add(mPtr, 0x20), VK_QK_COM_Y) - point_add( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - add(state, STATE_LINEARISED_POLYNOMIAL_X), - mPtr, - add(mPtr, 0x40) - ) - - - let qcp_opening_at_zeta := add(aproof, PROOF_OPENING_QCP_AT_ZETA) - let bsb_commitments := add(aproof, PROOF_BSB_COMMITMENTS) - for { - let i := 0 - } lt(i, VK_NB_CUSTOM_GATES) { - i := add(i, 1) - } { - mstore(mPtr, calldataload(bsb_commitments)) - mstore(add(mPtr, 0x20), calldataload(add(bsb_commitments, 0x20))) - point_acc_mul( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - mPtr, - calldataload(qcp_opening_at_zeta), - add(mPtr, 0x40) - ) - qcp_opening_at_zeta := add(qcp_opening_at_zeta, 0x20) - bsb_commitments := add(bsb_commitments, 0x40) - } - - - mstore(mPtr, VK_S3_COM_X) - mstore(add(mPtr, 0x20), VK_S3_COM_Y) - point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, s1, add(mPtr, 0x40)) - - mstore(mPtr, calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X))) - mstore(add(mPtr, 0x20), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_Y))) - point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, s2, add(mPtr, 0x40)) - - point_add( - add(state, STATE_LINEARISED_POLYNOMIAL_X), - add(state, STATE_LINEARISED_POLYNOMIAL_X), - add(state, STATE_FOLDED_H_X), - mPtr) - } - - /// @notice Compute the commitment to the linearized polynomial equal to - /// L(ζ)[Qₗ]+r(ζ)[Qᵣ]+R(ζ)L(ζ)[Qₘ]+O(ζ)[Qₒ]+[Qₖ]+Σᵢqc'ᵢ(ζ)[BsbCommitmentᵢ] + - /// α*( Z(μζ)(L(ζ)+β*S₁(ζ)+γ)*(R(ζ)+β*S₂(ζ)+γ)[S₃]-[Z](L(ζ)+β*id_{1}(ζ)+γ)*(R(ζ)+β*id_{2}(ζ)+γ)*(O(ζ)+β*id_{3}(ζ)+γ) ) + - /// α²*L₁(ζ)[Z] - Z_{H}(ζ)*(([H₀] + ζᵐ⁺²*[H₁] + ζ²⁽ᵐ⁺²⁾*[H₂]) - /// where - /// * id_1 = id, id_2 = vk_coset_shift*id, id_3 = vk_coset_shift^{2}*id - /// * the [] means that it's a commitment (i.e. a point on Bn254(F_p)) - /// * Z_{H}(ζ) = ζ^n-1 - /// @param aproof pointer to the proof - function compute_commitment_linearised_polynomial(aproof) { - let state := mload(0x40) - let l_beta := mload(add(state, STATE_BETA)) - let l_gamma := mload(add(state, STATE_GAMMA)) - let l_zeta := mload(add(state, STATE_ZETA)) - let l_alpha := mload(add(state, STATE_ALPHA)) - - let u := mulmod(calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA)), l_beta, R_MOD) - let v := mulmod(l_beta, calldataload(add(aproof, PROOF_S1_AT_ZETA)), R_MOD) - v := addmod(v, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) - v := addmod(v, l_gamma, R_MOD) - - let w := mulmod(l_beta, calldataload(add(aproof, PROOF_S2_AT_ZETA)), R_MOD) - w := addmod(w, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) - w := addmod(w, l_gamma, R_MOD) - - let s1 := mulmod(u, v, R_MOD) - s1 := mulmod(s1, w, R_MOD) - s1 := mulmod(s1, l_alpha, R_MOD) - - let coset_square := mulmod(VK_COSET_SHIFT, VK_COSET_SHIFT, R_MOD) - let betazeta := mulmod(l_beta, l_zeta, R_MOD) - u := addmod(betazeta, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) - u := addmod(u, l_gamma, R_MOD) - - v := mulmod(betazeta, VK_COSET_SHIFT, R_MOD) - v := addmod(v, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) - v := addmod(v, l_gamma, R_MOD) - - w := mulmod(betazeta, coset_square, R_MOD) - w := addmod(w, calldataload(add(aproof, PROOF_O_AT_ZETA)), R_MOD) - w := addmod(w, l_gamma, R_MOD) - - let s2 := mulmod(u, v, R_MOD) - s2 := mulmod(s2, w, R_MOD) - s2 := sub(R_MOD, s2) - s2 := mulmod(s2, l_alpha, R_MOD) - s2 := addmod(s2, mload(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0)), R_MOD) - - // at this stage: - // * s₁ = α*Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β - // * s₂ = -α*(l(ζ)+β*ζ+γ)*(r(ζ)+β*u*ζ+γ)*(o(ζ)+β*u²*ζ+γ) + α²*L₁(ζ) - - compute_commitment_linearised_polynomial_ec(aproof, s1, s2) - } - - /// @notice compute -z_h(ζ)*([H₁] + ζᵐ⁺²[H₂] + ζ²⁽ᵐ⁺²⁾[H₃]) and store the result at - /// state + state_folded_h - /// @param aproof pointer to the proof - function fold_h(aproof) { - let state := mload(0x40) - let n_plus_two := add(VK_DOMAIN_SIZE, 2) - let mPtr := add(mload(0x40), STATE_LAST_MEM) - let zeta_power_n_plus_two := pow(mload(add(state, STATE_ZETA)), n_plus_two, mPtr) - point_mul_calldata(add(state, STATE_FOLDED_H_X), add(aproof, PROOF_H_2_X), zeta_power_n_plus_two, mPtr) - point_add_calldata(add(state, STATE_FOLDED_H_X), add(state, STATE_FOLDED_H_X), add(aproof, PROOF_H_1_X), mPtr) - point_mul(add(state, STATE_FOLDED_H_X), add(state, STATE_FOLDED_H_X), zeta_power_n_plus_two, mPtr) - point_add_calldata(add(state, STATE_FOLDED_H_X), add(state, STATE_FOLDED_H_X), add(aproof, PROOF_H_0_X), mPtr) - point_mul(add(state, STATE_FOLDED_H_X), add(state, STATE_FOLDED_H_X), mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)), mPtr) - let folded_h_y := mload(add(state, STATE_FOLDED_H_Y)) - folded_h_y := sub(P_MOD, folded_h_y) - mstore(add(state, STATE_FOLDED_H_Y), folded_h_y) - } - - /// @notice check that the opening of the linearised polynomial at zeta is equal to - /// - [ PI(ζ) - α²*L₁(ζ) + α(l(ζ)+β*s1(ζ)+γ)(r(ζ)+β*s2(ζ)+γ)(o(ζ)+γ)*z(ωζ) ] - /// @param aproof pointer to the proof - function verify_opening_linearised_polynomial(aproof) { - - let state := mload(0x40) - - // (l(ζ)+β*s1(ζ)+γ) - let s1 - s1 := mulmod(calldataload(add(aproof, PROOF_S1_AT_ZETA)), mload(add(state, STATE_BETA)), R_MOD) - s1 := addmod(s1, mload(add(state, STATE_GAMMA)), R_MOD) - s1 := addmod(s1, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) - - // (r(ζ)+β*s2(ζ)+γ) - let s2 - s2 := mulmod(calldataload(add(aproof, PROOF_S2_AT_ZETA)), mload(add(state, STATE_BETA)), R_MOD) - s2 := addmod(s2, mload(add(state, STATE_GAMMA)), R_MOD) - s2 := addmod(s2, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) - - // (o(ζ)+γ) - let o - o := addmod(calldataload(add(aproof, PROOF_O_AT_ZETA)), mload(add(state, STATE_GAMMA)), R_MOD) - - // α*Z(μζ)*(l(ζ)+β*s1(ζ)+γ)*(r(ζ)+β*s2(ζ)+γ)*(o(ζ)+γ) - s1 := mulmod(s1, s2, R_MOD) - s1 := mulmod(s1, o, R_MOD) - s1 := mulmod(s1, mload(add(state, STATE_ALPHA)), R_MOD) - s1 := mulmod(s1, calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA)), R_MOD) - - // PI(ζ) - α²*L₁(ζ) + α(l(ζ)+β*s1(ζ)+γ)(r(ζ)+β*s2(ζ)+γ)(o(ζ)+γ)*z(ωζ) - s1 := addmod(s1, mload(add(state, STATE_PI)), R_MOD) - s2 := mload(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0)) - s2 := sub(R_MOD, s2) - s1 := addmod(s1, s2, R_MOD) - s1 := sub(R_MOD, s1) - - mstore(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA), s1) - } - - // BEGINNING utils math functions ------------------------------------------------- - - /// @param dst pointer storing the result - /// @param p pointer to the first point - /// @param q pointer to the second point - /// @param mPtr pointer to free memory - function point_add(dst, p, q, mPtr) { - mstore(mPtr, mload(p)) - mstore(add(mPtr, 0x20), mload(add(p, 0x20))) - mstore(add(mPtr, 0x40), mload(q)) - mstore(add(mPtr, 0x60), mload(add(q, 0x20))) - let l_success := staticcall(gas(),EC_ADD,mPtr,0x80,dst,0x40) - if iszero(l_success) { - error_ec_op() - } - } - - /// @param dst pointer storing the result - /// @param p pointer to the first point (calldata) - /// @param q pointer to the second point (calladata) - /// @param mPtr pointer to free memory - function point_add_calldata(dst, p, q, mPtr) { - mstore(mPtr, mload(p)) - mstore(add(mPtr, 0x20), mload(add(p, 0x20))) - mstore(add(mPtr, 0x40), calldataload(q)) - mstore(add(mPtr, 0x60), calldataload(add(q, 0x20))) - let l_success := staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40) - if iszero(l_success) { - error_ec_op() - } - } - - /// @parma dst pointer storing the result - /// @param src pointer to a point on Bn254(𝔽_p) - /// @param s scalar - /// @param mPtr free memory - function point_mul(dst,src,s, mPtr) { - mstore(mPtr,mload(src)) - mstore(add(mPtr,0x20),mload(add(src,0x20))) - mstore(add(mPtr,0x40),s) - let l_success := staticcall(gas(),EC_MUL,mPtr,0x60,dst,0x40) - if iszero(l_success) { - error_ec_op() - } - } - - /// @parma dst pointer storing the result - /// @param src pointer to a point on Bn254(𝔽_p) on calldata - /// @param s scalar - /// @param mPtr free memory - function point_mul_calldata(dst, src, s, mPtr) { - mstore(mPtr, calldataload(src)) - mstore(add(mPtr, 0x20), calldataload(add(src, 0x20))) - mstore(add(mPtr, 0x40), s) - let l_success := staticcall(gas(), EC_MUL, mPtr, 0x60, dst, 0x40) - if iszero(l_success) { - error_ec_op() - } - } - - /// @notice dst <- dst + [s]src (Elliptic curve) - /// @param dst pointer accumulator point storing the result - /// @param src pointer to the point to multiply and add - /// @param s scalar - /// @param mPtr free memory - function point_acc_mul(dst,src,s, mPtr) { - mstore(mPtr,mload(src)) - mstore(add(mPtr,0x20),mload(add(src,0x20))) - mstore(add(mPtr,0x40),s) - let l_success := staticcall(gas(),7,mPtr,0x60,mPtr,0x40) - mstore(add(mPtr,0x40),mload(dst)) - mstore(add(mPtr,0x60),mload(add(dst,0x20))) - l_success := and(l_success, staticcall(gas(),EC_ADD,mPtr,0x80,dst, 0x40)) - if iszero(l_success) { - error_ec_op() - } - } - - /// @notice dst <- dst + [s]src (Elliptic curve) - /// @param dst pointer accumulator point storing the result - /// @param src pointer to the point to multiply and add (on calldata) - /// @param s scalar - /// @mPtr free memory - function point_acc_mul_calldata(dst, src, s, mPtr) { - let state := mload(0x40) - mstore(mPtr, calldataload(src)) - mstore(add(mPtr, 0x20), calldataload(add(src, 0x20))) - mstore(add(mPtr, 0x40), s) - let l_success := staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) - mstore(add(mPtr, 0x40), mload(dst)) - mstore(add(mPtr, 0x60), mload(add(dst, 0x20))) - l_success := and(l_success, staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40)) - if iszero(l_success) { - error_ec_op() - } - } - - /// @notice dst <- dst + src*s (Fr) dst,src are addresses, s is a value - /// @param dst pointer storing the result - /// @param src pointer to the scalar to multiply and add (on calldata) - /// @param s scalar - function fr_acc_mul_calldata(dst, src, s) { - let tmp := mulmod(calldataload(src), s, R_MOD) - mstore(dst, addmod(mload(dst), tmp, R_MOD)) - } - - /// @param x element to exponentiate - /// @param e exponent - /// @param mPtr free memory - /// @return res x ** e mod r - function pow(x, e, mPtr)->res { - mstore(mPtr, 0x20) - mstore(add(mPtr, 0x20), 0x20) - mstore(add(mPtr, 0x40), 0x20) - mstore(add(mPtr, 0x60), x) - mstore(add(mPtr, 0x80), e) - mstore(add(mPtr, 0xa0), R_MOD) - let check_staticcall := staticcall(gas(),MOD_EXP,mPtr,0xc0,mPtr,0x20) - if eq(check_staticcall, 0) { - + uint256 private constant R_MOD = + 21888242871839275222246405745257275088548364400416034343698204186575808495617; + uint256 private constant R_MOD_MINUS_ONE = + 21888242871839275222246405745257275088548364400416034343698204186575808495616; + uint256 private constant P_MOD = + 21888242871839275222246405745257275088696311157297823662689037894645226208583; + + uint256 private constant G2_SRS_0_X_0 = + 11559732032986387107991004021392285783925812861821192530917403151452391805634; + uint256 private constant G2_SRS_0_X_1 = + 10857046999023057135944570762232829481370756359578518086990519993285655852781; + uint256 private constant G2_SRS_0_Y_0 = + 4082367875863433681332203403145435568316851327593401208105741076214120093531; + uint256 private constant G2_SRS_0_Y_1 = + 8495653923123431417604973247489272438418190587263600148770280649306958101930; + + uint256 private constant G2_SRS_1_X_0 = + 15805639136721018565402881920352193254830339253282065586954346329754995870280; + uint256 private constant G2_SRS_1_X_1 = + 19089565590083334368588890253123139704298730990782503769911324779715431555531; + uint256 private constant G2_SRS_1_Y_0 = + 9779648407879205346559610309258181044130619080926897934572699915909528404984; + uint256 private constant G2_SRS_1_Y_1 = + 6779728121489434657638426458390319301070371227460768374343986326751507916979; + + uint256 private constant G1_SRS_X = + 14312776538779914388377568895031746459131577658076416373430523308756343304251; + uint256 private constant G1_SRS_Y = + 11763105256161367503191792604679297387056316997144156930871823008787082098465; + + // ----------------------- vk --------------------- + uint256 private constant VK_NB_PUBLIC_INPUTS = 2; + uint256 private constant VK_DOMAIN_SIZE = 16777216; + uint256 private constant VK_INV_DOMAIN_SIZE = + 21888241567198334088790460357988866238279339518792980768180410072331574733841; + uint256 private constant VK_OMEGA = + 5709868443893258075976348696661355716898495876243883251619397131511003808859; + uint256 private constant VK_QL_COM_X = + 3290060728869345335154114718977447053330166483334167631366198142610428232620; + uint256 private constant VK_QL_COM_Y = + 19162119719409246272115813094185025995857052458470900198554531144420657384429; + uint256 private constant VK_QR_COM_X = + 20593285675028444864919533759061889592214551177771462207774701990433512561961; + uint256 private constant VK_QR_COM_Y = + 2037190768409221720866644069987363251819987312430306430360685249062434970888; + uint256 private constant VK_QM_COM_X = + 3243698466425196128341517132303061662197275421453284874501006751806324568406; + uint256 private constant VK_QM_COM_Y = + 1522093955203686116281629526048034563543666750312611984631281801989604375093; + uint256 private constant VK_QO_COM_X = + 18116824637133877774109916770339012329893346672063455581152619443461705941258; + uint256 private constant VK_QO_COM_Y = + 12065546623891456568116583509565259597148533132778310848302637027619241642160; + uint256 private constant VK_QK_COM_X = + 13141440805370550747455201471324318730010929401231584161046984899369324303111; + uint256 private constant VK_QK_COM_Y = + 12213720583880706739223964024508346683319146975553789702175775841006924916084; + + uint256 private constant VK_S1_COM_X = + 12793975975635479749073429864966625606798501224471844064009199522695564922740; + uint256 private constant VK_S1_COM_Y = + 8132923293671412095334718058521033016410241972572274691532700944443498103422; + + uint256 private constant VK_S2_COM_X = + 21657378963874914616650592302460330003572962134736577570012568301070663363623; + uint256 private constant VK_S2_COM_Y = + 1718513843029691644222560949246389014329795284083891303459043520417235854191; + + uint256 private constant VK_S3_COM_X = + 20415325187354694665500244845769422238048526183908185443188703734475579190071; + uint256 private constant VK_S3_COM_Y = + 18073955099179029460825044425464668031894304571793555401967621518843518905026; + + uint256 private constant VK_COSET_SHIFT = 5; + + uint256 private constant VK_QCP_0_X = + 12741358679119216268442671261008764468184354452248089481320165441775601729818; + uint256 private constant VK_QCP_0_Y = + 9936318890363003735758197368031202024870521212376882419342977488108314073196; + + uint256 private constant VK_INDEX_COMMIT_API_0 = 10703054; + uint256 private constant VK_NB_CUSTOM_GATES = 1; + + // ------------------------------------------------ + + // offset proof + + uint256 private constant PROOF_L_COM_X = 0x0; + uint256 private constant PROOF_L_COM_Y = 0x20; + uint256 private constant PROOF_R_COM_X = 0x40; + uint256 private constant PROOF_R_COM_Y = 0x60; + uint256 private constant PROOF_O_COM_X = 0x80; + uint256 private constant PROOF_O_COM_Y = 0xa0; + + // h = h_0 + x^{n+2}h_1 + x^{2(n+2)}h_2 + uint256 private constant PROOF_H_0_X = 0xc0; + uint256 private constant PROOF_H_0_Y = 0xe0; + uint256 private constant PROOF_H_1_X = 0x100; + uint256 private constant PROOF_H_1_Y = 0x120; + uint256 private constant PROOF_H_2_X = 0x140; + uint256 private constant PROOF_H_2_Y = 0x160; + + // wire values at zeta + uint256 private constant PROOF_L_AT_ZETA = 0x180; + uint256 private constant PROOF_R_AT_ZETA = 0x1a0; + uint256 private constant PROOF_O_AT_ZETA = 0x1c0; + + // S1(zeta),S2(zeta) + uint256 private constant PROOF_S1_AT_ZETA = 0x1e0; // Sσ1(zeta) + uint256 private constant PROOF_S2_AT_ZETA = 0x200; // Sσ2(zeta) + + // [Z] + uint256 private constant PROOF_GRAND_PRODUCT_COMMITMENT_X = 0x220; + uint256 private constant PROOF_GRAND_PRODUCT_COMMITMENT_Y = 0x240; + + uint256 private constant PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA = 0x260; // z(w*zeta) + + // Folded proof for the opening of linearised poly, l, r, o, s_1, s_2, qcp + uint256 private constant PROOF_BATCH_OPENING_AT_ZETA_X = 0x280; + uint256 private constant PROOF_BATCH_OPENING_AT_ZETA_Y = 0x2a0; + + uint256 private constant PROOF_OPENING_AT_ZETA_OMEGA_X = 0x2c0; + uint256 private constant PROOF_OPENING_AT_ZETA_OMEGA_Y = 0x2e0; + + uint256 private constant PROOF_OPENING_QCP_AT_ZETA = 0x300; + uint256 private constant PROOF_BSB_COMMITMENTS = 0x320; + + // -> next part of proof is + // [ openings_selector_commits || commitments_wires_commit_api] + + // -------- offset state + + // challenges to check the claimed quotient + + uint256 private constant STATE_ALPHA = 0x0; + uint256 private constant STATE_BETA = 0x20; + uint256 private constant STATE_GAMMA = 0x40; + uint256 private constant STATE_ZETA = 0x60; + uint256 private constant STATE_ALPHA_SQUARE_LAGRANGE_0 = 0x80; + uint256 private constant STATE_FOLDED_H_X = 0xa0; + uint256 private constant STATE_FOLDED_H_Y = 0xc0; + uint256 private constant STATE_LINEARISED_POLYNOMIAL_X = 0xe0; + uint256 private constant STATE_LINEARISED_POLYNOMIAL_Y = 0x100; + uint256 private constant STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA = 0x120; + uint256 private constant STATE_FOLDED_CLAIMED_VALUES = 0x140; // Folded proof for the opening of H, linearised poly, l, r, o, s_1, s_2, qcp + uint256 private constant STATE_FOLDED_DIGESTS_X = 0x160; // folded digests of H, linearised poly, l, r, o, s_1, s_2, qcp + uint256 private constant STATE_FOLDED_DIGESTS_Y = 0x180; + uint256 private constant STATE_PI = 0x1a0; + uint256 private constant STATE_ZETA_POWER_N_MINUS_ONE = 0x1c0; + uint256 private constant STATE_GAMMA_KZG = 0x1e0; + uint256 private constant STATE_SUCCESS = 0x200; + uint256 private constant STATE_CHECK_VAR = 0x220; // /!\ this slot is used for debugging only + uint256 private constant STATE_LAST_MEM = 0x240; + + // -------- utils (for Fiat Shamir) + uint256 private constant FS_ALPHA = 0x616C706861; // "alpha" + uint256 private constant FS_BETA = 0x62657461; // "beta" + uint256 private constant FS_GAMMA = 0x67616d6d61; // "gamma" + uint256 private constant FS_ZETA = 0x7a657461; // "zeta" + uint256 private constant FS_GAMMA_KZG = 0x67616d6d61; // "gamma" + + // -------- errors + uint256 private constant ERROR_STRING_ID = + 0x08c379a000000000000000000000000000000000000000000000000000000000; // selector for function Error(string) + + // -------- utils (for hash_fr) + uint256 private constant HASH_FR_BB = 340282366920938463463374607431768211456; // 2**128 + uint256 private constant HASH_FR_ZERO_UINT256 = 0; + uint8 private constant HASH_FR_LEN_IN_BYTES = 48; + uint8 private constant HASH_FR_SIZE_DOMAIN = 11; + uint8 private constant HASH_FR_ONE = 1; + uint8 private constant HASH_FR_TWO = 2; + + // -------- precompiles + uint8 private constant MOD_EXP = 0x5; + uint8 private constant EC_ADD = 0x6; + uint8 private constant EC_MUL = 0x7; + uint8 private constant EC_PAIR = 0x8; + + /// Verify a Plonk proof. + /// Reverts if the proof or the public inputs are malformed. + /// @param proof serialised plonk proof (using gnark's MarshalSolidity) + /// @param public_inputs (must be reduced) + /// @return success true if the proof passes false otherwise + function Verify(bytes calldata proof, uint256[] calldata public_inputs) + public + view + returns (bool success) + { + assembly { + let mem := mload(0x40) + let freeMem := add(mem, STATE_LAST_MEM) + + // sanity checks + check_number_of_public_inputs(public_inputs.length) + check_inputs_size(public_inputs.length, public_inputs.offset) + check_proof_size(proof.length) + check_proof_openings_size(proof.offset) + + // compute the challenges + let prev_challenge_non_reduced + prev_challenge_non_reduced := + derive_gamma(proof.offset, public_inputs.length, public_inputs.offset) + prev_challenge_non_reduced := derive_beta(prev_challenge_non_reduced) + prev_challenge_non_reduced := derive_alpha(proof.offset, prev_challenge_non_reduced) + derive_zeta(proof.offset, prev_challenge_non_reduced) + + // evaluation of Z=Xⁿ-1 at ζ, we save this value + let zeta := mload(add(mem, STATE_ZETA)) + let zeta_power_n_minus_one := + addmod(pow(zeta, VK_DOMAIN_SIZE, freeMem), sub(R_MOD, 1), R_MOD) + mstore(add(mem, STATE_ZETA_POWER_N_MINUS_ONE), zeta_power_n_minus_one) + + // public inputs contribution + let l_pi := sum_pi_wo_api_commit(public_inputs.offset, public_inputs.length, freeMem) + let l_pi_commit := sum_pi_commit(proof.offset, public_inputs.length, freeMem) + l_pi := addmod(l_pi_commit, l_pi, R_MOD) + mstore(add(mem, STATE_PI), l_pi) + + compute_alpha_square_lagrange_0() + verify_opening_linearised_polynomial(proof.offset) + fold_h(proof.offset) + compute_commitment_linearised_polynomial(proof.offset) + compute_gamma_kzg(proof.offset) + fold_state(proof.offset) + batch_verify_multi_points(proof.offset) + + success := mload(add(mem, STATE_SUCCESS)) + + // Beginning errors ------------------------------------------------- + + function error_nb_public_inputs() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x1d) + mstore(add(ptError, 0x44), "wrong number of public inputs") + revert(ptError, 0x64) + } + + /// Called when an operation on Bn254 fails + /// @dev for instance when calling EcMul on a point not on Bn254. + function error_ec_op() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x12) + mstore(add(ptError, 0x44), "error ec operation") + revert(ptError, 0x64) + } + + /// Called when one of the public inputs is not reduced. + function error_inputs_size() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x18) + mstore(add(ptError, 0x44), "inputs are bigger than r") + revert(ptError, 0x64) + } + + /// Called when the size proof is not as expected + /// @dev to avoid overflow attack for instance + function error_proof_size() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x10) + mstore(add(ptError, 0x44), "wrong proof size") + revert(ptError, 0x64) + } + + /// Called when one the openings is bigger than r + /// The openings are the claimed evalutions of a polynomial + /// in a Kzg proof. + function error_proof_openings_size() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x16) + mstore(add(ptError, 0x44), "openings bigger than r") + revert(ptError, 0x64) + } + + function error_pairing() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0xd) + mstore(add(ptError, 0x44), "error pairing") + revert(ptError, 0x64) + } + + function error_verify() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0xc) + mstore(add(ptError, 0x44), "error verify") + revert(ptError, 0x64) + } + + function error_random_generation() { + let ptError := mload(0x40) + mstore(ptError, ERROR_STRING_ID) // selector for function Error(string) + mstore(add(ptError, 0x4), 0x20) + mstore(add(ptError, 0x24), 0x14) + mstore(add(ptError, 0x44), "error random gen kzg") + revert(ptError, 0x64) + } + // end errors ------------------------------------------------- + + // Beginning checks ------------------------------------------------- + + /// @param s actual number of public inputs + function check_number_of_public_inputs(s) { + if iszero(eq(s, VK_NB_PUBLIC_INPUTS)) { error_nb_public_inputs() } + } + + /// Checks that the public inputs are < R_MOD. + /// @param s number of public inputs + /// @param p pointer to the public inputs array + function check_inputs_size(s, p) { + for { let i } lt(i, s) { i := add(i, 1) } { + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_inputs_size() } + p := add(p, 0x20) + } + } + + /// Checks if the proof is of the correct size + /// @param actual_proof_size size of the proof (not the expected size) + function check_proof_size(actual_proof_size) { + let expected_proof_size := add(0x300, mul(VK_NB_CUSTOM_GATES, 0x60)) + if iszero(eq(actual_proof_size, expected_proof_size)) { error_proof_size() } + } + + /// Checks if the multiple openings of the polynomials are < R_MOD. + /// @param aproof pointer to the beginning of the proof + /// @dev the 'a' prepending proof is to have a local name + function check_proof_openings_size(aproof) { + // PROOF_L_AT_ZETA + let p := add(aproof, PROOF_L_AT_ZETA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_R_AT_ZETA + p := add(aproof, PROOF_R_AT_ZETA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_O_AT_ZETA + p := add(aproof, PROOF_O_AT_ZETA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_S1_AT_ZETA + p := add(aproof, PROOF_S1_AT_ZETA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_S2_AT_ZETA + p := add(aproof, PROOF_S2_AT_ZETA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA + p := add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA) + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + + // PROOF_OPENING_QCP_AT_ZETA + + p := add(aproof, PROOF_OPENING_QCP_AT_ZETA) + for { let i := 0 } lt(i, VK_NB_CUSTOM_GATES) { i := add(i, 1) } { + if gt(calldataload(p), R_MOD_MINUS_ONE) { error_proof_openings_size() } + p := add(p, 0x20) + } + } + // end checks ------------------------------------------------- + + // Beginning challenges ------------------------------------------------- + + /// Derive gamma as Sha256() + /// @param aproof pointer to the proof + /// @param nb_pi number of public inputs + /// @param pi pointer to the array of public inputs + /// @return the challenge gamma, not reduced + /// @notice The transcript is the concatenation (in this order) of: + /// * the word "gamma" in ascii, equal to [0x67,0x61,0x6d, 0x6d, 0x61] and encoded as a uint256. + /// * the commitments to the permutation polynomials S1, S2, S3, where we concatenate the coordinates of those points + /// * the commitments of Ql, Qr, Qm, Qo, Qk + /// * the public inputs + /// * the commitments of the wires related to the custom gates (commitments_wires_commit_api) + /// * commitments to L, R, O (proof__com_) + /// The data described above is written starting at mPtr. "gamma" lies on 5 bytes, + /// and is encoded as a uint256 number n. In basis b = 256, the number looks like this + /// [0 0 0 .. 0x67 0x61 0x6d, 0x6d, 0x61]. The first non zero entry is at position 27=0x1b + /// Gamma reduced (the actual challenge) is stored at add(state, state_gamma) + function derive_gamma(aproof, nb_pi, pi) -> gamma_not_reduced { + let state := mload(0x40) + let mPtr := add(state, STATE_LAST_MEM) + + // gamma + // gamma in ascii is [0x67,0x61,0x6d, 0x6d, 0x61] + // (same for alpha, beta, zeta) + mstore(mPtr, FS_GAMMA) // "gamma" + + mstore(add(mPtr, 0x20), VK_S1_COM_X) + mstore(add(mPtr, 0x40), VK_S1_COM_Y) + mstore(add(mPtr, 0x60), VK_S2_COM_X) + mstore(add(mPtr, 0x80), VK_S2_COM_Y) + mstore(add(mPtr, 0xa0), VK_S3_COM_X) + mstore(add(mPtr, 0xc0), VK_S3_COM_Y) + mstore(add(mPtr, 0xe0), VK_QL_COM_X) + mstore(add(mPtr, 0x100), VK_QL_COM_Y) + mstore(add(mPtr, 0x120), VK_QR_COM_X) + mstore(add(mPtr, 0x140), VK_QR_COM_Y) + mstore(add(mPtr, 0x160), VK_QM_COM_X) + mstore(add(mPtr, 0x180), VK_QM_COM_Y) + mstore(add(mPtr, 0x1a0), VK_QO_COM_X) + mstore(add(mPtr, 0x1c0), VK_QO_COM_Y) + mstore(add(mPtr, 0x1e0), VK_QK_COM_X) + mstore(add(mPtr, 0x200), VK_QK_COM_Y) + + mstore(add(mPtr, 0x220), VK_QCP_0_X) + mstore(add(mPtr, 0x240), VK_QCP_0_Y) + + // public inputs + let _mPtr := add(mPtr, 0x260) + let size_pi_in_bytes := mul(nb_pi, 0x20) + calldatacopy(_mPtr, pi, size_pi_in_bytes) + _mPtr := add(_mPtr, size_pi_in_bytes) + + // commitments to l, r, o + let size_commitments_lro_in_bytes := 0xc0 + calldatacopy(_mPtr, aproof, size_commitments_lro_in_bytes) + _mPtr := add(_mPtr, size_commitments_lro_in_bytes) + + // total size is : + // sizegamma(=0x5) + 11*64(=0x2c0) + // + nb_public_inputs*0x20 + // + nb_custom gates*0x40 + let size := add(0x2c5, size_pi_in_bytes) + + size := add(size, mul(VK_NB_CUSTOM_GATES, 0x40)) + let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1b), size, mPtr, 0x20) //0x1b -> 000.."gamma" + if iszero(l_success) { error_verify() } + gamma_not_reduced := mload(mPtr) + mstore(add(state, STATE_GAMMA), mod(gamma_not_reduced, R_MOD)) + } + + /// derive beta as Sha256 + /// @param gamma_not_reduced the previous challenge (gamma) not reduced + /// @return beta_not_reduced the next challenge, beta, not reduced + /// @notice the transcript consists of the previous challenge only. + /// The reduced version of beta is stored at add(state, state_beta) + function derive_beta(gamma_not_reduced) -> beta_not_reduced { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + + // beta + mstore(mPtr, FS_BETA) // "beta" + mstore(add(mPtr, 0x20), gamma_not_reduced) + let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1c), 0x24, mPtr, 0x20) //0x1b -> 000.."gamma" + if iszero(l_success) { error_verify() } + beta_not_reduced := mload(mPtr) + mstore(add(state, STATE_BETA), mod(beta_not_reduced, R_MOD)) + } + + /// derive alpha as sha256 + /// @param aproof pointer to the proof object + /// @param beta_not_reduced the previous challenge (beta) not reduced + /// @return alpha_not_reduced the next challenge, alpha, not reduced + /// @notice the transcript consists of the previous challenge (beta) + /// not reduced, the commitments to the wires associated to the QCP_i, + /// and the commitment to the grand product polynomial + function derive_alpha(aproof, beta_not_reduced) -> alpha_not_reduced { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + let full_size := 0x65 // size("alpha") + 0x20 (previous challenge) + + // alpha + mstore(mPtr, FS_ALPHA) // "alpha" + let _mPtr := add(mPtr, 0x20) + mstore(_mPtr, beta_not_reduced) + _mPtr := add(_mPtr, 0x20) + + // Bsb22Commitments + let proof_bsb_commitments := add(aproof, PROOF_BSB_COMMITMENTS) + let size_bsb_commitments := mul(0x40, VK_NB_CUSTOM_GATES) + calldatacopy(_mPtr, proof_bsb_commitments, size_bsb_commitments) + _mPtr := add(_mPtr, size_bsb_commitments) + full_size := add(full_size, size_bsb_commitments) + + // [Z], the commitment to the grand product polynomial + calldatacopy(_mPtr, add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X), 0x40) + let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1b), full_size, mPtr, 0x20) + if iszero(l_success) { error_verify() } + + alpha_not_reduced := mload(mPtr) + mstore(add(state, STATE_ALPHA), mod(alpha_not_reduced, R_MOD)) + } + + /// derive zeta as sha256 + /// @param aproof pointer to the proof object + /// @param alpha_not_reduced the previous challenge (alpha) not reduced + /// The transcript consists of the previous challenge and the commitment to + /// the quotient polynomial h. + function derive_zeta(aproof, alpha_not_reduced) { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + + // zeta + mstore(mPtr, FS_ZETA) // "zeta" + mstore(add(mPtr, 0x20), alpha_not_reduced) + calldatacopy(add(mPtr, 0x40), add(aproof, PROOF_H_0_X), 0xc0) + let l_success := staticcall(gas(), 0x2, add(mPtr, 0x1c), 0xe4, mPtr, 0x20) + if iszero(l_success) { error_verify() } + let zeta_not_reduced := mload(mPtr) + mstore(add(state, STATE_ZETA), mod(zeta_not_reduced, R_MOD)) + } + // END challenges ------------------------------------------------- + + // BEGINNING compute_pi ------------------------------------------------- + + /// sum_pi_wo_api_commit computes the public inputs contributions, + /// except for the public inputs coming from the custom gate + /// @param ins pointer to the public inputs + /// @param n number of public inputs + /// @param mPtr free memory + /// @return pi_wo_commit public inputs contribution (except the public inputs coming from the custom gate) + function sum_pi_wo_api_commit(ins, n, mPtr) -> pi_wo_commit { + let state := mload(0x40) + let z := mload(add(state, STATE_ZETA)) + let zpnmo := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) + + let li := mPtr + batch_compute_lagranges_at_z(z, zpnmo, n, li) + + let tmp := 0 + for { let i := 0 } lt(i, n) { i := add(i, 1) } { + tmp := mulmod(mload(li), calldataload(ins), R_MOD) + pi_wo_commit := addmod(pi_wo_commit, tmp, R_MOD) + li := add(li, 0x20) + ins := add(ins, 0x20) + } + } + + /// batch_compute_lagranges_at_z computes [L_0(z), .., L_{n-1}(z)] + /// @param z point at which the Lagranges are evaluated + /// @param zpnmo ζⁿ-1 + /// @param n number of public inputs (number of Lagranges to compute) + /// @param mPtr pointer to which the results are stored + function batch_compute_lagranges_at_z(z, zpnmo, n, mPtr) { + let zn := mulmod(zpnmo, VK_INV_DOMAIN_SIZE, R_MOD) // 1/n * (ζⁿ - 1) + + let _w := 1 + let _mPtr := mPtr + for { let i := 0 } lt(i, n) { i := add(i, 1) } { + mstore(_mPtr, addmod(z, sub(R_MOD, _w), R_MOD)) + _w := mulmod(_w, VK_OMEGA, R_MOD) + _mPtr := add(_mPtr, 0x20) + } + batch_invert(mPtr, n, _mPtr) + _mPtr := mPtr + _w := 1 + for { let i := 0 } lt(i, n) { i := add(i, 1) } { + mstore(_mPtr, mulmod(mulmod(mload(_mPtr), zn, R_MOD), _w, R_MOD)) + _mPtr := add(_mPtr, 0x20) + _w := mulmod(_w, VK_OMEGA, R_MOD) + } + } + + /// @notice Montgomery trick for batch inversion mod R_MOD + /// @param ins pointer to the data to batch invert + /// @param number of elements to batch invert + /// @param mPtr free memory + function batch_invert(ins, nb_ins, mPtr) { + mstore(mPtr, 1) + let offset := 0 + for { let i := 0 } lt(i, nb_ins) { i := add(i, 1) } { + let prev := mload(add(mPtr, offset)) + let cur := mload(add(ins, offset)) + cur := mulmod(prev, cur, R_MOD) + offset := add(offset, 0x20) + mstore(add(mPtr, offset), cur) + } + ins := add(ins, sub(offset, 0x20)) + mPtr := add(mPtr, offset) + let inv := pow(mload(mPtr), sub(R_MOD, 2), add(mPtr, 0x20)) + for { let i := 0 } lt(i, nb_ins) { i := add(i, 1) } { + mPtr := sub(mPtr, 0x20) + let tmp := mload(ins) + let cur := mulmod(inv, mload(mPtr), R_MOD) + mstore(ins, cur) + inv := mulmod(inv, tmp, R_MOD) + ins := sub(ins, 0x20) + } + } + + /// Public inputs (the ones coming from the custom gate) contribution + /// @param aproof pointer to the proof + /// @param nb_public_inputs number of public inputs + /// @param mPtr pointer to free memory + /// @return pi_commit custom gate public inputs contribution + function sum_pi_commit(aproof, nb_public_inputs, mPtr) -> pi_commit { + let state := mload(0x40) + let z := mload(add(state, STATE_ZETA)) + let zpnmo := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) + + let p := add(aproof, PROOF_BSB_COMMITMENTS) + + let h_fr, ith_lagrange + + h_fr := hash_fr(calldataload(p), calldataload(add(p, 0x20)), mPtr) + ith_lagrange := + compute_ith_lagrange_at_z( + z, zpnmo, add(nb_public_inputs, VK_INDEX_COMMIT_API_0), mPtr + ) + pi_commit := addmod(pi_commit, mulmod(h_fr, ith_lagrange, R_MOD), R_MOD) + p := add(p, 0x40) + } + + /// Computes L_i(zeta) = ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) where: + /// @param z zeta + /// @param zpmno ζⁿ-1 + /// @param i i-th lagrange + /// @param mPtr free memory + /// @return res = ωⁱ/n * (ζⁿ-1)/(ζ-ωⁱ) + function compute_ith_lagrange_at_z(z, zpnmo, i, mPtr) -> res { + let w := pow(VK_OMEGA, i, mPtr) // w**i + i := addmod(z, sub(R_MOD, w), R_MOD) // z-w**i + w := mulmod(w, VK_INV_DOMAIN_SIZE, R_MOD) // w**i/n + i := pow(i, sub(R_MOD, 2), mPtr) // (z-w**i)**-1 + w := mulmod(w, i, R_MOD) // w**i/n*(z-w)**-1 + res := mulmod(w, zpnmo, R_MOD) + } + + /// @dev https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2 + /// @param x x coordinate of a point on Bn254(𝔽_p) + /// @param y y coordinate of a point on Bn254(𝔽_p) + /// @param mPtr free memory + /// @return res an element mod R_MOD + function hash_fr(x, y, mPtr) -> res { + // [0x00, .. , 0x00 || x, y, || 0, 48, 0, dst, HASH_FR_SIZE_DOMAIN] + // <- 64 bytes -> <-64b -> <- 1 bytes each -> + + // [0x00, .., 0x00] 64 bytes of zero + mstore(mPtr, HASH_FR_ZERO_UINT256) + mstore(add(mPtr, 0x20), HASH_FR_ZERO_UINT256) + + // msg = x || y , both on 32 bytes + mstore(add(mPtr, 0x40), x) + mstore(add(mPtr, 0x60), y) + + // 0 || 48 || 0 all on 1 byte + mstore8(add(mPtr, 0x80), 0) + mstore8(add(mPtr, 0x81), HASH_FR_LEN_IN_BYTES) + mstore8(add(mPtr, 0x82), 0) + + // "BSB22-Plonk" = [42, 53, 42, 32, 32, 2d, 50, 6c, 6f, 6e, 6b,] + mstore8(add(mPtr, 0x83), 0x42) + mstore8(add(mPtr, 0x84), 0x53) + mstore8(add(mPtr, 0x85), 0x42) + mstore8(add(mPtr, 0x86), 0x32) + mstore8(add(mPtr, 0x87), 0x32) + mstore8(add(mPtr, 0x88), 0x2d) + mstore8(add(mPtr, 0x89), 0x50) + mstore8(add(mPtr, 0x8a), 0x6c) + mstore8(add(mPtr, 0x8b), 0x6f) + mstore8(add(mPtr, 0x8c), 0x6e) + mstore8(add(mPtr, 0x8d), 0x6b) + + // size domain + mstore8(add(mPtr, 0x8e), HASH_FR_SIZE_DOMAIN) + + let l_success := staticcall(gas(), 0x2, mPtr, 0x8f, mPtr, 0x20) + if iszero(l_success) { error_verify() } + + let b0 := mload(mPtr) + + // [b0 || one || dst || HASH_FR_SIZE_DOMAIN] + // <-64bytes -> <- 1 byte each -> + mstore8(add(mPtr, 0x20), HASH_FR_ONE) // 1 + + mstore8(add(mPtr, 0x21), 0x42) // dst + mstore8(add(mPtr, 0x22), 0x53) + mstore8(add(mPtr, 0x23), 0x42) + mstore8(add(mPtr, 0x24), 0x32) + mstore8(add(mPtr, 0x25), 0x32) + mstore8(add(mPtr, 0x26), 0x2d) + mstore8(add(mPtr, 0x27), 0x50) + mstore8(add(mPtr, 0x28), 0x6c) + mstore8(add(mPtr, 0x29), 0x6f) + mstore8(add(mPtr, 0x2a), 0x6e) + mstore8(add(mPtr, 0x2b), 0x6b) + + mstore8(add(mPtr, 0x2c), HASH_FR_SIZE_DOMAIN) // size domain + l_success := staticcall(gas(), 0x2, mPtr, 0x2d, mPtr, 0x20) + if iszero(l_success) { error_verify() } + + // b1 is located at mPtr. We store b2 at add(mPtr, 0x20) + + // [b0^b1 || two || dst || HASH_FR_SIZE_DOMAIN] + // <-64bytes -> <- 1 byte each -> + mstore(add(mPtr, 0x20), xor(mload(mPtr), b0)) + mstore8(add(mPtr, 0x40), HASH_FR_TWO) + + mstore8(add(mPtr, 0x41), 0x42) // dst + mstore8(add(mPtr, 0x42), 0x53) + mstore8(add(mPtr, 0x43), 0x42) + mstore8(add(mPtr, 0x44), 0x32) + mstore8(add(mPtr, 0x45), 0x32) + mstore8(add(mPtr, 0x46), 0x2d) + mstore8(add(mPtr, 0x47), 0x50) + mstore8(add(mPtr, 0x48), 0x6c) + mstore8(add(mPtr, 0x49), 0x6f) + mstore8(add(mPtr, 0x4a), 0x6e) + mstore8(add(mPtr, 0x4b), 0x6b) + + mstore8(add(mPtr, 0x4c), HASH_FR_SIZE_DOMAIN) // size domain + + let offset := add(mPtr, 0x20) + l_success := staticcall(gas(), 0x2, offset, 0x2d, offset, 0x20) + if iszero(l_success) { error_verify() } + + // at this point we have mPtr = [ b1 || b2] where b1 is on 32byes and b2 in 16bytes. + // we interpret it as a big integer mod r in big endian (similar to regular decimal notation) + // the result is then 2**(8*16)*mPtr[32:] + mPtr[32:48] + res := mulmod(mload(mPtr), HASH_FR_BB, R_MOD) // <- res = 2**128 * mPtr[:32] + let b1 := shr(128, mload(add(mPtr, 0x20))) // b1 <- [0, 0, .., 0 || b2[:16] ] + res := addmod(res, b1, R_MOD) + } + + // END compute_pi ------------------------------------------------- + + /// @notice compute α² * 1/n * (ζ{n}-1)/(ζ - 1) where + /// * α = challenge derived in derive_gamma_beta_alpha_zeta + /// * n = vk_domain_size + /// * ω = vk_omega (generator of the multiplicative cyclic group of order n in (ℤ/rℤ)*) + /// * ζ = zeta (challenge derived with Fiat Shamir) + function compute_alpha_square_lagrange_0() { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + + let res := mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)) + let den := addmod(mload(add(state, STATE_ZETA)), sub(R_MOD, 1), R_MOD) + den := pow(den, sub(R_MOD, 2), mPtr) + den := mulmod(den, VK_INV_DOMAIN_SIZE, R_MOD) + res := mulmod(den, res, R_MOD) + + let l_alpha := mload(add(state, STATE_ALPHA)) + res := mulmod(res, l_alpha, R_MOD) + res := mulmod(res, l_alpha, R_MOD) + mstore(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0), res) + } + + /// @notice follows alg. p.13 of https://eprint.iacr.org/2019/953.pdf + /// with t₁ = t₂ = 1, and the proofs are ([digest] + [quotient] +purported evaluation): + /// * [state_folded_state_digests], [proof_batch_opening_at_zeta_x], state_folded_evals + /// * [proof_grand_product_commitment], [proof_opening_at_zeta_omega_x], [proof_grand_product_at_zeta_omega] + /// @param aproof pointer to the proof + function batch_verify_multi_points(aproof) { + let state := mload(0x40) + let mPtr := add(state, STATE_LAST_MEM) + + // derive a random number. As there is no random generator, we + // do an FS like challenge derivation, depending on both digests and + // ζ to ensure that the prover cannot control the random numger. + // Note: adding the other point ζω is not needed, as ω is known beforehand. + mstore(mPtr, mload(add(state, STATE_FOLDED_DIGESTS_X))) + mstore(add(mPtr, 0x20), mload(add(state, STATE_FOLDED_DIGESTS_Y))) + mstore(add(mPtr, 0x40), calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X))) + mstore(add(mPtr, 0x60), calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_Y))) + mstore(add(mPtr, 0x80), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X))) + mstore(add(mPtr, 0xa0), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_Y))) + mstore(add(mPtr, 0xc0), calldataload(add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X))) + mstore(add(mPtr, 0xe0), calldataload(add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_Y))) + mstore(add(mPtr, 0x100), mload(add(state, STATE_ZETA))) + mstore(add(mPtr, 0x120), mload(add(state, STATE_GAMMA_KZG))) + let random := staticcall(gas(), 0x2, mPtr, 0x140, mPtr, 0x20) + if iszero(random) { error_random_generation() } + random := mod(mload(mPtr), R_MOD) // use the same variable as we are one variable away from getting stack-too-deep error... + + let folded_quotients := mPtr + mPtr := add(folded_quotients, 0x40) + mstore(folded_quotients, calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X))) + mstore( + add(folded_quotients, 0x20), + calldataload(add(aproof, PROOF_BATCH_OPENING_AT_ZETA_Y)) + ) + point_acc_mul_calldata( + folded_quotients, add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X), random, mPtr + ) + + let folded_digests := add(state, STATE_FOLDED_DIGESTS_X) + point_acc_mul_calldata( + folded_digests, add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X), random, mPtr + ) + + let folded_evals := add(state, STATE_FOLDED_CLAIMED_VALUES) + fr_acc_mul_calldata( + folded_evals, add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA), random + ) + + let folded_evals_commit := mPtr + mPtr := add(folded_evals_commit, 0x40) + mstore(folded_evals_commit, G1_SRS_X) + mstore(add(folded_evals_commit, 0x20), G1_SRS_Y) + mstore(add(folded_evals_commit, 0x40), mload(folded_evals)) + let check_staticcall := + staticcall(gas(), 7, folded_evals_commit, 0x60, folded_evals_commit, 0x40) + if iszero(check_staticcall) { error_verify() } + + let folded_evals_commit_y := add(folded_evals_commit, 0x20) + mstore(folded_evals_commit_y, sub(P_MOD, mload(folded_evals_commit_y))) + point_add(folded_digests, folded_digests, folded_evals_commit, mPtr) + + let folded_points_quotients := mPtr + mPtr := add(mPtr, 0x40) + point_mul_calldata( + folded_points_quotients, + add(aproof, PROOF_BATCH_OPENING_AT_ZETA_X), + mload(add(state, STATE_ZETA)), + mPtr + ) + let zeta_omega := mulmod(mload(add(state, STATE_ZETA)), VK_OMEGA, R_MOD) + random := mulmod(random, zeta_omega, R_MOD) + point_acc_mul_calldata( + folded_points_quotients, + add(aproof, PROOF_OPENING_AT_ZETA_OMEGA_X), + random, + mPtr + ) + + point_add(folded_digests, folded_digests, folded_points_quotients, mPtr) + + let folded_quotients_y := add(folded_quotients, 0x20) + mstore(folded_quotients_y, sub(P_MOD, mload(folded_quotients_y))) + + mstore(mPtr, mload(folded_digests)) + mstore(add(mPtr, 0x20), mload(add(folded_digests, 0x20))) + mstore(add(mPtr, 0x40), G2_SRS_0_X_0) // the 4 lines are the canonical G2 point on BN254 + mstore(add(mPtr, 0x60), G2_SRS_0_X_1) + mstore(add(mPtr, 0x80), G2_SRS_0_Y_0) + mstore(add(mPtr, 0xa0), G2_SRS_0_Y_1) + mstore(add(mPtr, 0xc0), mload(folded_quotients)) + mstore(add(mPtr, 0xe0), mload(add(folded_quotients, 0x20))) + mstore(add(mPtr, 0x100), G2_SRS_1_X_0) + mstore(add(mPtr, 0x120), G2_SRS_1_X_1) + mstore(add(mPtr, 0x140), G2_SRS_1_Y_0) + mstore(add(mPtr, 0x160), G2_SRS_1_Y_1) + check_pairing_kzg(mPtr) + } + + /// @notice check_pairing_kzg checks the result of the final pairing product of the batched + /// kzg verification. The purpose of this function is to avoid exhausting the stack + /// in the function batch_verify_multi_points. + /// @param mPtr pointer storing the tuple of pairs + function check_pairing_kzg(mPtr) { + let state := mload(0x40) + + let l_success := staticcall(gas(), 8, mPtr, 0x180, 0x00, 0x20) + if iszero(l_success) { error_pairing() } + let res_pairing := mload(0x00) + mstore(add(state, STATE_SUCCESS), res_pairing) + } + + /// @notice Fold the opening proofs at ζ: + /// * at state+state_folded_digest we store: [Linearised_polynomial]+γ[L] + γ²[R] + γ³[O] + γ⁴[S₁] +γ⁵[S₂] + ∑ᵢγ⁵⁺ⁱ[Pi_{i}] + /// * at state+state_folded_claimed_values we store: H(ζ) + γLinearised_polynomial(ζ)+γ²L(ζ) + γ³R(ζ)+ γ⁴O(ζ) + γ⁵S₁(ζ) +γ⁶S₂(ζ) + ∑ᵢγ⁶⁺ⁱPi_{i}(ζ) + /// @param aproof pointer to the proof + /// acc_gamma stores the γⁱ + function fold_state(aproof) { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + let mPtr20 := add(mPtr, 0x20) + let mPtr40 := add(mPtr, 0x40) + + let l_gamma_kzg := mload(add(state, STATE_GAMMA_KZG)) + let acc_gamma := l_gamma_kzg + let state_folded_digests := add(state, STATE_FOLDED_DIGESTS_X) + + mstore( + add(state, STATE_FOLDED_DIGESTS_X), + mload(add(state, STATE_LINEARISED_POLYNOMIAL_X)) + ) + mstore( + add(state, STATE_FOLDED_DIGESTS_Y), + mload(add(state, STATE_LINEARISED_POLYNOMIAL_Y)) + ) + mstore( + add(state, STATE_FOLDED_CLAIMED_VALUES), + mload(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA)) + ) + + point_acc_mul_calldata( + add(state, STATE_FOLDED_DIGESTS_X), add(aproof, PROOF_L_COM_X), acc_gamma, mPtr + ) + fr_acc_mul_calldata( + add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_L_AT_ZETA), acc_gamma + ) + + acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) + point_acc_mul_calldata( + state_folded_digests, add(aproof, PROOF_R_COM_X), acc_gamma, mPtr + ) + fr_acc_mul_calldata( + add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_R_AT_ZETA), acc_gamma + ) + + acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) + point_acc_mul_calldata( + state_folded_digests, add(aproof, PROOF_O_COM_X), acc_gamma, mPtr + ) + fr_acc_mul_calldata( + add(state, STATE_FOLDED_CLAIMED_VALUES), add(aproof, PROOF_O_AT_ZETA), acc_gamma + ) + + acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) + mstore(mPtr, VK_S1_COM_X) + mstore(mPtr20, VK_S1_COM_Y) + point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) + fr_acc_mul_calldata( + add(state, STATE_FOLDED_CLAIMED_VALUES), + add(aproof, PROOF_S1_AT_ZETA), + acc_gamma + ) + + acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) + mstore(mPtr, VK_S2_COM_X) + mstore(mPtr20, VK_S2_COM_Y) + point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) + fr_acc_mul_calldata( + add(state, STATE_FOLDED_CLAIMED_VALUES), + add(aproof, PROOF_S2_AT_ZETA), + acc_gamma + ) + let poqaz := add(aproof, PROOF_OPENING_QCP_AT_ZETA) + + acc_gamma := mulmod(acc_gamma, l_gamma_kzg, R_MOD) + mstore(mPtr, VK_QCP_0_X) + mstore(mPtr20, VK_QCP_0_Y) + point_acc_mul(state_folded_digests, mPtr, acc_gamma, mPtr40) + fr_acc_mul_calldata(add(state, STATE_FOLDED_CLAIMED_VALUES), poqaz, acc_gamma) + poqaz := add(poqaz, 0x20) + } + + /// @notice generate the challenge (using Fiat Shamir) to fold the opening proofs + /// at ζ. + /// The process for deriving γ is the same as in derive_gamma but this time the inputs are + /// in this order (the [] means it's a commitment): + /// * ζ + /// * [Linearised polynomial] + /// * [L], [R], [O] + /// * [S₁] [S₂] + /// * [Pi_{i}] (wires associated to custom gates) + /// Then there are the purported evaluations of the previous committed polynomials: + /// * Linearised_polynomial(ζ) + /// * L(ζ), R(ζ), O(ζ), S₁(ζ), S₂(ζ) + /// * Pi_{i}(ζ) + /// * Z(ζω) + /// @param aproof pointer to the proof + function compute_gamma_kzg(aproof) { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + mstore(mPtr, FS_GAMMA_KZG) // "gamma" + mstore(add(mPtr, 0x20), mload(add(state, STATE_ZETA))) + mstore(add(mPtr, 0x40), mload(add(state, STATE_LINEARISED_POLYNOMIAL_X))) + mstore(add(mPtr, 0x60), mload(add(state, STATE_LINEARISED_POLYNOMIAL_Y))) + calldatacopy(add(mPtr, 0x80), add(aproof, PROOF_L_COM_X), 0xc0) + mstore(add(mPtr, 0x140), VK_S1_COM_X) + mstore(add(mPtr, 0x160), VK_S1_COM_Y) + mstore(add(mPtr, 0x180), VK_S2_COM_X) + mstore(add(mPtr, 0x1a0), VK_S2_COM_Y) + + let offset := 0x1c0 + + mstore(add(mPtr, offset), VK_QCP_0_X) + mstore(add(mPtr, add(offset, 0x20)), VK_QCP_0_Y) + offset := add(offset, 0x40) + mstore( + add(mPtr, offset), mload(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA)) + ) + mstore(add(mPtr, add(offset, 0x20)), calldataload(add(aproof, PROOF_L_AT_ZETA))) + mstore(add(mPtr, add(offset, 0x40)), calldataload(add(aproof, PROOF_R_AT_ZETA))) + mstore(add(mPtr, add(offset, 0x60)), calldataload(add(aproof, PROOF_O_AT_ZETA))) + mstore(add(mPtr, add(offset, 0x80)), calldataload(add(aproof, PROOF_S1_AT_ZETA))) + mstore(add(mPtr, add(offset, 0xa0)), calldataload(add(aproof, PROOF_S2_AT_ZETA))) + + let _mPtr := add(mPtr, add(offset, 0xc0)) + + let _poqaz := add(aproof, PROOF_OPENING_QCP_AT_ZETA) + calldatacopy(_mPtr, _poqaz, mul(VK_NB_CUSTOM_GATES, 0x20)) + _mPtr := add(_mPtr, mul(VK_NB_CUSTOM_GATES, 0x20)) + + mstore(_mPtr, calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA))) + + let start_input := 0x1b // 00.."gamma" + let size_input := add(0x14, mul(VK_NB_CUSTOM_GATES, 3)) // number of 32bytes elmts = 0x17 (zeta+3*6 for the digests+openings) + 3*VK_NB_CUSTOM_GATES (for the commitments of the selectors) + 1 (opening of Z at ζω) + size_input := add(0x5, mul(size_input, 0x20)) // size in bytes: 15*32 bytes + 5 bytes for gamma + let check_staticcall := + staticcall( + gas(), + 0x2, + add(mPtr, start_input), + size_input, + add(state, STATE_GAMMA_KZG), + 0x20 + ) + if iszero(check_staticcall) { error_verify() } + mstore(add(state, STATE_GAMMA_KZG), mod(mload(add(state, STATE_GAMMA_KZG)), R_MOD)) + } + + function compute_commitment_linearised_polynomial_ec(aproof, s1, s2) { + let state := mload(0x40) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + + mstore(mPtr, VK_QL_COM_X) + mstore(add(mPtr, 0x20), VK_QL_COM_Y) + point_mul( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + mPtr, + calldataload(add(aproof, PROOF_L_AT_ZETA)), + add(mPtr, 0x40) + ) + + mstore(mPtr, VK_QR_COM_X) + mstore(add(mPtr, 0x20), VK_QR_COM_Y) + point_acc_mul( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + mPtr, + calldataload(add(aproof, PROOF_R_AT_ZETA)), + add(mPtr, 0x40) + ) + + let rl := + mulmod( + calldataload(add(aproof, PROOF_L_AT_ZETA)), + calldataload(add(aproof, PROOF_R_AT_ZETA)), + R_MOD + ) + mstore(mPtr, VK_QM_COM_X) + mstore(add(mPtr, 0x20), VK_QM_COM_Y) + point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, rl, add(mPtr, 0x40)) + + mstore(mPtr, VK_QO_COM_X) + mstore(add(mPtr, 0x20), VK_QO_COM_Y) + point_acc_mul( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + mPtr, + calldataload(add(aproof, PROOF_O_AT_ZETA)), + add(mPtr, 0x40) + ) + + mstore(mPtr, VK_QK_COM_X) + mstore(add(mPtr, 0x20), VK_QK_COM_Y) + point_add( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + add(state, STATE_LINEARISED_POLYNOMIAL_X), + mPtr, + add(mPtr, 0x40) + ) + + let qcp_opening_at_zeta := add(aproof, PROOF_OPENING_QCP_AT_ZETA) + let bsb_commitments := add(aproof, PROOF_BSB_COMMITMENTS) + for { let i := 0 } lt(i, VK_NB_CUSTOM_GATES) { i := add(i, 1) } { + mstore(mPtr, calldataload(bsb_commitments)) + mstore(add(mPtr, 0x20), calldataload(add(bsb_commitments, 0x20))) + point_acc_mul( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + mPtr, + calldataload(qcp_opening_at_zeta), + add(mPtr, 0x40) + ) + qcp_opening_at_zeta := add(qcp_opening_at_zeta, 0x20) + bsb_commitments := add(bsb_commitments, 0x40) + } + + mstore(mPtr, VK_S3_COM_X) + mstore(add(mPtr, 0x20), VK_S3_COM_Y) + point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, s1, add(mPtr, 0x40)) + + mstore(mPtr, calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_X))) + mstore(add(mPtr, 0x20), calldataload(add(aproof, PROOF_GRAND_PRODUCT_COMMITMENT_Y))) + point_acc_mul(add(state, STATE_LINEARISED_POLYNOMIAL_X), mPtr, s2, add(mPtr, 0x40)) + + point_add( + add(state, STATE_LINEARISED_POLYNOMIAL_X), + add(state, STATE_LINEARISED_POLYNOMIAL_X), + add(state, STATE_FOLDED_H_X), + mPtr + ) + } + + /// @notice Compute the commitment to the linearized polynomial equal to + /// L(ζ)[Qₗ]+r(ζ)[Qᵣ]+R(ζ)L(ζ)[Qₘ]+O(ζ)[Qₒ]+[Qₖ]+Σᵢqc'ᵢ(ζ)[BsbCommitmentᵢ] + + /// α*( Z(μζ)(L(ζ)+β*S₁(ζ)+γ)*(R(ζ)+β*S₂(ζ)+γ)[S₃]-[Z](L(ζ)+β*id_{1}(ζ)+γ)*(R(ζ)+β*id_{2}(ζ)+γ)*(O(ζ)+β*id_{3}(ζ)+γ) ) + + /// α²*L₁(ζ)[Z] - Z_{H}(ζ)*(([H₀] + ζᵐ⁺²*[H₁] + ζ²⁽ᵐ⁺²⁾*[H₂]) + /// where + /// * id_1 = id, id_2 = vk_coset_shift*id, id_3 = vk_coset_shift^{2}*id + /// * the [] means that it's a commitment (i.e. a point on Bn254(F_p)) + /// * Z_{H}(ζ) = ζ^n-1 + /// @param aproof pointer to the proof + function compute_commitment_linearised_polynomial(aproof) { + let state := mload(0x40) + let l_beta := mload(add(state, STATE_BETA)) + let l_gamma := mload(add(state, STATE_GAMMA)) + let l_zeta := mload(add(state, STATE_ZETA)) + let l_alpha := mload(add(state, STATE_ALPHA)) + + let u := + mulmod(calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA)), l_beta, R_MOD) + let v := mulmod(l_beta, calldataload(add(aproof, PROOF_S1_AT_ZETA)), R_MOD) + v := addmod(v, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) + v := addmod(v, l_gamma, R_MOD) + + let w := mulmod(l_beta, calldataload(add(aproof, PROOF_S2_AT_ZETA)), R_MOD) + w := addmod(w, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) + w := addmod(w, l_gamma, R_MOD) + + let s1 := mulmod(u, v, R_MOD) + s1 := mulmod(s1, w, R_MOD) + s1 := mulmod(s1, l_alpha, R_MOD) + + let coset_square := mulmod(VK_COSET_SHIFT, VK_COSET_SHIFT, R_MOD) + let betazeta := mulmod(l_beta, l_zeta, R_MOD) + u := addmod(betazeta, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) + u := addmod(u, l_gamma, R_MOD) + + v := mulmod(betazeta, VK_COSET_SHIFT, R_MOD) + v := addmod(v, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) + v := addmod(v, l_gamma, R_MOD) + + w := mulmod(betazeta, coset_square, R_MOD) + w := addmod(w, calldataload(add(aproof, PROOF_O_AT_ZETA)), R_MOD) + w := addmod(w, l_gamma, R_MOD) + + let s2 := mulmod(u, v, R_MOD) + s2 := mulmod(s2, w, R_MOD) + s2 := sub(R_MOD, s2) + s2 := mulmod(s2, l_alpha, R_MOD) + s2 := addmod(s2, mload(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0)), R_MOD) + + // at this stage: + // * s₁ = α*Z(μζ)(l(ζ)+β*s₁(ζ)+γ)*(r(ζ)+β*s₂(ζ)+γ)*β + // * s₂ = -α*(l(ζ)+β*ζ+γ)*(r(ζ)+β*u*ζ+γ)*(o(ζ)+β*u²*ζ+γ) + α²*L₁(ζ) + + compute_commitment_linearised_polynomial_ec(aproof, s1, s2) + } + + /// @notice compute -z_h(ζ)*([H₁] + ζᵐ⁺²[H₂] + ζ²⁽ᵐ⁺²⁾[H₃]) and store the result at + /// state + state_folded_h + /// @param aproof pointer to the proof + function fold_h(aproof) { + let state := mload(0x40) + let n_plus_two := add(VK_DOMAIN_SIZE, 2) + let mPtr := add(mload(0x40), STATE_LAST_MEM) + let zeta_power_n_plus_two := pow(mload(add(state, STATE_ZETA)), n_plus_two, mPtr) + point_mul_calldata( + add(state, STATE_FOLDED_H_X), + add(aproof, PROOF_H_2_X), + zeta_power_n_plus_two, + mPtr + ) + point_add_calldata( + add(state, STATE_FOLDED_H_X), + add(state, STATE_FOLDED_H_X), + add(aproof, PROOF_H_1_X), + mPtr + ) + point_mul( + add(state, STATE_FOLDED_H_X), + add(state, STATE_FOLDED_H_X), + zeta_power_n_plus_two, + mPtr + ) + point_add_calldata( + add(state, STATE_FOLDED_H_X), + add(state, STATE_FOLDED_H_X), + add(aproof, PROOF_H_0_X), + mPtr + ) + point_mul( + add(state, STATE_FOLDED_H_X), + add(state, STATE_FOLDED_H_X), + mload(add(state, STATE_ZETA_POWER_N_MINUS_ONE)), + mPtr + ) + let folded_h_y := mload(add(state, STATE_FOLDED_H_Y)) + folded_h_y := sub(P_MOD, folded_h_y) + mstore(add(state, STATE_FOLDED_H_Y), folded_h_y) + } + + /// @notice check that the opening of the linearised polynomial at zeta is equal to + /// - [ PI(ζ) - α²*L₁(ζ) + α(l(ζ)+β*s1(ζ)+γ)(r(ζ)+β*s2(ζ)+γ)(o(ζ)+γ)*z(ωζ) ] + /// @param aproof pointer to the proof + function verify_opening_linearised_polynomial(aproof) { + let state := mload(0x40) + + // (l(ζ)+β*s1(ζ)+γ) + let s1 + s1 := + mulmod( + calldataload(add(aproof, PROOF_S1_AT_ZETA)), + mload(add(state, STATE_BETA)), + R_MOD + ) + s1 := addmod(s1, mload(add(state, STATE_GAMMA)), R_MOD) + s1 := addmod(s1, calldataload(add(aproof, PROOF_L_AT_ZETA)), R_MOD) + + // (r(ζ)+β*s2(ζ)+γ) + let s2 + s2 := + mulmod( + calldataload(add(aproof, PROOF_S2_AT_ZETA)), + mload(add(state, STATE_BETA)), + R_MOD + ) + s2 := addmod(s2, mload(add(state, STATE_GAMMA)), R_MOD) + s2 := addmod(s2, calldataload(add(aproof, PROOF_R_AT_ZETA)), R_MOD) + + // (o(ζ)+γ) + let o + o := + addmod( + calldataload(add(aproof, PROOF_O_AT_ZETA)), + mload(add(state, STATE_GAMMA)), + R_MOD + ) + + // α*Z(μζ)*(l(ζ)+β*s1(ζ)+γ)*(r(ζ)+β*s2(ζ)+γ)*(o(ζ)+γ) + s1 := mulmod(s1, s2, R_MOD) + s1 := mulmod(s1, o, R_MOD) + s1 := mulmod(s1, mload(add(state, STATE_ALPHA)), R_MOD) + s1 := + mulmod(s1, calldataload(add(aproof, PROOF_GRAND_PRODUCT_AT_ZETA_OMEGA)), R_MOD) + + // PI(ζ) - α²*L₁(ζ) + α(l(ζ)+β*s1(ζ)+γ)(r(ζ)+β*s2(ζ)+γ)(o(ζ)+γ)*z(ωζ) + s1 := addmod(s1, mload(add(state, STATE_PI)), R_MOD) + s2 := mload(add(state, STATE_ALPHA_SQUARE_LAGRANGE_0)) + s2 := sub(R_MOD, s2) + s1 := addmod(s1, s2, R_MOD) + s1 := sub(R_MOD, s1) + + mstore(add(state, STATE_OPENING_LINEARISED_POLYNOMIAL_ZETA), s1) + } + + // BEGINNING utils math functions ------------------------------------------------- + + /// @param dst pointer storing the result + /// @param p pointer to the first point + /// @param q pointer to the second point + /// @param mPtr pointer to free memory + function point_add(dst, p, q, mPtr) { + mstore(mPtr, mload(p)) + mstore(add(mPtr, 0x20), mload(add(p, 0x20))) + mstore(add(mPtr, 0x40), mload(q)) + mstore(add(mPtr, 0x60), mload(add(q, 0x20))) + let l_success := staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40) + if iszero(l_success) { error_ec_op() } + } + + /// @param dst pointer storing the result + /// @param p pointer to the first point (calldata) + /// @param q pointer to the second point (calladata) + /// @param mPtr pointer to free memory + function point_add_calldata(dst, p, q, mPtr) { + mstore(mPtr, mload(p)) + mstore(add(mPtr, 0x20), mload(add(p, 0x20))) + mstore(add(mPtr, 0x40), calldataload(q)) + mstore(add(mPtr, 0x60), calldataload(add(q, 0x20))) + let l_success := staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40) + if iszero(l_success) { error_ec_op() } + } + + /// @parma dst pointer storing the result + /// @param src pointer to a point on Bn254(𝔽_p) + /// @param s scalar + /// @param mPtr free memory + function point_mul(dst, src, s, mPtr) { + mstore(mPtr, mload(src)) + mstore(add(mPtr, 0x20), mload(add(src, 0x20))) + mstore(add(mPtr, 0x40), s) + let l_success := staticcall(gas(), EC_MUL, mPtr, 0x60, dst, 0x40) + if iszero(l_success) { error_ec_op() } + } + + /// @parma dst pointer storing the result + /// @param src pointer to a point on Bn254(𝔽_p) on calldata + /// @param s scalar + /// @param mPtr free memory + function point_mul_calldata(dst, src, s, mPtr) { + mstore(mPtr, calldataload(src)) + mstore(add(mPtr, 0x20), calldataload(add(src, 0x20))) + mstore(add(mPtr, 0x40), s) + let l_success := staticcall(gas(), EC_MUL, mPtr, 0x60, dst, 0x40) + if iszero(l_success) { error_ec_op() } + } + + /// @notice dst <- dst + [s]src (Elliptic curve) + /// @param dst pointer accumulator point storing the result + /// @param src pointer to the point to multiply and add + /// @param s scalar + /// @param mPtr free memory + function point_acc_mul(dst, src, s, mPtr) { + mstore(mPtr, mload(src)) + mstore(add(mPtr, 0x20), mload(add(src, 0x20))) + mstore(add(mPtr, 0x40), s) + let l_success := staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) + mstore(add(mPtr, 0x40), mload(dst)) + mstore(add(mPtr, 0x60), mload(add(dst, 0x20))) + l_success := and(l_success, staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40)) + if iszero(l_success) { error_ec_op() } + } + + /// @notice dst <- dst + [s]src (Elliptic curve) + /// @param dst pointer accumulator point storing the result + /// @param src pointer to the point to multiply and add (on calldata) + /// @param s scalar + /// @mPtr free memory + function point_acc_mul_calldata(dst, src, s, mPtr) { + let state := mload(0x40) + mstore(mPtr, calldataload(src)) + mstore(add(mPtr, 0x20), calldataload(add(src, 0x20))) + mstore(add(mPtr, 0x40), s) + let l_success := staticcall(gas(), 7, mPtr, 0x60, mPtr, 0x40) + mstore(add(mPtr, 0x40), mload(dst)) + mstore(add(mPtr, 0x60), mload(add(dst, 0x20))) + l_success := and(l_success, staticcall(gas(), EC_ADD, mPtr, 0x80, dst, 0x40)) + if iszero(l_success) { error_ec_op() } + } + + /// @notice dst <- dst + src*s (Fr) dst,src are addresses, s is a value + /// @param dst pointer storing the result + /// @param src pointer to the scalar to multiply and add (on calldata) + /// @param s scalar + function fr_acc_mul_calldata(dst, src, s) { + let tmp := mulmod(calldataload(src), s, R_MOD) + mstore(dst, addmod(mload(dst), tmp, R_MOD)) + } + + /// @param x element to exponentiate + /// @param e exponent + /// @param mPtr free memory + /// @return res x ** e mod r + function pow(x, e, mPtr) -> res { + mstore(mPtr, 0x20) + mstore(add(mPtr, 0x20), 0x20) + mstore(add(mPtr, 0x40), 0x20) + mstore(add(mPtr, 0x60), x) + mstore(add(mPtr, 0x80), e) + mstore(add(mPtr, 0xa0), R_MOD) + let check_staticcall := staticcall(gas(), MOD_EXP, mPtr, 0xc0, mPtr, 0x20) + if eq(check_staticcall, 0) {} + res := mload(mPtr) + } } - res := mload(mPtr) - } } - } } diff --git a/contracts/src/v3.0.0-rc1/SP1VerifierPlonk.sol b/contracts/src/v3.0.0-rc1/SP1VerifierPlonk.sol index 7bdc064..8d582ca 100644 --- a/contracts/src/v3.0.0-rc1/SP1VerifierPlonk.sol +++ b/contracts/src/v3.0.0-rc1/SP1VerifierPlonk.sol @@ -28,9 +28,7 @@ contract SP1Verifier is PlonkVerifier, ISP1VerifierWithHash { /// @notice Hashes the public values to a field elements inside Bn254. /// @param publicValues The public values. - function hashPublicValues( - bytes calldata publicValues - ) public pure returns (bytes32) { + function hashPublicValues(bytes calldata publicValues) public pure returns (bytes32) { return sha256(publicValues) & bytes32(uint256((1 << 253) - 1)); }