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Contract Source Code Verified (Exact Match)
Contract Name:
Verifier
Compiler Version
v0.8.20+commit.a1b79de6
Optimization Enabled:
Yes with 9999999 runs
Other Settings:
paris EvmVersion
Contract Source Code (Solidity Standard Json-Input format)
pragma solidity 0.8.20;
// SPDX-License-Identifier: MIT
import "./interfaces/IVerifier.sol";
/* solhint-disable max-line-length */
/// @author Matter Labs
/// @notice Modified version of the Permutations over Lagrange-bases for Oecumenical Noninteractive arguments of
/// Knowledge (PLONK) verifier.
/// Modifications have been made to optimize the proof system for zkSync Era circuits.
/// @dev It uses a custom memory layout inside the inline assembly block. Each reserved memory cell is declared in the
/// constants below.
/// @dev For a better understanding of the verifier algorithm please refer to the following papers:
/// * Original Plonk Article: https://eprint.iacr.org/2019/953.pdf
/// * Original LookUp Article: https://eprint.iacr.org/2020/315.pdf
/// * Plonk for zkSync v1.1: https://github.com/matter-labs/solidity_plonk_verifier/raw/recursive/bellman_vk_codegen_recursive/RecursivePlonkUnrolledForEthereum.pdf
/// The notation used in the code is the same as in the papers.
/* solhint-enable max-line-length */
contract Verifier is IVerifier {
/*//////////////////////////////////////////////////////////////
Verification keys
//////////////////////////////////////////////////////////////*/
// Memory slots from 0x000 to 0x200 are reserved for intermediate computations and call to precompiles.
uint256 internal constant VK_GATE_SETUP_0_X_SLOT = 0x200 + 0x000;
uint256 internal constant VK_GATE_SETUP_0_Y_SLOT = 0x200 + 0x020;
uint256 internal constant VK_GATE_SETUP_1_X_SLOT = 0x200 + 0x040;
uint256 internal constant VK_GATE_SETUP_1_Y_SLOT = 0x200 + 0x060;
uint256 internal constant VK_GATE_SETUP_2_X_SLOT = 0x200 + 0x080;
uint256 internal constant VK_GATE_SETUP_2_Y_SLOT = 0x200 + 0x0a0;
uint256 internal constant VK_GATE_SETUP_3_X_SLOT = 0x200 + 0x0c0;
uint256 internal constant VK_GATE_SETUP_3_Y_SLOT = 0x200 + 0x0e0;
uint256 internal constant VK_GATE_SETUP_4_X_SLOT = 0x200 + 0x100;
uint256 internal constant VK_GATE_SETUP_4_Y_SLOT = 0x200 + 0x120;
uint256 internal constant VK_GATE_SETUP_5_X_SLOT = 0x200 + 0x140;
uint256 internal constant VK_GATE_SETUP_5_Y_SLOT = 0x200 + 0x160;
uint256 internal constant VK_GATE_SETUP_6_X_SLOT = 0x200 + 0x180;
uint256 internal constant VK_GATE_SETUP_6_Y_SLOT = 0x200 + 0x1a0;
uint256 internal constant VK_GATE_SETUP_7_X_SLOT = 0x200 + 0x1c0;
uint256 internal constant VK_GATE_SETUP_7_Y_SLOT = 0x200 + 0x1e0;
uint256 internal constant VK_GATE_SELECTORS_0_X_SLOT = 0x200 + 0x200;
uint256 internal constant VK_GATE_SELECTORS_0_Y_SLOT = 0x200 + 0x220;
uint256 internal constant VK_GATE_SELECTORS_1_X_SLOT = 0x200 + 0x240;
uint256 internal constant VK_GATE_SELECTORS_1_Y_SLOT = 0x200 + 0x260;
uint256 internal constant VK_PERMUTATION_0_X_SLOT = 0x200 + 0x280;
uint256 internal constant VK_PERMUTATION_0_Y_SLOT = 0x200 + 0x2a0;
uint256 internal constant VK_PERMUTATION_1_X_SLOT = 0x200 + 0x2c0;
uint256 internal constant VK_PERMUTATION_1_Y_SLOT = 0x200 + 0x2e0;
uint256 internal constant VK_PERMUTATION_2_X_SLOT = 0x200 + 0x300;
uint256 internal constant VK_PERMUTATION_2_Y_SLOT = 0x200 + 0x320;
uint256 internal constant VK_PERMUTATION_3_X_SLOT = 0x200 + 0x340;
uint256 internal constant VK_PERMUTATION_3_Y_SLOT = 0x200 + 0x360;
uint256 internal constant VK_LOOKUP_SELECTOR_X_SLOT = 0x200 + 0x380;
uint256 internal constant VK_LOOKUP_SELECTOR_Y_SLOT = 0x200 + 0x3a0;
uint256 internal constant VK_LOOKUP_TABLE_0_X_SLOT = 0x200 + 0x3c0;
uint256 internal constant VK_LOOKUP_TABLE_0_Y_SLOT = 0x200 + 0x3e0;
uint256 internal constant VK_LOOKUP_TABLE_1_X_SLOT = 0x200 + 0x400;
uint256 internal constant VK_LOOKUP_TABLE_1_Y_SLOT = 0x200 + 0x420;
uint256 internal constant VK_LOOKUP_TABLE_2_X_SLOT = 0x200 + 0x440;
uint256 internal constant VK_LOOKUP_TABLE_2_Y_SLOT = 0x200 + 0x460;
uint256 internal constant VK_LOOKUP_TABLE_3_X_SLOT = 0x200 + 0x480;
uint256 internal constant VK_LOOKUP_TABLE_3_Y_SLOT = 0x200 + 0x4a0;
uint256 internal constant VK_LOOKUP_TABLE_TYPE_X_SLOT = 0x200 + 0x4c0;
uint256 internal constant VK_LOOKUP_TABLE_TYPE_Y_SLOT = 0x200 + 0x4e0;
uint256 internal constant VK_RECURSIVE_FLAG_SLOT = 0x200 + 0x500;
/*//////////////////////////////////////////////////////////////
Proof
//////////////////////////////////////////////////////////////*/
uint256 internal constant PROOF_PUBLIC_INPUT = 0x200 + 0x520 + 0x000;
uint256 internal constant PROOF_STATE_POLYS_0_X_SLOT = 0x200 + 0x520 + 0x020;
uint256 internal constant PROOF_STATE_POLYS_0_Y_SLOT = 0x200 + 0x520 + 0x040;
uint256 internal constant PROOF_STATE_POLYS_1_X_SLOT = 0x200 + 0x520 + 0x060;
uint256 internal constant PROOF_STATE_POLYS_1_Y_SLOT = 0x200 + 0x520 + 0x080;
uint256 internal constant PROOF_STATE_POLYS_2_X_SLOT = 0x200 + 0x520 + 0x0a0;
uint256 internal constant PROOF_STATE_POLYS_2_Y_SLOT = 0x200 + 0x520 + 0x0c0;
uint256 internal constant PROOF_STATE_POLYS_3_X_SLOT = 0x200 + 0x520 + 0x0e0;
uint256 internal constant PROOF_STATE_POLYS_3_Y_SLOT = 0x200 + 0x520 + 0x100;
uint256 internal constant PROOF_COPY_PERMUTATION_GRAND_PRODUCT_X_SLOT = 0x200 + 0x520 + 0x120;
uint256 internal constant PROOF_COPY_PERMUTATION_GRAND_PRODUCT_Y_SLOT = 0x200 + 0x520 + 0x140;
uint256 internal constant PROOF_LOOKUP_S_POLY_X_SLOT = 0x200 + 0x520 + 0x160;
uint256 internal constant PROOF_LOOKUP_S_POLY_Y_SLOT = 0x200 + 0x520 + 0x180;
uint256 internal constant PROOF_LOOKUP_GRAND_PRODUCT_X_SLOT = 0x200 + 0x520 + 0x1a0;
uint256 internal constant PROOF_LOOKUP_GRAND_PRODUCT_Y_SLOT = 0x200 + 0x520 + 0x1c0;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_0_X_SLOT = 0x200 + 0x520 + 0x1e0;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_0_Y_SLOT = 0x200 + 0x520 + 0x200;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_1_X_SLOT = 0x200 + 0x520 + 0x220;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_1_Y_SLOT = 0x200 + 0x520 + 0x240;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_2_X_SLOT = 0x200 + 0x520 + 0x260;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_2_Y_SLOT = 0x200 + 0x520 + 0x280;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_3_X_SLOT = 0x200 + 0x520 + 0x2a0;
uint256 internal constant PROOF_QUOTIENT_POLY_PARTS_3_Y_SLOT = 0x200 + 0x520 + 0x2c0;
uint256 internal constant PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x2e0;
uint256 internal constant PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x300;
uint256 internal constant PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x320;
uint256 internal constant PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x340;
uint256 internal constant PROOF_STATE_POLYS_3_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x360;
uint256 internal constant PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x380;
uint256 internal constant PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x3a0;
uint256 internal constant PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x3c0;
uint256 internal constant PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x3e0;
uint256 internal constant PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x400;
uint256 internal constant PROOF_LOOKUP_S_POLY_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x420;
uint256 internal constant PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x440;
uint256 internal constant PROOF_LOOKUP_T_POLY_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x460;
uint256 internal constant PROOF_LOOKUP_T_POLY_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x480;
uint256 internal constant PROOF_LOOKUP_SELECTOR_POLY_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x4a0;
uint256 internal constant PROOF_LOOKUP_TABLE_TYPE_POLY_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x4c0;
uint256 internal constant PROOF_QUOTIENT_POLY_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x4e0;
uint256 internal constant PROOF_LINEARISATION_POLY_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x500;
uint256 internal constant PROOF_OPENING_PROOF_AT_Z_X_SLOT = 0x200 + 0x520 + 0x520;
uint256 internal constant PROOF_OPENING_PROOF_AT_Z_Y_SLOT = 0x200 + 0x520 + 0x540;
uint256 internal constant PROOF_OPENING_PROOF_AT_Z_OMEGA_X_SLOT = 0x200 + 0x520 + 0x560;
uint256 internal constant PROOF_OPENING_PROOF_AT_Z_OMEGA_Y_SLOT = 0x200 + 0x520 + 0x580;
uint256 internal constant PROOF_RECURSIVE_PART_P1_X_SLOT = 0x200 + 0x520 + 0x5a0;
uint256 internal constant PROOF_RECURSIVE_PART_P1_Y_SLOT = 0x200 + 0x520 + 0x5c0;
uint256 internal constant PROOF_RECURSIVE_PART_P2_X_SLOT = 0x200 + 0x520 + 0x5e0;
uint256 internal constant PROOF_RECURSIVE_PART_P2_Y_SLOT = 0x200 + 0x520 + 0x600;
/*//////////////////////////////////////////////////////////////
Transcript slot
//////////////////////////////////////////////////////////////*/
uint256 internal constant TRANSCRIPT_BEGIN_SLOT = 0x200 + 0x520 + 0x620 + 0x00;
uint256 internal constant TRANSCRIPT_DST_BYTE_SLOT = 0x200 + 0x520 + 0x620 + 0x03;
uint256 internal constant TRANSCRIPT_STATE_0_SLOT = 0x200 + 0x520 + 0x620 + 0x04;
uint256 internal constant TRANSCRIPT_STATE_1_SLOT = 0x200 + 0x520 + 0x620 + 0x24;
uint256 internal constant TRANSCRIPT_CHALLENGE_SLOT = 0x200 + 0x520 + 0x620 + 0x44;
/*//////////////////////////////////////////////////////////////
Partial verifier state
//////////////////////////////////////////////////////////////*/
uint256 internal constant STATE_ALPHA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x000;
uint256 internal constant STATE_BETA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x020;
uint256 internal constant STATE_GAMMA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x040;
uint256 internal constant STATE_POWER_OF_ALPHA_2_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x060;
uint256 internal constant STATE_POWER_OF_ALPHA_3_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x080;
uint256 internal constant STATE_POWER_OF_ALPHA_4_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x0a0;
uint256 internal constant STATE_POWER_OF_ALPHA_5_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x0c0;
uint256 internal constant STATE_POWER_OF_ALPHA_6_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x0e0;
uint256 internal constant STATE_POWER_OF_ALPHA_7_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x100;
uint256 internal constant STATE_POWER_OF_ALPHA_8_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x120;
uint256 internal constant STATE_ETA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x140;
uint256 internal constant STATE_BETA_LOOKUP_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x160;
uint256 internal constant STATE_GAMMA_LOOKUP_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x180;
uint256 internal constant STATE_BETA_PLUS_ONE_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x1a0;
uint256 internal constant STATE_BETA_GAMMA_PLUS_GAMMA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x1c0;
uint256 internal constant STATE_V_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x1e0;
uint256 internal constant STATE_U_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x200;
uint256 internal constant STATE_Z_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x220;
uint256 internal constant STATE_Z_MINUS_LAST_OMEGA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x240;
uint256 internal constant STATE_L_0_AT_Z_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x260;
uint256 internal constant STATE_L_N_MINUS_ONE_AT_Z_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x280;
uint256 internal constant STATE_Z_IN_DOMAIN_SIZE = 0x200 + 0x520 + 0x620 + 0x80 + 0x2a0;
/*//////////////////////////////////////////////////////////////
Queries
//////////////////////////////////////////////////////////////*/
uint256 internal constant QUERIES_BUFFER_POINT_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x00;
uint256 internal constant QUERIES_AT_Z_0_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x40;
uint256 internal constant QUERIES_AT_Z_0_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x60;
uint256 internal constant QUERIES_AT_Z_1_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x80;
uint256 internal constant QUERIES_AT_Z_1_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0xa0;
uint256 internal constant QUERIES_T_POLY_AGGREGATED_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0xc0;
uint256 internal constant QUERIES_T_POLY_AGGREGATED_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0xe0;
/*//////////////////////////////////////////////////////////////
Aggregated commitment
//////////////////////////////////////////////////////////////*/
uint256 internal constant AGGREGATED_AT_Z_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x00;
uint256 internal constant AGGREGATED_AT_Z_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x20;
uint256 internal constant AGGREGATED_AT_Z_OMEGA_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x40;
uint256 internal constant AGGREGATED_AT_Z_OMEGA_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x60;
uint256 internal constant AGGREGATED_OPENING_AT_Z_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x80;
uint256 internal constant AGGREGATED_OPENING_AT_Z_OMEGA_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0xa0;
/*//////////////////////////////////////////////////////////////
Pairing data
//////////////////////////////////////////////////////////////*/
uint256 internal constant PAIRING_BUFFER_POINT_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0xc0 + 0x00;
uint256 internal constant PAIRING_BUFFER_POINT_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0xc0 + 0x20;
uint256 internal constant PAIRING_PAIR_WITH_GENERATOR_X_SLOT =
0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0xc0 + 0x40;
uint256 internal constant PAIRING_PAIR_WITH_GENERATOR_Y_SLOT =
0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0xc0 + 0x60;
uint256 internal constant PAIRING_PAIR_WITH_X_X_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x100 + 0x80;
uint256 internal constant PAIRING_PAIR_WITH_X_Y_SLOT = 0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x100 + 0xa0;
/*//////////////////////////////////////////////////////////////
Slots for scalar multiplication optimizations
//////////////////////////////////////////////////////////////*/
uint256 internal constant COPY_PERMUTATION_FIRST_AGGREGATED_COMMITMENT_COEFF =
0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x100 + 0xc0;
uint256 internal constant LOOKUP_GRAND_PRODUCT_FIRST_AGGREGATED_COMMITMENT_COEFF =
0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x100 + 0xe0;
uint256 internal constant LOOKUP_S_FIRST_AGGREGATED_COMMITMENT_COEFF =
0x200 + 0x520 + 0x620 + 0x80 + 0x2c0 + 0x100 + 0x100 + 0x100;
/*//////////////////////////////////////////////////////////////
Constants
//////////////////////////////////////////////////////////////*/
uint256 internal constant OMEGA = 0x1951441010b2b95a6e47a6075066a50a036f5ba978c050f2821df86636c0facb;
uint256 internal constant DOMAIN_SIZE = 0x1000000; // 2^24
uint256 internal constant Q_MOD = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
uint256 internal constant R_MOD = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
/// @dev flip of 0xe000000000000000000000000000000000000000000000000000000000000000;
uint256 internal constant FR_MASK = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff;
// non residues
uint256 internal constant NON_RESIDUES_0 = 0x05;
uint256 internal constant NON_RESIDUES_1 = 0x07;
uint256 internal constant NON_RESIDUES_2 = 0x0a;
// trusted setup g2 elements
uint256 internal constant G2_ELEMENTS_0_X1 = 0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2;
uint256 internal constant G2_ELEMENTS_0_X2 = 0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed;
uint256 internal constant G2_ELEMENTS_0_Y1 = 0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b;
uint256 internal constant G2_ELEMENTS_0_Y2 = 0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa;
uint256 internal constant G2_ELEMENTS_1_X1 = 0x260e01b251f6f1c7e7ff4e580791dee8ea51d87a358e038b4efe30fac09383c1;
uint256 internal constant G2_ELEMENTS_1_X2 = 0x0118c4d5b837bcc2bc89b5b398b5974e9f5944073b32078b7e231fec938883b0;
uint256 internal constant G2_ELEMENTS_1_Y1 = 0x04fc6369f7110fe3d25156c1bb9a72859cf2a04641f99ba4ee413c80da6a5fe4;
uint256 internal constant G2_ELEMENTS_1_Y2 = 0x22febda3c0c0632a56475b4214e5615e11e6dd3f96e6cea2854a87d4dacc5e55;
/// @notice Calculates a keccak256 hash of the runtime loaded verification keys.
/// @return vkHash The keccak256 hash of the loaded verification keys.
function verificationKeyHash() external pure returns (bytes32 vkHash) {
_loadVerificationKey();
assembly {
let start := VK_GATE_SETUP_0_X_SLOT
let end := VK_RECURSIVE_FLAG_SLOT
let length := add(sub(end, start), 0x20)
vkHash := keccak256(start, length)
}
}
/// @notice Load verification keys to memory in runtime.
/// @dev The constants are loaded into memory in a specific layout declared in the constants starting from
/// `VK_` prefix.
/// NOTE: Function may corrupt the memory state if some memory was used before this function was called.
/// The VK consists of commitments to setup polynomials:
/// [q_a], [q_b], [q_c], [q_d], - main gate setup commitments
/// [q_{d_next}], [q_ab], [q_ac], [q_const] /
/// [main_gate_selector], [custom_gate_selector] - gate selectors commitments
/// [sigma_0], [sigma_1], [sigma_2], [sigma_3] - permutation polynomials commitments
/// [lookup_selector] - lookup selector commitment
/// [col_0], [col_1], [col_2], [col_3] - lookup columns commitments
/// [table_type] - lookup table type commitment
function _loadVerificationKey() internal pure virtual {
assembly {
// gate setup commitments
mstore(VK_GATE_SETUP_0_X_SLOT, 0x236c54d6ae3745765605abfdd3d1533aaf27c583bbac66c43f5555e2b087db42)
mstore(VK_GATE_SETUP_0_Y_SLOT, 0x0b2b13c749c19a0be311c0eec76abddbc0848e2454cc7323605a714256ef101a)
mstore(VK_GATE_SETUP_1_X_SLOT, 0x04659caf7b05471ba5ba85b1ab62267aa6c456836e625f169f7119d55b9462d2)
mstore(VK_GATE_SETUP_1_Y_SLOT, 0x0ea63403692148d2ad22189a1e5420076312f4d46e62036a043a6b0b84d5b410)
mstore(VK_GATE_SETUP_2_X_SLOT, 0x0e6696d09d65fce1e42805be03fca1f14aea247281f688981f925e77d4ce2291)
mstore(VK_GATE_SETUP_2_Y_SLOT, 0x0228f6cf8fe20c1e07e5b78bf8c41d50e55975a126d22a198d1e56acd4bbb3dd)
mstore(VK_GATE_SETUP_3_X_SLOT, 0x14685dafe340b1dec5eafcd5e7faddaf24f3781ddc53309cc25d0b42c00541dd)
mstore(VK_GATE_SETUP_3_Y_SLOT, 0x0e651cff9447cb360198899b80fa23e89ec13bc94ff161729aa841d2b55ea5be)
mstore(VK_GATE_SETUP_4_X_SLOT, 0x16e9ef76cb68f2750eb0ee72382dd9911a982308d0ab10ef94dada13c382ae73)
mstore(VK_GATE_SETUP_4_Y_SLOT, 0x22e404bc91350f3bc7daad1d1025113742436983c85eac5ab7b42221a181b81e)
mstore(VK_GATE_SETUP_5_X_SLOT, 0x0d9b29613037a5025655c82b143d2b7449c98f3aea358307c8529249cc54f3b9)
mstore(VK_GATE_SETUP_5_Y_SLOT, 0x15b3c4c946ad1babfc4c03ff7c2423fd354af3a9305c499b7fb3aaebe2fee746)
mstore(VK_GATE_SETUP_6_X_SLOT, 0x08aa077804a60caf18621f96c63d7d1b532f44b13c273956f81b4c41f1f8f076)
mstore(VK_GATE_SETUP_6_Y_SLOT, 0x01fcb7c6e22aab56eb8b61bae6f457411bd41bcc5f1e8311421a98ccee23b72e)
mstore(VK_GATE_SETUP_7_X_SLOT, 0x283344a1ab3e55ecfd904d0b8e9f4faea338df5a4ead2fa9a42f0e103da40abc)
mstore(VK_GATE_SETUP_7_Y_SLOT, 0x223b37b83b9687512d322993edd70e508dd80adb10bcf7321a3cc8a44c269521)
// gate selectors commitments
mstore(VK_GATE_SELECTORS_0_X_SLOT, 0x1f67f0ba5f7e837bc680acb4e612ebd938ad35211aa6e05b96cad19e66b82d2d)
mstore(VK_GATE_SELECTORS_0_Y_SLOT, 0x2820641a84d2e8298ac2ac42bd4b912c0c37f768ecc83d3a29e7c720763d15a1)
mstore(VK_GATE_SELECTORS_1_X_SLOT, 0x0353257957562270292a17860ca8e8827703f828f440ee004848b1e23fdf9de2)
mstore(VK_GATE_SELECTORS_1_Y_SLOT, 0x305f4137fee253dff8b2bfe579038e8f25d5bd217865072af5d89fc8800ada24)
// permutation commitments
mstore(VK_PERMUTATION_0_X_SLOT, 0x13a600154b369ff3237706d00948e465ee1c32c7a6d3e18bccd9c4a15910f2e5)
mstore(VK_PERMUTATION_0_Y_SLOT, 0x138aa24fbf4cdddc75114811b3d59040394c218ecef3eb46ef9bd646f7e53776)
mstore(VK_PERMUTATION_1_X_SLOT, 0x277fff1f80c409357e2d251d79f6e3fd2164b755ce69cfd72de5c690289df662)
mstore(VK_PERMUTATION_1_Y_SLOT, 0x25235588e28c70eea3e35531c80deac25cd9b53ea3f98993f120108bc7abf670)
mstore(VK_PERMUTATION_2_X_SLOT, 0x0990e07a9b001048b947d0e5bd6157214c7359b771f01bf52bd771ba563a900e)
mstore(VK_PERMUTATION_2_Y_SLOT, 0x05e5fb090dd40914c8606d875e301167ae3047d684a02b44d9d36f1eaf43d0b4)
mstore(VK_PERMUTATION_3_X_SLOT, 0x1d4656690b33299db5631401a282afab3e16c78ee2c9ad9efea628171dcbc6bc)
mstore(VK_PERMUTATION_3_Y_SLOT, 0x0ebda2ebe582f601f813ec1e3970d13ef1500c742a85cce9b7f190f333de03b0)
// lookup tables commitments
mstore(VK_LOOKUP_TABLE_0_X_SLOT, 0x2c513ed74d9d57a5ec901e074032741036353a2c4513422e96e7b53b302d765b)
mstore(VK_LOOKUP_TABLE_0_Y_SLOT, 0x04dd964427e430f16004076d708c0cb21e225056cc1d57418cfbd3d472981468)
mstore(VK_LOOKUP_TABLE_1_X_SLOT, 0x1ea83e5e65c6f8068f4677e2911678cf329b28259642a32db1f14b8347828aac)
mstore(VK_LOOKUP_TABLE_1_Y_SLOT, 0x1d22bc884a2da4962a893ba8de13f57aaeb785ed52c5e686994839cab8f7475d)
mstore(VK_LOOKUP_TABLE_2_X_SLOT, 0x0b2e7212d0d9cff26d0bdf3d79b2cac029a25dfeb1cafdf49e2349d7db348d89)
mstore(VK_LOOKUP_TABLE_2_Y_SLOT, 0x1301f9b252419ea240eb67fda720ca0b16d92364027285f95e9b1349490fa283)
mstore(VK_LOOKUP_TABLE_3_X_SLOT, 0x02f7b99fdfa5b418548c2d777785820e02383cfc87e7085e280a375a358153bf)
mstore(VK_LOOKUP_TABLE_3_Y_SLOT, 0x09d004fe08dc4d19c382df36fad22ef676185663543703e6a4b40203e50fd8a6)
// lookup selector commitment
mstore(VK_LOOKUP_SELECTOR_X_SLOT, 0x2f4d347c7fb61daaadfff881e24f4b5dcfdc0d70a95bcb148168b90ef93e0007)
mstore(VK_LOOKUP_SELECTOR_Y_SLOT, 0x2322632465ba8e28cd0a4befd813ea85a972f4f6fa8e8603cf5d062dbcb14065)
// table type commitment
mstore(VK_LOOKUP_TABLE_TYPE_X_SLOT, 0x1e3c9fc98c118e4bc34f1f93d214a5d86898e980c40d8e2c180c6ada377a7467)
mstore(VK_LOOKUP_TABLE_TYPE_Y_SLOT, 0x2260a13535c35a15c173f5e5797d4b675b55d164a9995bfb7624971324bd84a8)
// flag for using recursive part
mstore(VK_RECURSIVE_FLAG_SLOT, 0)
}
}
/// @dev Verifies a zk-SNARK proof.
/// @return A boolean value indicating whether the zk-SNARK proof is valid.
/// Note: The function may revert execution instead of returning false in some cases.
function verify(
uint256[] calldata, // _publicInputs
uint256[] calldata, // _proof
uint256[] calldata // _recursiveAggregationInput
) external view returns (bool) {
// No memory was accessed yet, so keys can be loaded into the right place and not corrupt any other memory.
_loadVerificationKey();
// Begining of the big inline assembly block that makes all the verification work.
// Note: We use the custom memory layout, so the return value should be returned from the assembly, not
// Solidity code.
assembly {
/*//////////////////////////////////////////////////////////////
Utils
//////////////////////////////////////////////////////////////*/
/// @dev Reverts execution with a provided revert reason.
/// @param len The byte length of the error message string, which is expected to be no more than 32.
/// @param reason The 1-word revert reason string, encoded in ASCII.
function revertWithMessage(len, reason) {
// "Error(string)" signature: bytes32(bytes4(keccak256("Error(string)")))
mstore(0x00, 0x08c379a000000000000000000000000000000000000000000000000000000000)
// Data offset
mstore(0x04, 0x0000000000000000000000000000000000000000000000000000000000000020)
// Length of revert string
mstore(0x24, len)
// Revert reason
mstore(0x44, reason)
// Revert
revert(0x00, 0x64)
}
/// @dev Performs modular exponentiation using the formula (value ^ power) mod R_MOD.
function modexp(value, power) -> res {
mstore(0x00, 0x20)
mstore(0x20, 0x20)
mstore(0x40, 0x20)
mstore(0x60, value)
mstore(0x80, power)
mstore(0xa0, R_MOD)
if iszero(staticcall(gas(), 5, 0, 0xc0, 0x00, 0x20)) {
revertWithMessage(24, "modexp precompile failed")
}
res := mload(0x00)
}
/// @dev Performs a point multiplication operation and stores the result in a given memory destination.
function pointMulIntoDest(point, s, dest) {
mstore(0x00, mload(point))
mstore(0x20, mload(add(point, 0x20)))
mstore(0x40, s)
if iszero(staticcall(gas(), 7, 0, 0x60, dest, 0x40)) {
revertWithMessage(30, "pointMulIntoDest: ecMul failed")
}
}
/// @dev Performs a point addition operation and stores the result in a given memory destination.
function pointAddIntoDest(p1, p2, dest) {
mstore(0x00, mload(p1))
mstore(0x20, mload(add(p1, 0x20)))
mstore(0x40, mload(p2))
mstore(0x60, mload(add(p2, 0x20)))
if iszero(staticcall(gas(), 6, 0x00, 0x80, dest, 0x40)) {
revertWithMessage(30, "pointAddIntoDest: ecAdd failed")
}
}
/// @dev Performs a point subtraction operation and updates the first point with the result.
function pointSubAssign(p1, p2) {
mstore(0x00, mload(p1))
mstore(0x20, mload(add(p1, 0x20)))
mstore(0x40, mload(p2))
mstore(0x60, sub(Q_MOD, mload(add(p2, 0x20))))
if iszero(staticcall(gas(), 6, 0x00, 0x80, p1, 0x40)) {
revertWithMessage(28, "pointSubAssign: ecAdd failed")
}
}
/// @dev Performs a point addition operation and updates the first point with the result.
function pointAddAssign(p1, p2) {
mstore(0x00, mload(p1))
mstore(0x20, mload(add(p1, 0x20)))
mstore(0x40, mload(p2))
mstore(0x60, mload(add(p2, 0x20)))
if iszero(staticcall(gas(), 6, 0x00, 0x80, p1, 0x40)) {
revertWithMessage(28, "pointAddAssign: ecAdd failed")
}
}
/// @dev Performs a point multiplication operation and then adds the result to the destination point.
function pointMulAndAddIntoDest(point, s, dest) {
mstore(0x00, mload(point))
mstore(0x20, mload(add(point, 0x20)))
mstore(0x40, s)
let success := staticcall(gas(), 7, 0, 0x60, 0, 0x40)
mstore(0x40, mload(dest))
mstore(0x60, mload(add(dest, 0x20)))
success := and(success, staticcall(gas(), 6, 0x00, 0x80, dest, 0x40))
if iszero(success) {
revertWithMessage(22, "pointMulAndAddIntoDest")
}
}
/// @dev Negates an elliptic curve point by changing the sign of the y-coordinate.
function pointNegate(point) {
let pY := mload(add(point, 0x20))
switch pY
case 0 {
if mload(point) {
revertWithMessage(26, "pointNegate: invalid point")
}
}
default {
mstore(add(point, 0x20), sub(Q_MOD, pY))
}
}
/*//////////////////////////////////////////////////////////////
Transcript helpers
//////////////////////////////////////////////////////////////*/
/// @dev Updates the transcript state with a new challenge value.
function updateTranscript(value) {
mstore8(TRANSCRIPT_DST_BYTE_SLOT, 0x00)
mstore(TRANSCRIPT_CHALLENGE_SLOT, value)
let newState0 := keccak256(TRANSCRIPT_BEGIN_SLOT, 0x64)
mstore8(TRANSCRIPT_DST_BYTE_SLOT, 0x01)
let newState1 := keccak256(TRANSCRIPT_BEGIN_SLOT, 0x64)
mstore(TRANSCRIPT_STATE_1_SLOT, newState1)
mstore(TRANSCRIPT_STATE_0_SLOT, newState0)
}
/// @dev Retrieves a transcript challenge.
function getTranscriptChallenge(numberOfChallenge) -> challenge {
mstore8(TRANSCRIPT_DST_BYTE_SLOT, 0x02)
mstore(TRANSCRIPT_CHALLENGE_SLOT, shl(224, numberOfChallenge))
challenge := and(keccak256(TRANSCRIPT_BEGIN_SLOT, 0x48), FR_MASK)
}
/*//////////////////////////////////////////////////////////////
1. Load Proof
//////////////////////////////////////////////////////////////*/
/// @dev This function loads a zk-SNARK proof, ensures it's properly formatted, and stores it in memory.
/// It ensures the number of inputs and the elliptic curve point's validity.
/// Note: It does NOT reject inputs that exceed these module sizes, but rather wraps them within the
/// module bounds.
/// The proof consists of:
/// 1. Public input: (1 field element from F_r)
///
/// 2. Polynomial commitments (elliptic curve points over F_q):
/// [a], [b], [c], [d] - state polynomials commitments
/// [z_perm] - copy-permutation grand product commitment
/// [s] - polynomial for lookup argument commitment
/// [z_lookup] - lookup grand product commitment
/// [t_0], [t_1], [t_2], [t_3] - quotient polynomial parts commitments
/// [W], [W'] - proof openings commitments
///
/// 3. Polynomial evaluations at z and z*omega (field elements from F_r):
/// t(z) - quotient polynomial opening
/// a(z), b(z), c(z), d(z), d(z*omega) - state polynomials openings
/// main_gate_selector(z) - main gate selector opening
/// sigma_0(z), sigma_1(z), sigma_2(z) - permutation polynomials openings
/// z_perm(z*omega) - copy-permutation grand product opening
/// z_lookup(z*omega) - lookup grand product opening
/// lookup_selector(z) - lookup selector opening
/// s(x*omega), t(z*omega), table_type(z) - lookup argument polynomial openings
/// r(z) - linearisation polynomial opening
///
/// 4. Recursive proof (0 or 2 elliptic curve points over F_q)
function loadProof() {
// 1. Load public input
let offset := calldataload(0x04)
let publicInputLengthInWords := calldataload(add(offset, 0x04))
let isValid := eq(publicInputLengthInWords, 1) // We expect only one public input
mstore(PROOF_PUBLIC_INPUT, and(calldataload(add(offset, 0x24)), FR_MASK))
// 2. Load the proof (except for the recursive part)
offset := calldataload(0x24)
let proofLengthInWords := calldataload(add(offset, 0x04))
isValid := and(eq(proofLengthInWords, 44), isValid)
// PROOF_STATE_POLYS_0
{
let x := mod(calldataload(add(offset, 0x024)), Q_MOD)
let y := mod(calldataload(add(offset, 0x044)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_STATE_POLYS_0_X_SLOT, x)
mstore(PROOF_STATE_POLYS_0_Y_SLOT, y)
}
// PROOF_STATE_POLYS_1
{
let x := mod(calldataload(add(offset, 0x064)), Q_MOD)
let y := mod(calldataload(add(offset, 0x084)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_STATE_POLYS_1_X_SLOT, x)
mstore(PROOF_STATE_POLYS_1_Y_SLOT, y)
}
// PROOF_STATE_POLYS_2
{
let x := mod(calldataload(add(offset, 0x0a4)), Q_MOD)
let y := mod(calldataload(add(offset, 0x0c4)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_STATE_POLYS_2_X_SLOT, x)
mstore(PROOF_STATE_POLYS_2_Y_SLOT, y)
}
// PROOF_STATE_POLYS_3
{
let x := mod(calldataload(add(offset, 0x0e4)), Q_MOD)
let y := mod(calldataload(add(offset, 0x104)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_STATE_POLYS_3_X_SLOT, x)
mstore(PROOF_STATE_POLYS_3_Y_SLOT, y)
}
// PROOF_COPY_PERMUTATION_GRAND_PRODUCT
{
let x := mod(calldataload(add(offset, 0x124)), Q_MOD)
let y := mod(calldataload(add(offset, 0x144)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_X_SLOT, x)
mstore(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_Y_SLOT, y)
}
// PROOF_LOOKUP_S_POLY
{
let x := mod(calldataload(add(offset, 0x164)), Q_MOD)
let y := mod(calldataload(add(offset, 0x184)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_LOOKUP_S_POLY_X_SLOT, x)
mstore(PROOF_LOOKUP_S_POLY_Y_SLOT, y)
}
// PROOF_LOOKUP_GRAND_PRODUCT
{
let x := mod(calldataload(add(offset, 0x1a4)), Q_MOD)
let y := mod(calldataload(add(offset, 0x1c4)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_LOOKUP_GRAND_PRODUCT_X_SLOT, x)
mstore(PROOF_LOOKUP_GRAND_PRODUCT_Y_SLOT, y)
}
// PROOF_QUOTIENT_POLY_PARTS_0
{
let x := mod(calldataload(add(offset, 0x1e4)), Q_MOD)
let y := mod(calldataload(add(offset, 0x204)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_QUOTIENT_POLY_PARTS_0_X_SLOT, x)
mstore(PROOF_QUOTIENT_POLY_PARTS_0_Y_SLOT, y)
}
// PROOF_QUOTIENT_POLY_PARTS_1
{
let x := mod(calldataload(add(offset, 0x224)), Q_MOD)
let y := mod(calldataload(add(offset, 0x244)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_QUOTIENT_POLY_PARTS_1_X_SLOT, x)
mstore(PROOF_QUOTIENT_POLY_PARTS_1_Y_SLOT, y)
}
// PROOF_QUOTIENT_POLY_PARTS_2
{
let x := mod(calldataload(add(offset, 0x264)), Q_MOD)
let y := mod(calldataload(add(offset, 0x284)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_QUOTIENT_POLY_PARTS_2_X_SLOT, x)
mstore(PROOF_QUOTIENT_POLY_PARTS_2_Y_SLOT, y)
}
// PROOF_QUOTIENT_POLY_PARTS_3
{
let x := mod(calldataload(add(offset, 0x2a4)), Q_MOD)
let y := mod(calldataload(add(offset, 0x2c4)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_QUOTIENT_POLY_PARTS_3_X_SLOT, x)
mstore(PROOF_QUOTIENT_POLY_PARTS_3_Y_SLOT, y)
}
mstore(PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x2e4)), R_MOD))
mstore(PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x304)), R_MOD))
mstore(PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x324)), R_MOD))
mstore(PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x344)), R_MOD))
mstore(PROOF_STATE_POLYS_3_OPENING_AT_Z_OMEGA_SLOT, mod(calldataload(add(offset, 0x364)), R_MOD))
mstore(PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x384)), R_MOD))
mstore(PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x3a4)), R_MOD))
mstore(PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x3c4)), R_MOD))
mstore(PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x3e4)), R_MOD))
mstore(
PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT,
mod(calldataload(add(offset, 0x404)), R_MOD)
)
mstore(PROOF_LOOKUP_S_POLY_OPENING_AT_Z_OMEGA_SLOT, mod(calldataload(add(offset, 0x424)), R_MOD))
mstore(PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT, mod(calldataload(add(offset, 0x444)), R_MOD))
mstore(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x464)), R_MOD))
mstore(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_OMEGA_SLOT, mod(calldataload(add(offset, 0x484)), R_MOD))
mstore(PROOF_LOOKUP_SELECTOR_POLY_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x4a4)), R_MOD))
mstore(PROOF_LOOKUP_TABLE_TYPE_POLY_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x4c4)), R_MOD))
mstore(PROOF_QUOTIENT_POLY_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x4e4)), R_MOD))
mstore(PROOF_LINEARISATION_POLY_OPENING_AT_Z_SLOT, mod(calldataload(add(offset, 0x504)), R_MOD))
// PROOF_OPENING_PROOF_AT_Z
{
let x := mod(calldataload(add(offset, 0x524)), Q_MOD)
let y := mod(calldataload(add(offset, 0x544)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_OPENING_PROOF_AT_Z_X_SLOT, x)
mstore(PROOF_OPENING_PROOF_AT_Z_Y_SLOT, y)
}
// PROOF_OPENING_PROOF_AT_Z_OMEGA
{
let x := mod(calldataload(add(offset, 0x564)), Q_MOD)
let y := mod(calldataload(add(offset, 0x584)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_OPENING_PROOF_AT_Z_OMEGA_X_SLOT, x)
mstore(PROOF_OPENING_PROOF_AT_Z_OMEGA_Y_SLOT, y)
}
// 3. Load the recursive part of the proof
offset := calldataload(0x44)
let recursiveProofLengthInWords := calldataload(add(offset, 0x04))
switch mload(VK_RECURSIVE_FLAG_SLOT)
case 0 {
// recursive part should be empty
isValid := and(iszero(recursiveProofLengthInWords), isValid)
}
default {
// recursive part should be consist of 2 points
isValid := and(eq(recursiveProofLengthInWords, 4), isValid)
// PROOF_RECURSIVE_PART_P1
{
let x := mod(calldataload(add(offset, 0x024)), Q_MOD)
let y := mod(calldataload(add(offset, 0x044)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_RECURSIVE_PART_P1_X_SLOT, x)
mstore(PROOF_RECURSIVE_PART_P1_Y_SLOT, y)
}
// PROOF_RECURSIVE_PART_P2
{
let x := mod(calldataload(add(offset, 0x064)), Q_MOD)
let y := mod(calldataload(add(offset, 0x084)), Q_MOD)
let xx := mulmod(x, x, Q_MOD)
isValid := and(eq(mulmod(y, y, Q_MOD), addmod(mulmod(x, xx, Q_MOD), 3, Q_MOD)), isValid)
mstore(PROOF_RECURSIVE_PART_P2_X_SLOT, x)
mstore(PROOF_RECURSIVE_PART_P2_Y_SLOT, y)
}
}
// Revert if a proof is not valid
if iszero(isValid) {
revertWithMessage(27, "loadProof: Proof is invalid")
}
}
/*//////////////////////////////////////////////////////////////
2. Transcript initialization
//////////////////////////////////////////////////////////////*/
/// @notice Recomputes all challenges
/// @dev The process is the following:
/// Commit: PI, [a], [b], [c], [d]
/// Get: eta
/// Commit: [s]
/// Get: beta, gamma
/// Commit: [z_perm]
/// Get: beta', gamma'
/// Commit: [z_lookup]
/// Get: alpha
/// Commit: [t_0], [t_1], [t_2], [t_3]
/// Get: z
/// Commit: t(z), a(z), b(z), c(z), d(z), d(z*omega),
/// main_gate_selector(z),
/// sigma_0(z), sigma_1(z), sigma_2(z),
/// z_perm(z*omega),
/// t(z), lookup_selector(z), table_type(z),
/// s(x*omega), z_lookup(z*omega), t(z*omega),
/// r(z)
/// Get: v
/// Commit: [W], [W']
/// Get: u
function initializeTranscript() {
// Round 1
updateTranscript(mload(PROOF_PUBLIC_INPUT))
updateTranscript(mload(PROOF_STATE_POLYS_0_X_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_0_Y_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_1_X_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_1_Y_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_2_X_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_2_Y_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_3_X_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_3_Y_SLOT))
mstore(STATE_ETA_SLOT, getTranscriptChallenge(0))
// Round 1.5
updateTranscript(mload(PROOF_LOOKUP_S_POLY_X_SLOT))
updateTranscript(mload(PROOF_LOOKUP_S_POLY_Y_SLOT))
mstore(STATE_BETA_SLOT, getTranscriptChallenge(1))
mstore(STATE_GAMMA_SLOT, getTranscriptChallenge(2))
// Round 2
updateTranscript(mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_X_SLOT))
updateTranscript(mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_Y_SLOT))
mstore(STATE_BETA_LOOKUP_SLOT, getTranscriptChallenge(3))
mstore(STATE_GAMMA_LOOKUP_SLOT, getTranscriptChallenge(4))
// Round 2.5
updateTranscript(mload(PROOF_LOOKUP_GRAND_PRODUCT_X_SLOT))
updateTranscript(mload(PROOF_LOOKUP_GRAND_PRODUCT_Y_SLOT))
mstore(STATE_ALPHA_SLOT, getTranscriptChallenge(5))
// Round 3
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_0_X_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_0_Y_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_1_X_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_1_Y_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_2_X_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_2_Y_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_3_X_SLOT))
updateTranscript(mload(PROOF_QUOTIENT_POLY_PARTS_3_Y_SLOT))
{
let z := getTranscriptChallenge(6)
mstore(STATE_Z_SLOT, z)
mstore(STATE_Z_IN_DOMAIN_SIZE, modexp(z, DOMAIN_SIZE))
}
// Round 4
updateTranscript(mload(PROOF_QUOTIENT_POLY_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_OMEGA_SLOT))
updateTranscript(mload(PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT))
updateTranscript(mload(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_LOOKUP_SELECTOR_POLY_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_LOOKUP_TABLE_TYPE_POLY_OPENING_AT_Z_SLOT))
updateTranscript(mload(PROOF_LOOKUP_S_POLY_OPENING_AT_Z_OMEGA_SLOT))
updateTranscript(mload(PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT))
updateTranscript(mload(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_OMEGA_SLOT))
updateTranscript(mload(PROOF_LINEARISATION_POLY_OPENING_AT_Z_SLOT))
mstore(STATE_V_SLOT, getTranscriptChallenge(7))
// Round 5
updateTranscript(mload(PROOF_OPENING_PROOF_AT_Z_X_SLOT))
updateTranscript(mload(PROOF_OPENING_PROOF_AT_Z_Y_SLOT))
updateTranscript(mload(PROOF_OPENING_PROOF_AT_Z_OMEGA_X_SLOT))
updateTranscript(mload(PROOF_OPENING_PROOF_AT_Z_OMEGA_Y_SLOT))
mstore(STATE_U_SLOT, getTranscriptChallenge(8))
}
/*//////////////////////////////////////////////////////////////
3. Verifying quotient evaluation
//////////////////////////////////////////////////////////////*/
/// @notice Compute linearisation polynomial's constant term: r_0
/// @dev To save a verifier scalar multiplication, we split linearisation polynomial
/// into its constant and non-constant terms. The constant term is computed with the formula:
///
/// r_0 = alpha^0 * L_0(z) * PI * q_{main selector}(z) + r(z) -- main gate contribution
///
/// - alpha^4 * z_perm(z*omega)(sigma_0(z) * beta + gamma + a(z)) \
/// (sigma_1(z) * beta + gamma + b(z)) |
/// (sigma_2(z) * beta + gamma + c(z)) | - permutation contribution
/// (sigma_3(z) + gamma) |
/// - alpha^5 * L_0(z) /
///
/// + alpha^6 * (s(z*omega) * beta' + gamma' (beta' + 1)) \
/// * (z - omega^{n-1}) * z_lookup(z*omega) | - lookup contribution
/// - alpha^7 * L_0(z) |
/// - alpha^8 * L_{n-1}(z) * (gamma' (beta' + 1))^{n-1} /
///
/// In the end we should check that t(z)*Z_H(z) = r(z) + r_0!
function verifyQuotientEvaluation() {
// Compute power of alpha
{
let alpha := mload(STATE_ALPHA_SLOT)
let currentAlpha := mulmod(alpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_2_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_3_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_4_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_5_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_6_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_7_SLOT, currentAlpha)
currentAlpha := mulmod(currentAlpha, alpha, R_MOD)
mstore(STATE_POWER_OF_ALPHA_8_SLOT, currentAlpha)
}
// z
let stateZ := mload(STATE_Z_SLOT)
// L_0(z)
mstore(STATE_L_0_AT_Z_SLOT, evaluateLagrangePolyOutOfDomain(0, stateZ))
// L_{n-1}(z)
mstore(STATE_L_N_MINUS_ONE_AT_Z_SLOT, evaluateLagrangePolyOutOfDomain(sub(DOMAIN_SIZE, 1), stateZ))
// L_0(z) * PI
let stateT := mulmod(mload(STATE_L_0_AT_Z_SLOT), mload(PROOF_PUBLIC_INPUT), R_MOD)
// Compute main gate contribution
let result := mulmod(stateT, mload(PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT), R_MOD)
// Compute permutation contribution
result := addmod(result, permutationQuotientContribution(), R_MOD)
// Compute lookup contribution
result := addmod(result, lookupQuotientContribution(), R_MOD)
// Check that r(z) + r_0 = t(z) * Z_H(z)
result := addmod(mload(PROOF_LINEARISATION_POLY_OPENING_AT_Z_SLOT), result, R_MOD)
let vanishing := addmod(mload(STATE_Z_IN_DOMAIN_SIZE), sub(R_MOD, 1), R_MOD)
let lhs := mulmod(mload(PROOF_QUOTIENT_POLY_OPENING_AT_Z_SLOT), vanishing, R_MOD)
if iszero(eq(lhs, result)) {
revertWithMessage(27, "invalid quotient evaluation")
}
}
/// @notice Evaluating L_{polyNum}(at) out of domain
/// @dev L_i is a Lagrange polynomial for our domain such that:
/// L_i(omega^i) = 1 and L_i(omega^j) = 0 for all j != i
function evaluateLagrangePolyOutOfDomain(polyNum, at) -> res {
let omegaPower := 1
if polyNum {
omegaPower := modexp(OMEGA, polyNum)
}
res := addmod(modexp(at, DOMAIN_SIZE), sub(R_MOD, 1), R_MOD)
// Vanishing polynomial can not be zero at point `at`
if iszero(res) {
revertWithMessage(28, "invalid vanishing polynomial")
}
res := mulmod(res, omegaPower, R_MOD)
let denominator := addmod(at, sub(R_MOD, omegaPower), R_MOD)
denominator := mulmod(denominator, DOMAIN_SIZE, R_MOD)
denominator := modexp(denominator, sub(R_MOD, 2))
res := mulmod(res, denominator, R_MOD)
}
/// @notice Compute permutation contribution to linearisation polynomial's constant term
function permutationQuotientContribution() -> res {
// res = alpha^4 * z_perm(z*omega)
res := mulmod(
mload(STATE_POWER_OF_ALPHA_4_SLOT),
mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT),
R_MOD
)
{
let gamma := mload(STATE_GAMMA_SLOT)
let beta := mload(STATE_BETA_SLOT)
let factorMultiplier
{
// res *= sigma_0(z) * beta + gamma + a(z)
factorMultiplier := mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT), beta, R_MOD)
factorMultiplier := addmod(factorMultiplier, gamma, R_MOD)
factorMultiplier := addmod(
factorMultiplier,
mload(PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT),
R_MOD
)
res := mulmod(res, factorMultiplier, R_MOD)
}
{
// res *= sigma_1(z) * beta + gamma + b(z)
factorMultiplier := mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT), beta, R_MOD)
factorMultiplier := addmod(factorMultiplier, gamma, R_MOD)
factorMultiplier := addmod(
factorMultiplier,
mload(PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT),
R_MOD
)
res := mulmod(res, factorMultiplier, R_MOD)
}
{
// res *= sigma_2(z) * beta + gamma + c(z)
factorMultiplier := mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT), beta, R_MOD)
factorMultiplier := addmod(factorMultiplier, gamma, R_MOD)
factorMultiplier := addmod(
factorMultiplier,
mload(PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT),
R_MOD
)
res := mulmod(res, factorMultiplier, R_MOD)
}
// res *= sigma_3(z) + gamma
res := mulmod(res, addmod(mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT), gamma, R_MOD), R_MOD)
}
// res = -res
res := sub(R_MOD, res)
// -= L_0(z) * alpha^5
let l0AtZ := mload(STATE_L_0_AT_Z_SLOT)
l0AtZ := mulmod(l0AtZ, mload(STATE_POWER_OF_ALPHA_5_SLOT), R_MOD)
res := addmod(res, sub(R_MOD, l0AtZ), R_MOD)
}
/// @notice Compute lookup contribution to linearisation polynomial's constant term
function lookupQuotientContribution() -> res {
let betaLookup := mload(STATE_BETA_LOOKUP_SLOT)
let gammaLookup := mload(STATE_GAMMA_LOOKUP_SLOT)
let betaPlusOne := addmod(betaLookup, 1, R_MOD)
let betaGamma := mulmod(betaPlusOne, gammaLookup, R_MOD)
mstore(STATE_BETA_PLUS_ONE_SLOT, betaPlusOne)
mstore(STATE_BETA_GAMMA_PLUS_GAMMA_SLOT, betaGamma)
// res = alpha^6 * (s(z*omega) * beta' + gamma' (beta' + 1)) * z_lookup(z*omega)
res := mulmod(mload(PROOF_LOOKUP_S_POLY_OPENING_AT_Z_OMEGA_SLOT), betaLookup, R_MOD)
res := addmod(res, betaGamma, R_MOD)
res := mulmod(res, mload(PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT), R_MOD)
res := mulmod(res, mload(STATE_POWER_OF_ALPHA_6_SLOT), R_MOD)
// res *= z - omega^{n-1}
{
let lastOmega := modexp(OMEGA, sub(DOMAIN_SIZE, 1))
let zMinusLastOmega := addmod(mload(STATE_Z_SLOT), sub(R_MOD, lastOmega), R_MOD)
mstore(STATE_Z_MINUS_LAST_OMEGA_SLOT, zMinusLastOmega)
res := mulmod(res, zMinusLastOmega, R_MOD)
}
// res -= alpha^7 * L_{0}(z)
{
let intermediateValue := mulmod(
mload(STATE_L_0_AT_Z_SLOT),
mload(STATE_POWER_OF_ALPHA_7_SLOT),
R_MOD
)
res := addmod(res, sub(R_MOD, intermediateValue), R_MOD)
}
// res -= alpha^8 * L_{n-1}(z) * (gamma' (beta' + 1))^{n-1}
{
let lnMinusOneAtZ := mload(STATE_L_N_MINUS_ONE_AT_Z_SLOT)
let betaGammaPowered := modexp(betaGamma, sub(DOMAIN_SIZE, 1))
let alphaPower8 := mload(STATE_POWER_OF_ALPHA_8_SLOT)
let subtrahend := mulmod(mulmod(lnMinusOneAtZ, betaGammaPowered, R_MOD), alphaPower8, R_MOD)
res := addmod(res, sub(R_MOD, subtrahend), R_MOD)
}
}
/// @notice Compute main gate contribution to linearisation polynomial commitment multiplied by v
function mainGateLinearisationContributionWithV(
dest,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
) {
// += a(z) * [q_a]
pointMulIntoDest(VK_GATE_SETUP_0_X_SLOT, stateOpening0AtZ, dest)
// += b(z) * [q_b]
pointMulAndAddIntoDest(VK_GATE_SETUP_1_X_SLOT, stateOpening1AtZ, dest)
// += c(z) * [q_c]
pointMulAndAddIntoDest(VK_GATE_SETUP_2_X_SLOT, stateOpening2AtZ, dest)
// += d(z) * [q_d]
pointMulAndAddIntoDest(VK_GATE_SETUP_3_X_SLOT, stateOpening3AtZ, dest)
// += a(z) * b(z) * [q_ab]
pointMulAndAddIntoDest(VK_GATE_SETUP_4_X_SLOT, mulmod(stateOpening0AtZ, stateOpening1AtZ, R_MOD), dest)
// += a(z) * c(z) * [q_ac]
pointMulAndAddIntoDest(VK_GATE_SETUP_5_X_SLOT, mulmod(stateOpening0AtZ, stateOpening2AtZ, R_MOD), dest)
// += [q_const]
pointAddAssign(dest, VK_GATE_SETUP_6_X_SLOT)
// += d(z*omega) * [q_{d_next}]
pointMulAndAddIntoDest(VK_GATE_SETUP_7_X_SLOT, mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_OMEGA_SLOT), dest)
// *= v * main_gate_selector(z)
let coeff := mulmod(mload(PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT), mload(STATE_V_SLOT), R_MOD)
pointMulIntoDest(dest, coeff, dest)
}
/// @notice Compute custom gate contribution to linearisation polynomial commitment multiplied by v
function addAssignRescueCustomGateLinearisationContributionWithV(
dest,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
) {
let accumulator
let intermediateValue
// = alpha * (a(z)^2 - b(z))
accumulator := mulmod(stateOpening0AtZ, stateOpening0AtZ, R_MOD)
accumulator := addmod(accumulator, sub(R_MOD, stateOpening1AtZ), R_MOD)
accumulator := mulmod(accumulator, mload(STATE_ALPHA_SLOT), R_MOD)
// += alpha^2 * (b(z)^2 - c(z))
intermediateValue := mulmod(stateOpening1AtZ, stateOpening1AtZ, R_MOD)
intermediateValue := addmod(intermediateValue, sub(R_MOD, stateOpening2AtZ), R_MOD)
intermediateValue := mulmod(intermediateValue, mload(STATE_POWER_OF_ALPHA_2_SLOT), R_MOD)
accumulator := addmod(accumulator, intermediateValue, R_MOD)
// += alpha^3 * (c(z) * a(z) - d(z))
intermediateValue := mulmod(stateOpening2AtZ, stateOpening0AtZ, R_MOD)
intermediateValue := addmod(intermediateValue, sub(R_MOD, stateOpening3AtZ), R_MOD)
intermediateValue := mulmod(intermediateValue, mload(STATE_POWER_OF_ALPHA_3_SLOT), R_MOD)
accumulator := addmod(accumulator, intermediateValue, R_MOD)
// *= v * [custom_gate_selector]
accumulator := mulmod(accumulator, mload(STATE_V_SLOT), R_MOD)
pointMulAndAddIntoDest(VK_GATE_SELECTORS_1_X_SLOT, accumulator, dest)
}
/// @notice Compute copy-permutation contribution to linearisation polynomial commitment multiplied by v
function addAssignPermutationLinearisationContributionWithV(
dest,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
) {
// alpha^4
let factor := mload(STATE_POWER_OF_ALPHA_4_SLOT)
// Calculate the factor
{
// *= (a(z) + beta * z + gamma)
let zMulBeta := mulmod(mload(STATE_Z_SLOT), mload(STATE_BETA_SLOT), R_MOD)
let gamma := mload(STATE_GAMMA_SLOT)
let intermediateValue := addmod(addmod(zMulBeta, gamma, R_MOD), stateOpening0AtZ, R_MOD)
factor := mulmod(factor, intermediateValue, R_MOD)
// (b(z) + beta * z * k0 + gamma)
intermediateValue := addmod(
addmod(mulmod(zMulBeta, NON_RESIDUES_0, R_MOD), gamma, R_MOD),
stateOpening1AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
// (c(z) + beta * z * k1 + gamma)
intermediateValue := addmod(
addmod(mulmod(zMulBeta, NON_RESIDUES_1, R_MOD), gamma, R_MOD),
stateOpening2AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
// (d(z) + beta * z * k2 + gamma)
intermediateValue := addmod(
addmod(mulmod(zMulBeta, NON_RESIDUES_2, R_MOD), gamma, R_MOD),
stateOpening3AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
}
// += alpha^5 * L_0(z)
let l0AtZ := mload(STATE_L_0_AT_Z_SLOT)
factor := addmod(factor, mulmod(l0AtZ, mload(STATE_POWER_OF_ALPHA_5_SLOT), R_MOD), R_MOD)
// Here we can optimize one scalar multiplication by aggregating coefficients near [z_perm] during
// computing [F]
// We will sum them and add and make one scalar multiplication: (coeff1 + coeff2) * [z_perm]
factor := mulmod(factor, mload(STATE_V_SLOT), R_MOD)
mstore(COPY_PERMUTATION_FIRST_AGGREGATED_COMMITMENT_COEFF, factor)
// alpha^4 * beta * z_perm(z*omega)
factor := mulmod(mload(STATE_POWER_OF_ALPHA_4_SLOT), mload(STATE_BETA_SLOT), R_MOD)
factor := mulmod(factor, mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT), R_MOD)
{
// *= (a(z) + beta * sigma_0(z) + gamma)
let beta := mload(STATE_BETA_SLOT)
let gamma := mload(STATE_GAMMA_SLOT)
let intermediateValue := addmod(
addmod(
mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT), beta, R_MOD),
gamma,
R_MOD
),
stateOpening0AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
// *= (b(z) + beta * sigma_1(z) + gamma)
intermediateValue := addmod(
addmod(
mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT), beta, R_MOD),
gamma,
R_MOD
),
stateOpening1AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
// *= (c(z) + beta * sigma_2(z) + gamma)
intermediateValue := addmod(
addmod(
mulmod(mload(PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT), beta, R_MOD),
gamma,
R_MOD
),
stateOpening2AtZ,
R_MOD
)
factor := mulmod(factor, intermediateValue, R_MOD)
}
// *= v * [sigma_3]
factor := mulmod(factor, mload(STATE_V_SLOT), R_MOD)
pointMulIntoDest(VK_PERMUTATION_3_X_SLOT, factor, QUERIES_BUFFER_POINT_SLOT)
pointSubAssign(dest, QUERIES_BUFFER_POINT_SLOT)
}
/// @notice Compute lookup contribution to linearisation polynomial commitment multiplied by v
function addAssignLookupLinearisationContributionWithV(
dest,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ
) {
// alpha^6 * v * z_lookup(z*omega) * (z - omega^{n-1}) * [s]
let factor := mload(PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT)
factor := mulmod(factor, mload(STATE_POWER_OF_ALPHA_6_SLOT), R_MOD)
factor := mulmod(factor, mload(STATE_Z_MINUS_LAST_OMEGA_SLOT), R_MOD)
factor := mulmod(factor, mload(STATE_V_SLOT), R_MOD)
// Here we can optimize one scalar multiplication by aggregating coefficients near [s] during
// computing [F]
// We will sum them and add and make one scalar multiplication: (coeff1 + coeff2) * [s]
mstore(LOOKUP_S_FIRST_AGGREGATED_COMMITMENT_COEFF, factor)
// gamma(1 + beta) + t(x) + beta * t(x*omega)
factor := mload(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_OMEGA_SLOT)
factor := mulmod(factor, mload(STATE_BETA_LOOKUP_SLOT), R_MOD)
factor := addmod(factor, mload(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_SLOT), R_MOD)
factor := addmod(factor, mload(STATE_BETA_GAMMA_PLUS_GAMMA_SLOT), R_MOD)
// *= (gamma + f(z))
// We should use fact that f(x) =
// lookup_selector(x) * (a(x) + eta * b(x) + eta^2 * c(x) + eta^3 * table_type(x))
// to restore f(z)
let fReconstructed
{
fReconstructed := stateOpening0AtZ
let eta := mload(STATE_ETA_SLOT)
let currentEta := eta
fReconstructed := addmod(fReconstructed, mulmod(currentEta, stateOpening1AtZ, R_MOD), R_MOD)
currentEta := mulmod(currentEta, eta, R_MOD)
fReconstructed := addmod(fReconstructed, mulmod(currentEta, stateOpening2AtZ, R_MOD), R_MOD)
currentEta := mulmod(currentEta, eta, R_MOD)
// add type of table
fReconstructed := addmod(
fReconstructed,
mulmod(mload(PROOF_LOOKUP_TABLE_TYPE_POLY_OPENING_AT_Z_SLOT), currentEta, R_MOD),
R_MOD
)
fReconstructed := mulmod(fReconstructed, mload(PROOF_LOOKUP_SELECTOR_POLY_OPENING_AT_Z_SLOT), R_MOD)
fReconstructed := addmod(fReconstructed, mload(STATE_GAMMA_LOOKUP_SLOT), R_MOD)
}
// *= -alpha^6 * (beta + 1) * (z - omega^{n-1})
factor := mulmod(factor, fReconstructed, R_MOD)
factor := mulmod(factor, mload(STATE_BETA_PLUS_ONE_SLOT), R_MOD)
factor := sub(R_MOD, factor)
factor := mulmod(factor, mload(STATE_POWER_OF_ALPHA_6_SLOT), R_MOD)
factor := mulmod(factor, mload(STATE_Z_MINUS_LAST_OMEGA_SLOT), R_MOD)
// += alpha^7 * L_0(z)
factor := addmod(
factor,
mulmod(mload(STATE_L_0_AT_Z_SLOT), mload(STATE_POWER_OF_ALPHA_7_SLOT), R_MOD),
R_MOD
)
// += alpha^8 * L_{n-1}(z)
factor := addmod(
factor,
mulmod(mload(STATE_L_N_MINUS_ONE_AT_Z_SLOT), mload(STATE_POWER_OF_ALPHA_8_SLOT), R_MOD),
R_MOD
)
// Here we can optimize one scalar multiplication by aggregating coefficients near [z_lookup] during
// computing [F]
// We will sum them and add and make one scalar multiplication: (coeff1 + coeff2) * [z_lookup]
factor := mulmod(factor, mload(STATE_V_SLOT), R_MOD)
mstore(LOOKUP_GRAND_PRODUCT_FIRST_AGGREGATED_COMMITMENT_COEFF, factor)
}
/*//////////////////////////////////////////////////////////////
4. Prepare queries
//////////////////////////////////////////////////////////////*/
/// @dev Here we compute the first and second parts of batched polynomial commitment
/// We use the formula:
/// [D0] = [t_0] + z^n * [t_1] + z^{2n} * [t_2] + z^{3n} * [t_3]
/// and
/// [D1] = main_gate_selector(z) * ( \
/// a(z) * [q_a] + b(z) * [q_b] + c(z) * [q_c] + d(z) * [q_d] + | - main gate contribution
/// a(z) * b(z) * [q_ab] + a(z) * c(z) * [q_ac] + |
/// [q_const] + d(z*omega) * [q_{d_next}]) /
///
/// + alpha * [custom_gate_selector] * ( \
/// (a(z)^2 - b(z)) + | - custom gate contribution
/// (b(z)^2 - c(z)) * alpha + |
/// (a(z)*c(z) - d(z)) * alpha^2 ) /
///
/// + alpha^4 * [z_perm] * \
/// (a(z) + beta * z + gamma) * |
/// (b(z) + beta * z * k0 + gamma) * |
/// (c(z) + beta * z * k1 + gamma) * |
/// (d(z) + beta * z * k2 + gamma) | - permutation contribution
/// - alpha^4 * z_perm(z*omega) * beta * [sigma_3] * |
/// (a(z) + beta * sigma_0(z) + gamma) * |
/// (b(z) + beta * sigma_1(z) + gamma) * |
/// (c(z) + beta * sigma_2(z) + gamma) * |
/// + alpha^5 * L_0(z) * [z_perm] /
///
/// - alpha^6 * (1 + beta') * (gamma' + f(z)) * (z - omega^{n-1}) * \
/// (gamma'(1 + beta') + t(z) + beta' * t(z*omega)) * [z_lookup] |
/// + alpha^6 * z_lookup(z*omega) * (z - omega^{n-1}) * [s] | - lookup contribution
/// + alpha^7 * L_0(z) * [z_lookup] |
/// + alpha^8 * L_{n-1}(z) * [z_lookup] /
function prepareQueries() {
// Calculate [D0]
{
let zInDomainSize := mload(STATE_Z_IN_DOMAIN_SIZE)
let currentZ := zInDomainSize
mstore(QUERIES_AT_Z_0_X_SLOT, mload(PROOF_QUOTIENT_POLY_PARTS_0_X_SLOT))
mstore(QUERIES_AT_Z_0_Y_SLOT, mload(PROOF_QUOTIENT_POLY_PARTS_0_Y_SLOT))
pointMulAndAddIntoDest(PROOF_QUOTIENT_POLY_PARTS_1_X_SLOT, currentZ, QUERIES_AT_Z_0_X_SLOT)
currentZ := mulmod(currentZ, zInDomainSize, R_MOD)
pointMulAndAddIntoDest(PROOF_QUOTIENT_POLY_PARTS_2_X_SLOT, currentZ, QUERIES_AT_Z_0_X_SLOT)
currentZ := mulmod(currentZ, zInDomainSize, R_MOD)
pointMulAndAddIntoDest(PROOF_QUOTIENT_POLY_PARTS_3_X_SLOT, currentZ, QUERIES_AT_Z_0_X_SLOT)
}
// Calculate v * [D1]
// We are going to multiply all the points in the sum by v to save
// one scalar multiplication during [F] computation
{
let stateOpening0AtZ := mload(PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT)
let stateOpening1AtZ := mload(PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT)
let stateOpening2AtZ := mload(PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT)
let stateOpening3AtZ := mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT)
mainGateLinearisationContributionWithV(
QUERIES_AT_Z_1_X_SLOT,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
)
addAssignRescueCustomGateLinearisationContributionWithV(
QUERIES_AT_Z_1_X_SLOT,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
)
addAssignPermutationLinearisationContributionWithV(
QUERIES_AT_Z_1_X_SLOT,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ,
stateOpening3AtZ
)
addAssignLookupLinearisationContributionWithV(
QUERIES_AT_Z_1_X_SLOT,
stateOpening0AtZ,
stateOpening1AtZ,
stateOpening2AtZ
)
}
// Also we should restore [t] for future computations
// [t] = [col_0] + eta*[col_1] + eta^2*[col_2] + eta^3*[col_3]
{
mstore(QUERIES_T_POLY_AGGREGATED_X_SLOT, mload(VK_LOOKUP_TABLE_0_X_SLOT))
mstore(QUERIES_T_POLY_AGGREGATED_Y_SLOT, mload(VK_LOOKUP_TABLE_0_Y_SLOT))
let eta := mload(STATE_ETA_SLOT)
let currentEta := eta
pointMulAndAddIntoDest(VK_LOOKUP_TABLE_1_X_SLOT, currentEta, QUERIES_T_POLY_AGGREGATED_X_SLOT)
currentEta := mulmod(currentEta, eta, R_MOD)
pointMulAndAddIntoDest(VK_LOOKUP_TABLE_2_X_SLOT, currentEta, QUERIES_T_POLY_AGGREGATED_X_SLOT)
currentEta := mulmod(currentEta, eta, R_MOD)
pointMulAndAddIntoDest(VK_LOOKUP_TABLE_3_X_SLOT, currentEta, QUERIES_T_POLY_AGGREGATED_X_SLOT)
}
}
/*//////////////////////////////////////////////////////////////
5. Prepare aggregated commitment
//////////////////////////////////////////////////////////////*/
/// @dev Here we compute aggregated commitment for the final pairing
/// We use the formula:
/// [E] = ( t(z) + v * r(z)
/// + v^2*a(z) + v^3*b(z) + v^4*c(z) + v^5*d(z)
/// + v^6*main_gate_selector(z)
/// + v^7*sigma_0(z) + v^8*sigma_1(z) + v^9*sigma_2(z)
/// + v^10*t(z) + v^11*lookup_selector(z) + v^12*table_type(z)
/// + u * (v^13*z_perm(z*omega) + v^14*d(z*omega)
/// + v^15*s(z*omega) + v^16*z_lookup(z*omega) + v^17*t(z*omega)
/// )
/// ) * [1]
/// and
/// [F] = [D0] + v * [D1]
/// + v^2*[a] + v^3*[b] + v^4*[c] + v^5*[d]
/// + v^6*[main_gate_selector]
/// + v^7*[sigma_0] + v^8*[sigma_1] + v^9*[sigma_2]
/// + v^10*[t] + v^11*[lookup_selector] + v^12*[table_type]
/// + u * ( v^13*[z_perm] + v^14*[d]
/// + v^15*[s] + v^16*[z_lookup] + v^17*[t]
/// )
function prepareAggregatedCommitment() {
// Here we compute parts of [E] and [F] without u multiplier
let aggregationChallenge := 1
let firstDCoeff
let firstTCoeff
mstore(AGGREGATED_AT_Z_X_SLOT, mload(QUERIES_AT_Z_0_X_SLOT))
mstore(AGGREGATED_AT_Z_Y_SLOT, mload(QUERIES_AT_Z_0_Y_SLOT))
let aggregatedOpeningAtZ := mload(PROOF_QUOTIENT_POLY_OPENING_AT_Z_SLOT)
{
function updateAggregationChallenge(
queriesCommitmentPoint,
valueAtZ,
curAggregationChallenge,
curAggregatedOpeningAtZ
) -> newAggregationChallenge, newAggregatedOpeningAtZ {
newAggregationChallenge := mulmod(curAggregationChallenge, mload(STATE_V_SLOT), R_MOD)
pointMulAndAddIntoDest(queriesCommitmentPoint, newAggregationChallenge, AGGREGATED_AT_Z_X_SLOT)
newAggregatedOpeningAtZ := addmod(
curAggregatedOpeningAtZ,
mulmod(newAggregationChallenge, mload(valueAtZ), R_MOD),
R_MOD
)
}
// We don't need to multiply by v, because we have already computed v * [D1]
pointAddIntoDest(AGGREGATED_AT_Z_X_SLOT, QUERIES_AT_Z_1_X_SLOT, AGGREGATED_AT_Z_X_SLOT)
aggregationChallenge := mulmod(aggregationChallenge, mload(STATE_V_SLOT), R_MOD)
aggregatedOpeningAtZ := addmod(
aggregatedOpeningAtZ,
mulmod(aggregationChallenge, mload(PROOF_LINEARISATION_POLY_OPENING_AT_Z_SLOT), R_MOD),
R_MOD
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
PROOF_STATE_POLYS_0_X_SLOT,
PROOF_STATE_POLYS_0_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
PROOF_STATE_POLYS_1_X_SLOT,
PROOF_STATE_POLYS_1_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
PROOF_STATE_POLYS_2_X_SLOT,
PROOF_STATE_POLYS_2_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
// Here we can optimize one scalar multiplication by aggregating coefficients near [d]
// We will sum them and add and make one scalar multiplication: (coeff1 + coeff2) * [d]
aggregationChallenge := mulmod(aggregationChallenge, mload(STATE_V_SLOT), R_MOD)
firstDCoeff := aggregationChallenge
aggregatedOpeningAtZ := addmod(
aggregatedOpeningAtZ,
mulmod(aggregationChallenge, mload(PROOF_STATE_POLYS_3_OPENING_AT_Z_SLOT), R_MOD),
R_MOD
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_GATE_SELECTORS_0_X_SLOT,
PROOF_GATE_SELECTORS_0_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_PERMUTATION_0_X_SLOT,
PROOF_COPY_PERMUTATION_POLYS_0_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_PERMUTATION_1_X_SLOT,
PROOF_COPY_PERMUTATION_POLYS_1_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_PERMUTATION_2_X_SLOT,
PROOF_COPY_PERMUTATION_POLYS_2_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
// Here we can optimize one scalar multiplication by aggregating coefficients near [t]
// We will sum them and add and make one scalar multiplication: (coeff1 + coeff2) * [t]
aggregationChallenge := mulmod(aggregationChallenge, mload(STATE_V_SLOT), R_MOD)
firstTCoeff := aggregationChallenge
aggregatedOpeningAtZ := addmod(
aggregatedOpeningAtZ,
mulmod(aggregationChallenge, mload(PROOF_LOOKUP_T_POLY_OPENING_AT_Z_SLOT), R_MOD),
R_MOD
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_LOOKUP_SELECTOR_X_SLOT,
PROOF_LOOKUP_SELECTOR_POLY_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
aggregationChallenge, aggregatedOpeningAtZ := updateAggregationChallenge(
VK_LOOKUP_TABLE_TYPE_X_SLOT,
PROOF_LOOKUP_TABLE_TYPE_POLY_OPENING_AT_Z_SLOT,
aggregationChallenge,
aggregatedOpeningAtZ
)
}
mstore(AGGREGATED_OPENING_AT_Z_SLOT, aggregatedOpeningAtZ)
// Here we compute parts of [E] and [F] with u multiplier
aggregationChallenge := mulmod(aggregationChallenge, mload(STATE_V_SLOT), R_MOD)
let copyPermutationCoeff := addmod(
mload(COPY_PERMUTATION_FIRST_AGGREGATED_COMMITMENT_COEFF),
mulmod(aggregationChallenge, mload(STATE_U_SLOT), R_MOD),
R_MOD
)
pointMulIntoDest(
PROOF_COPY_PERMUTATION_GRAND_PRODUCT_X_SLOT,
copyPermutationCoeff,
AGGREGATED_AT_Z_OMEGA_X_SLOT
)
let aggregatedOpeningAtZOmega := mulmod(
mload(PROOF_COPY_PERMUTATION_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT),
aggregationChallenge,
R_MOD
)
{
function updateAggregationChallenge(
queriesCommitmentPoint,
valueAtZ_Omega,
previousCoeff,
curAggregationChallenge,
curAggregatedOpeningAtZ_Omega
) -> newAggregationChallenge, newAggregatedOpeningAtZ_Omega {
newAggregationChallenge := mulmod(curAggregationChallenge, mload(STATE_V_SLOT), R_MOD)
let finalCoeff := addmod(
previousCoeff,
mulmod(newAggregationChallenge, mload(STATE_U_SLOT), R_MOD),
R_MOD
)
pointMulAndAddIntoDest(queriesCommitmentPoint, finalCoeff, AGGREGATED_AT_Z_OMEGA_X_SLOT)
newAggregatedOpeningAtZ_Omega := addmod(
curAggregatedOpeningAtZ_Omega,
mulmod(newAggregationChallenge, mload(valueAtZ_Omega), R_MOD),
R_MOD
)
}
aggregationChallenge, aggregatedOpeningAtZOmega := updateAggregationChallenge(
PROOF_STATE_POLYS_3_X_SLOT,
PROOF_STATE_POLYS_3_OPENING_AT_Z_OMEGA_SLOT,
firstDCoeff,
aggregationChallenge,
aggregatedOpeningAtZOmega
)
aggregationChallenge, aggregatedOpeningAtZOmega := updateAggregationChallenge(
PROOF_LOOKUP_S_POLY_X_SLOT,
PROOF_LOOKUP_S_POLY_OPENING_AT_Z_OMEGA_SLOT,
mload(LOOKUP_S_FIRST_AGGREGATED_COMMITMENT_COEFF),
aggregationChallenge,
aggregatedOpeningAtZOmega
)
aggregationChallenge, aggregatedOpeningAtZOmega := updateAggregationChallenge(
PROOF_LOOKUP_GRAND_PRODUCT_X_SLOT,
PROOF_LOOKUP_GRAND_PRODUCT_OPENING_AT_Z_OMEGA_SLOT,
mload(LOOKUP_GRAND_PRODUCT_FIRST_AGGREGATED_COMMITMENT_COEFF),
aggregationChallenge,
aggregatedOpeningAtZOmega
)
aggregationChallenge, aggregatedOpeningAtZOmega := updateAggregationChallenge(
QUERIES_T_POLY_AGGREGATED_X_SLOT,
PROOF_LOOKUP_T_POLY_OPENING_AT_Z_OMEGA_SLOT,
firstTCoeff,
aggregationChallenge,
aggregatedOpeningAtZOmega
)
}
mstore(AGGREGATED_OPENING_AT_Z_OMEGA_SLOT, aggregatedOpeningAtZOmega)
// Now we can merge both parts and get [E] and [F]
let u := mload(STATE_U_SLOT)
// [F]
pointAddIntoDest(
AGGREGATED_AT_Z_X_SLOT,
AGGREGATED_AT_Z_OMEGA_X_SLOT,
PAIRING_PAIR_WITH_GENERATOR_X_SLOT
)
// [E] = (aggregatedOpeningAtZ + u * aggregatedOpeningAtZOmega) * [1]
let aggregatedValue := addmod(
mulmod(mload(AGGREGATED_OPENING_AT_Z_OMEGA_SLOT), u, R_MOD),
mload(AGGREGATED_OPENING_AT_Z_SLOT),
R_MOD
)
mstore(PAIRING_BUFFER_POINT_X_SLOT, 1)
mstore(PAIRING_BUFFER_POINT_Y_SLOT, 2)
pointMulIntoDest(PAIRING_BUFFER_POINT_X_SLOT, aggregatedValue, PAIRING_BUFFER_POINT_X_SLOT)
}
/*//////////////////////////////////////////////////////////////
5. Pairing
//////////////////////////////////////////////////////////////*/
/// @notice Checks the final pairing
/// @dev We should check the equation:
/// e([W] + u * [W'], [x]_2) = e(z * [W] + u * z * omega * [W'] + [F] - [E], [1]_2),
/// where [F] and [E] were computed previously
///
/// Also we need to check that e([P1], [x]_2) = e([P2], [1]_2)
/// if we have the recursive part of the proof
/// where [P1] and [P2] are parts of the recursive proof
///
/// We can aggregate both pairings into one for gas optimization:
/// e([W] + u * [W'] + u^2 * [P1], [x]_2) =
/// e(z * [W] + u * z * omega * [W'] + [F] - [E] + u^2 * [P2], [1]_2)
///
/// u is a valid challenge for such aggregation,
/// because [P1] and [P2] are used in PI
function finalPairing() {
let u := mload(STATE_U_SLOT)
let z := mload(STATE_Z_SLOT)
let zOmega := mulmod(mload(STATE_Z_SLOT), OMEGA, R_MOD)
// [F] - [E]
pointSubAssign(PAIRING_PAIR_WITH_GENERATOR_X_SLOT, PAIRING_BUFFER_POINT_X_SLOT)
// +z * [W] + u * z * omega * [W']
pointMulAndAddIntoDest(PROOF_OPENING_PROOF_AT_Z_X_SLOT, z, PAIRING_PAIR_WITH_GENERATOR_X_SLOT)
pointMulAndAddIntoDest(
PROOF_OPENING_PROOF_AT_Z_OMEGA_X_SLOT,
mulmod(zOmega, u, R_MOD),
PAIRING_PAIR_WITH_GENERATOR_X_SLOT
)
// [W] + u * [W']
mstore(PAIRING_PAIR_WITH_X_X_SLOT, mload(PROOF_OPENING_PROOF_AT_Z_X_SLOT))
mstore(PAIRING_PAIR_WITH_X_Y_SLOT, mload(PROOF_OPENING_PROOF_AT_Z_Y_SLOT))
pointMulAndAddIntoDest(PROOF_OPENING_PROOF_AT_Z_OMEGA_X_SLOT, u, PAIRING_PAIR_WITH_X_X_SLOT)
pointNegate(PAIRING_PAIR_WITH_X_X_SLOT)
// Add recursive proof part if needed
if mload(VK_RECURSIVE_FLAG_SLOT) {
let uu := mulmod(u, u, R_MOD)
pointMulAndAddIntoDest(PROOF_RECURSIVE_PART_P1_X_SLOT, uu, PAIRING_PAIR_WITH_GENERATOR_X_SLOT)
pointMulAndAddIntoDest(PROOF_RECURSIVE_PART_P2_X_SLOT, uu, PAIRING_PAIR_WITH_X_X_SLOT)
}
// Calculate pairing
{
mstore(0x000, mload(PAIRING_PAIR_WITH_GENERATOR_X_SLOT))
mstore(0x020, mload(PAIRING_PAIR_WITH_GENERATOR_Y_SLOT))
mstore(0x040, G2_ELEMENTS_0_X1)
mstore(0x060, G2_ELEMENTS_0_X2)
mstore(0x080, G2_ELEMENTS_0_Y1)
mstore(0x0a0, G2_ELEMENTS_0_Y2)
mstore(0x0c0, mload(PAIRING_PAIR_WITH_X_X_SLOT))
mstore(0x0e0, mload(PAIRING_PAIR_WITH_X_Y_SLOT))
mstore(0x100, G2_ELEMENTS_1_X1)
mstore(0x120, G2_ELEMENTS_1_X2)
mstore(0x140, G2_ELEMENTS_1_Y1)
mstore(0x160, G2_ELEMENTS_1_Y2)
let success := staticcall(gas(), 8, 0, 0x180, 0x00, 0x20)
if iszero(success) {
revertWithMessage(32, "finalPairing: precompile failure")
}
if iszero(mload(0)) {
revertWithMessage(29, "finalPairing: pairing failure")
}
}
}
/*//////////////////////////////////////////////////////////////
Verification
//////////////////////////////////////////////////////////////*/
// Step 1: Load the proof and check the correctness of its parts
loadProof()
// Step 2: Recompute all the challenges with the transcript
initializeTranscript()
// Step 3: Check the quotient equality
verifyQuotientEvaluation()
// Step 4: Compute queries [D0] and v * [D1]
prepareQueries()
// Step 5: Compute [E] and [F]
prepareAggregatedCommitment()
// Step 6: Check the final pairing with aggregated recursive proof
finalPairing()
mstore(0, true)
return(0, 32)
}
}
}pragma solidity 0.8.20;
// SPDX-License-Identifier: MIT
interface IVerifier {
function verify(
uint256[] calldata _publicInputs,
uint256[] calldata _proof,
uint256[] calldata _recursiveAggregationInput
) external view returns (bool);
function verificationKeyHash() external pure returns (bytes32);
}{
"optimizer": {
"enabled": true,
"runs": 9999999
},
"outputSelection": {
"*": {
"*": [
"evm.bytecode",
"evm.deployedBytecode",
"devdoc",
"userdoc",
"metadata",
"abi"
]
}
},
"evmVersion": "paris",
"libraries": {}
}Contract Security Audit
- No Contract Security Audit Submitted- Submit Audit Here
[{"inputs":[],"name":"verificationKeyHash","outputs":[{"internalType":"bytes32","name":"vkHash","type":"bytes32"}],"stateMutability":"pure","type":"function"},{"inputs":[{"internalType":"uint256[]","name":"","type":"uint256[]"},{"internalType":"uint256[]","name":"","type":"uint256[]"},{"internalType":"uint256[]","name":"","type":"uint256[]"}],"name":"verify","outputs":[{"internalType":"bool","name":"","type":"bool"}],"stateMutability":"view","type":"function"}]Contract Creation Code
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Multichain Portfolio | 30 Chains
| Chain | Token | Portfolio % | Price | Amount | Value |
|---|---|---|---|---|---|
| ZKSYNC | 100.00% | $3,118.13 | 0.00007 | $0.218269 |
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A contract address hosts a smart contract, which is a set of code stored on the blockchain that runs when predetermined conditions are met. Learn more about addresses in our Knowledge Base.