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pragma solidity ^0.8.13;

// SPDX-License-Identifier: MIT



import "./Plonk4VerifierWithAccessToDNext.sol";
import "../common/libraries/UncheckedMath.sol";

contract Verifier is Plonk4VerifierWithAccessToDNext {
    using UncheckedMath for uint256;

    function get_verification_key() public pure returns (VerificationKey memory vk) {
        vk.num_inputs = 1;
        vk.domain_size = 67108864;
        vk.omega = PairingsBn254.new_fr(0x1dba8b5bdd64ef6ce29a9039aca3c0e524395c43b9227b96c75090cc6cc7ec97);
        // coefficients
        vk.gate_setup_commitments[0] = PairingsBn254.new_g1(
            0x14c289d746e37aa82ec428491881c4732766492a8bc2e8e3cca2000a40c0ea27,
            0x2f617a7eb9808ad9843d1e080b7cfbf99d61bb1b02076c905f31adb12731bc41
        );
        vk.gate_setup_commitments[1] = PairingsBn254.new_g1(
            0x210b5cc8e6a85d63b65b701b8fb5ad24ff9c41f923432de17fe4ebae04526a8c,
            0x05c10ab17ea731b2b87fb890fa5b10bd3d6832917a616b807a9b640888ebc731
        );
        vk.gate_setup_commitments[2] = PairingsBn254.new_g1(
            0x29d4d14adcfe67a2ac690d6369db6b75e82d8ab3124bc4fa1dd145f41ca6949c,
            0x004f6cd229373f1c1f735ccf49aef6a5c32025bc36c3328596dd0db7d87bef67
        );
        vk.gate_setup_commitments[3] = PairingsBn254.new_g1(
            0x06d15382e8cabae9f98374a9fbdadd424f48e24da7e4c65bf710fd7d7d59a05a,
            0x22e438ad5c51673879ce17073a3d2d29327a97dc3ce61c4f88540e00087695f6
        );
        vk.gate_setup_commitments[4] = PairingsBn254.new_g1(
            0x274a668dfc485cf192d0086f214146d9e02b3040a5a586df344c53c16a87882b,
            0x15f5bb7ad01f162b70fc77c8ea456d67d15a6ce98acbbfd521222810f8ec0a66
        );
        vk.gate_setup_commitments[5] = PairingsBn254.new_g1(
            0x0ba53bf4fb0446927857e33978d02abf45948fc68f4091394ae0827a22cf1e47,
            0x0720d818751ce5b3f11c716e925f60df4679ea90bed516499bdec066f5ff108f
        );
        vk.gate_setup_commitments[6] = PairingsBn254.new_g1(
            0x2e986ba2ea495e5ec6af532980b1dc567f1430bfa82f8de07c12fc097c0e0483,
            0x1555d189f6164e82d78de1b8313c2e923e616b3c8ed0e350c3b61c94516d0b58
        );
        vk.gate_setup_commitments[7] = PairingsBn254.new_g1(
            0x0925959592604ca73c917f9b2e029aa2563c318ddcc5ca29c11badb7b880127b,
            0x2b4a430fcb2fa7d6d67d6c358e01cf0524c7df7e1e56442f65b39bc1a1052367
        );
        // gate selectors
        vk.gate_selectors_commitments[0] = PairingsBn254.new_g1(
            0x28f2a0a95af79ba67e9dd1986bd3190199f661b710a693fc82fb395c126edcbd,
            0x0db75db5de5192d1ba1c24710fc00da16fa8029ac7fe82d855674dcd6d090e05
        );
        vk.gate_selectors_commitments[1] = PairingsBn254.new_g1(
            0x143471a174dfcb2d9cb5ae621e519387bcc93c9dcfc011160b2f5c5f88e32cbe,
            0x2a0194c0224c3d964223a96c4c99e015719bc879125aa0df3f0715d154e71a31
        );
        // permutation
        vk.permutation_commitments[0] = PairingsBn254.new_g1(
            0x1423fa82e00ba22c280181afb12c56eea541933eeb5ec39119b0365b6beab4b9,
            0x0efdcd3423a38f5e2ecf8c7e4fd46f13189f8fed392ad9d8d393e8ba568b06e4
        );
        vk.permutation_commitments[1] = PairingsBn254.new_g1(
            0x0e9b5b12c1090d62224e64aa1696c009aa59a9c3eec458e781fae773e1f4eca5,
            0x1fe3df508c7e9750eb37d9cae5e7437ad11a21fa36530ff821b407b165a79a55
        );
        vk.permutation_commitments[2] = PairingsBn254.new_g1(
            0x25d1a714bd1e258f196e38d6b2826153382c2d04b870d0b7ec250296005129ae,
            0x0883a121b41ca7beaa9de97ecf4417e62aa2eeb9434f24ddacbfed57cbf016a8
        );
        vk.permutation_commitments[3] = PairingsBn254.new_g1(
            0x2f3ede68e854a6b3b14589851cf077a606e2aeb3205c43cc579b7abae39d8f58,
            0x178ccd4b1f78fd79ee248e376b6fc8297d5450900d1e15e8c03e3ed2c171ac8c
        );
        // lookup table commitments
        vk.lookup_selector_commitment = PairingsBn254.new_g1(
            0x1f814e2d87c332e964eeef94ec695eef9d2caaac58b682a43da5107693b06f30,
            0x196d56fb01907e66af9303886fd95328d398e5b2b72906882a9d12c1718e2ee2
        );
        vk.lookup_tables_commitments[0] = PairingsBn254.new_g1(
            0x0ebe0de4a2f39df3b903da484c1641ffdffb77ff87ce4f9508c548659eb22d3c,
            0x12a3209440242d5662729558f1017ed9dcc08fe49a99554dd45f5f15da5e4e0b
        );
        vk.lookup_tables_commitments[1] = PairingsBn254.new_g1(
            0x1b7d54f8065ca63bed0bfbb9280a1011b886d07e0c0a26a66ecc96af68c53bf9,
            0x2c51121fff5b8f58c302f03c74e0cb176ae5a1d1730dec4696eb9cce3fe284ca
        );
        vk.lookup_tables_commitments[2] = PairingsBn254.new_g1(
            0x0138733c5faa9db6d4b8df9748081e38405999e511fb22d40f77cf3aef293c44,
            0x269bee1c1ac28053238f7fe789f1ea2e481742d6d16ae78ed81e87c254af0765
        );
        vk.lookup_tables_commitments[3] = PairingsBn254.new_g1(
            0x1b1be7279d59445065a95f01f16686adfa798ec4f1e6845ffcec9b837e88372e,
            0x057c90cb96d8259238ed86b05f629efd55f472a721efeeb56926e979433e6c0e
        );
        vk.lookup_table_type_commitment = PairingsBn254.new_g1(
            0x2f85df2d6249ccbcc11b91727333cc800459de6ee274f29c657c8d56f6f01563,
            0x088e1df178c47116a69c3c8f6d0c5feb530e2a72493694a623b1cceb7d44a76c
        );
        // non residues
        vk.non_residues[0] = PairingsBn254.new_fr(0x0000000000000000000000000000000000000000000000000000000000000005);
        vk.non_residues[1] = PairingsBn254.new_fr(0x0000000000000000000000000000000000000000000000000000000000000007);
        vk.non_residues[2] = PairingsBn254.new_fr(0x000000000000000000000000000000000000000000000000000000000000000a);

        // g2 elements
        vk.g2_elements[0] = PairingsBn254.new_g2(
            [
                0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2,
                0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed
            ],
            [
                0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b,
                0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa
            ]
        );
        vk.g2_elements[1] = PairingsBn254.new_g2(
            [
                0x260e01b251f6f1c7e7ff4e580791dee8ea51d87a358e038b4efe30fac09383c1,
                0x0118c4d5b837bcc2bc89b5b398b5974e9f5944073b32078b7e231fec938883b0
            ],
            [
                0x04fc6369f7110fe3d25156c1bb9a72859cf2a04641f99ba4ee413c80da6a5fe4,
                0x22febda3c0c0632a56475b4214e5615e11e6dd3f96e6cea2854a87d4dacc5e55
            ]
        );
    }

    function deserialize_proof(uint256[] calldata public_inputs, uint256[] calldata serialized_proof)
        internal
        pure
        returns (Proof memory proof)
    {
        require(serialized_proof.length == 44);
        proof.input_values = new uint256[](public_inputs.length);
        for (uint256 i = 0; i < public_inputs.length; i = i.uncheckedInc()) {
            proof.input_values[i] = public_inputs[i];
        }

        uint256 j;
        for (uint256 i = 0; i < STATE_WIDTH; i = i.uncheckedInc()) {
            proof.state_polys_commitments[i] = PairingsBn254.new_g1_checked(
                serialized_proof[j],
                serialized_proof[j.uncheckedInc()]
            );

            j = j.uncheckedAdd(2);
        }
        proof.copy_permutation_grand_product_commitment = PairingsBn254.new_g1_checked(
            serialized_proof[j],
            serialized_proof[j.uncheckedInc()]
        );
        j = j.uncheckedAdd(2);

        proof.lookup_s_poly_commitment = PairingsBn254.new_g1_checked(
            serialized_proof[j],
            serialized_proof[j.uncheckedInc()]
        );
        j = j.uncheckedAdd(2);

        proof.lookup_grand_product_commitment = PairingsBn254.new_g1_checked(
            serialized_proof[j],
            serialized_proof[j.uncheckedInc()]
        );
        j = j.uncheckedAdd(2);
        for (uint256 i = 0; i < proof.quotient_poly_parts_commitments.length; i = i.uncheckedInc()) {
            proof.quotient_poly_parts_commitments[i] = PairingsBn254.new_g1_checked(
                serialized_proof[j],
                serialized_proof[j.uncheckedInc()]
            );
            j = j.uncheckedAdd(2);
        }

        for (uint256 i = 0; i < proof.state_polys_openings_at_z.length; i = i.uncheckedInc()) {
            proof.state_polys_openings_at_z[i] = PairingsBn254.new_fr(serialized_proof[j]);

            j = j.uncheckedInc();
        }

        for (uint256 i = 0; i < proof.state_polys_openings_at_z_omega.length; i = i.uncheckedInc()) {
            proof.state_polys_openings_at_z_omega[i] = PairingsBn254.new_fr(serialized_proof[j]);

            j = j.uncheckedInc();
        }
        for (uint256 i = 0; i < proof.gate_selectors_openings_at_z.length; i = i.uncheckedInc()) {
            proof.gate_selectors_openings_at_z[i] = PairingsBn254.new_fr(serialized_proof[j]);

            j = j.uncheckedInc();
        }
        for (uint256 i = 0; i < proof.copy_permutation_polys_openings_at_z.length; i = i.uncheckedInc()) {
            proof.copy_permutation_polys_openings_at_z[i] = PairingsBn254.new_fr(serialized_proof[j]);

            j = j.uncheckedInc();
        }
        proof.copy_permutation_grand_product_opening_at_z_omega = PairingsBn254.new_fr(serialized_proof[j]);

        j = j.uncheckedInc();
        proof.lookup_s_poly_opening_at_z_omega = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.lookup_grand_product_opening_at_z_omega = PairingsBn254.new_fr(serialized_proof[j]);

        j = j.uncheckedInc();
        proof.lookup_t_poly_opening_at_z = PairingsBn254.new_fr(serialized_proof[j]);

        j = j.uncheckedInc();
        proof.lookup_t_poly_opening_at_z_omega = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.lookup_selector_poly_opening_at_z = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.lookup_table_type_poly_opening_at_z = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.quotient_poly_opening_at_z = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.linearization_poly_opening_at_z = PairingsBn254.new_fr(serialized_proof[j]);
        j = j.uncheckedInc();
        proof.opening_proof_at_z = PairingsBn254.new_g1_checked(
            serialized_proof[j],
            serialized_proof[j.uncheckedInc()]
        );
        j = j.uncheckedAdd(2);
        proof.opening_proof_at_z_omega = PairingsBn254.new_g1_checked(
            serialized_proof[j],
            serialized_proof[j.uncheckedInc()]
        );
    }

    function verify_serialized_proof(uint256[] calldata public_inputs, uint256[] calldata serialized_proof)
        public
        view
        returns (bool)
    {
        VerificationKey memory vk = get_verification_key();
        require(vk.num_inputs == public_inputs.length);

        Proof memory proof = deserialize_proof(public_inputs, serialized_proof);

        return verify(proof, vk);
    }
}

pragma solidity ^0.8.13;

// SPDX-License-Identifier: MIT



library UncheckedMath {
    function uncheckedInc(uint256 _number) internal pure returns (uint256) {
        unchecked {
            return _number + 1;
        }
    }

    function uncheckedAdd(uint256 _lhs, uint256 _rhs) internal pure returns (uint256) {
        unchecked {
            return _lhs + _rhs;
        }
    }
}

pragma solidity ^0.8.13;

// SPDX-License-Identifier: MIT



import "./libraries/PairingsBn254.sol";
import "./libraries/TranscriptLib.sol";
import "../common/libraries/UncheckedMath.sol";

uint256 constant STATE_WIDTH = 4;
uint256 constant NUM_G2_ELS = 2;

struct VerificationKey {
    uint256 domain_size;
    uint256 num_inputs;
    PairingsBn254.Fr omega;
    PairingsBn254.G1Point[2] gate_selectors_commitments;
    PairingsBn254.G1Point[8] gate_setup_commitments;
    PairingsBn254.G1Point[STATE_WIDTH] permutation_commitments;
    PairingsBn254.G1Point lookup_selector_commitment;
    PairingsBn254.G1Point[4] lookup_tables_commitments;
    PairingsBn254.G1Point lookup_table_type_commitment;
    PairingsBn254.Fr[STATE_WIDTH - 1] non_residues;
    PairingsBn254.G2Point[NUM_G2_ELS] g2_elements;
}

contract Plonk4VerifierWithAccessToDNext {
    using PairingsBn254 for PairingsBn254.G1Point;
    using PairingsBn254 for PairingsBn254.G2Point;
    using PairingsBn254 for PairingsBn254.Fr;

    using TranscriptLib for TranscriptLib.Transcript;

    using UncheckedMath for uint256;

    struct Proof {
        uint256[] input_values;
        // commitments
        PairingsBn254.G1Point[STATE_WIDTH] state_polys_commitments;
        PairingsBn254.G1Point copy_permutation_grand_product_commitment;
        PairingsBn254.G1Point[STATE_WIDTH] quotient_poly_parts_commitments;
        // openings
        PairingsBn254.Fr[STATE_WIDTH] state_polys_openings_at_z;
        PairingsBn254.Fr[1] state_polys_openings_at_z_omega;
        PairingsBn254.Fr[1] gate_selectors_openings_at_z;
        PairingsBn254.Fr[STATE_WIDTH - 1] copy_permutation_polys_openings_at_z;
        PairingsBn254.Fr copy_permutation_grand_product_opening_at_z_omega;
        PairingsBn254.Fr quotient_poly_opening_at_z;
        PairingsBn254.Fr linearization_poly_opening_at_z;
        // lookup commitments
        PairingsBn254.G1Point lookup_s_poly_commitment;
        PairingsBn254.G1Point lookup_grand_product_commitment;
        // lookup openings
        PairingsBn254.Fr lookup_s_poly_opening_at_z_omega;
        PairingsBn254.Fr lookup_grand_product_opening_at_z_omega;
        PairingsBn254.Fr lookup_t_poly_opening_at_z;
        PairingsBn254.Fr lookup_t_poly_opening_at_z_omega;
        PairingsBn254.Fr lookup_selector_poly_opening_at_z;
        PairingsBn254.Fr lookup_table_type_poly_opening_at_z;
        PairingsBn254.G1Point opening_proof_at_z;
        PairingsBn254.G1Point opening_proof_at_z_omega;
    }

    struct PartialVerifierState {
        PairingsBn254.Fr zero;
        PairingsBn254.Fr alpha;
        PairingsBn254.Fr beta;
        PairingsBn254.Fr gamma;
        PairingsBn254.Fr[9] alpha_values;
        PairingsBn254.Fr eta;
        PairingsBn254.Fr beta_lookup;
        PairingsBn254.Fr gamma_lookup;
        PairingsBn254.Fr beta_plus_one;
        PairingsBn254.Fr beta_gamma;
        PairingsBn254.Fr v;
        PairingsBn254.Fr u;
        PairingsBn254.Fr z;
        PairingsBn254.Fr z_omega;
        PairingsBn254.Fr z_minus_last_omega;
        PairingsBn254.Fr l_0_at_z;
        PairingsBn254.Fr l_n_minus_one_at_z;
        PairingsBn254.Fr t;
        PairingsBn254.G1Point tp;
    }

    function evaluate_l0_at_point(uint256 domain_size, PairingsBn254.Fr memory at)
        internal
        view
        returns (PairingsBn254.Fr memory num)
    {
        PairingsBn254.Fr memory one = PairingsBn254.new_fr(1);

        PairingsBn254.Fr memory size_fe = PairingsBn254.new_fr(domain_size);
        PairingsBn254.Fr memory den = at.copy();
        den.sub_assign(one);
        den.mul_assign(size_fe);

        den = den.inverse();

        num = at.pow(domain_size);
        num.sub_assign(one);
        num.mul_assign(den);
    }

    function evaluate_lagrange_poly_out_of_domain(
        uint256 poly_num,
        uint256 domain_size,
        PairingsBn254.Fr memory omega,
        PairingsBn254.Fr memory at
    ) internal view returns (PairingsBn254.Fr memory res) {
        // (omega^i / N) / (X - omega^i) * (X^N - 1)
        require(poly_num < domain_size);
        PairingsBn254.Fr memory one = PairingsBn254.new_fr(1);
        PairingsBn254.Fr memory omega_power = omega.pow(poly_num);
        res = at.pow(domain_size);
        res.sub_assign(one);
        require(res.value != 0); // Vanishing polynomial can not be zero at point `at`
        res.mul_assign(omega_power);

        PairingsBn254.Fr memory den = PairingsBn254.copy(at);
        den.sub_assign(omega_power);
        den.mul_assign(PairingsBn254.new_fr(domain_size));

        den = den.inverse();

        res.mul_assign(den);
    }

    function evaluate_vanishing(uint256 domain_size, PairingsBn254.Fr memory at)
        internal
        view
        returns (PairingsBn254.Fr memory res)
    {
        res = at.pow(domain_size);
        res.sub_assign(PairingsBn254.new_fr(1));
    }

    function initialize_transcript(Proof memory proof, VerificationKey memory vk)
        internal
        pure
        returns (PartialVerifierState memory state)
    {
        TranscriptLib.Transcript memory transcript = TranscriptLib.new_transcript();

        for (uint256 i = 0; i < vk.num_inputs; i = i.uncheckedInc()) {
            transcript.update_with_u256(proof.input_values[i]);
        }

        for (uint256 i = 0; i < STATE_WIDTH; i = i.uncheckedInc()) {
            transcript.update_with_g1(proof.state_polys_commitments[i]);
        }

        state.eta = transcript.get_challenge();
        transcript.update_with_g1(proof.lookup_s_poly_commitment);

        state.beta = transcript.get_challenge();
        state.gamma = transcript.get_challenge();

        transcript.update_with_g1(proof.copy_permutation_grand_product_commitment);
        state.beta_lookup = transcript.get_challenge();
        state.gamma_lookup = transcript.get_challenge();
        transcript.update_with_g1(proof.lookup_grand_product_commitment);
        state.alpha = transcript.get_challenge();

        for (uint256 i = 0; i < proof.quotient_poly_parts_commitments.length; i = i.uncheckedInc()) {
            transcript.update_with_g1(proof.quotient_poly_parts_commitments[i]);
        }
        state.z = transcript.get_challenge();

        transcript.update_with_fr(proof.quotient_poly_opening_at_z);

        for (uint256 i = 0; i < proof.state_polys_openings_at_z.length; i = i.uncheckedInc()) {
            transcript.update_with_fr(proof.state_polys_openings_at_z[i]);
        }

        for (uint256 i = 0; i < proof.state_polys_openings_at_z_omega.length; i = i.uncheckedInc()) {
            transcript.update_with_fr(proof.state_polys_openings_at_z_omega[i]);
        }
        for (uint256 i = 0; i < proof.gate_selectors_openings_at_z.length; i = i.uncheckedInc()) {
            transcript.update_with_fr(proof.gate_selectors_openings_at_z[i]);
        }
        for (uint256 i = 0; i < proof.copy_permutation_polys_openings_at_z.length; i = i.uncheckedInc()) {
            transcript.update_with_fr(proof.copy_permutation_polys_openings_at_z[i]);
        }

        state.z_omega = state.z.copy();
        state.z_omega.mul_assign(vk.omega);

        transcript.update_with_fr(proof.copy_permutation_grand_product_opening_at_z_omega);

        transcript.update_with_fr(proof.lookup_t_poly_opening_at_z);
        transcript.update_with_fr(proof.lookup_selector_poly_opening_at_z);
        transcript.update_with_fr(proof.lookup_table_type_poly_opening_at_z);
        transcript.update_with_fr(proof.lookup_s_poly_opening_at_z_omega);
        transcript.update_with_fr(proof.lookup_grand_product_opening_at_z_omega);
        transcript.update_with_fr(proof.lookup_t_poly_opening_at_z_omega);
        transcript.update_with_fr(proof.linearization_poly_opening_at_z);

        state.v = transcript.get_challenge();

        transcript.update_with_g1(proof.opening_proof_at_z);
        transcript.update_with_g1(proof.opening_proof_at_z_omega);

        state.u = transcript.get_challenge();
    }

    // compute some powers of challenge alpha([alpha^1, .. alpha^8])
    function compute_powers_of_alpha(PartialVerifierState memory state) public pure {
        require(state.alpha.value != 0);
        state.alpha_values[0] = PairingsBn254.new_fr(1);
        state.alpha_values[1] = state.alpha.copy();
        PairingsBn254.Fr memory current_alpha = state.alpha.copy();
        for (uint256 i = 2; i < state.alpha_values.length; i = i.uncheckedInc()) {
            current_alpha.mul_assign(state.alpha);
            state.alpha_values[i] = current_alpha.copy();
        }
    }

    function verify(Proof memory proof, VerificationKey memory vk) internal view returns (bool) {
        // we initialize all challenges beforehand, we can draw each challenge in its own place
        PartialVerifierState memory state = initialize_transcript(proof, vk);
        if (verify_quotient_evaluation(vk, proof, state) == false) {
            return false;
        }
        require(proof.state_polys_openings_at_z_omega.length == 1);

        PairingsBn254.G1Point memory quotient_result = proof.quotient_poly_parts_commitments[0].copy_g1();
        {
            // block scope
            PairingsBn254.Fr memory z_in_domain_size = state.z.pow(vk.domain_size);
            PairingsBn254.Fr memory current_z = z_in_domain_size.copy();
            PairingsBn254.G1Point memory tp;
            // start from i =1
            for (uint256 i = 1; i < proof.quotient_poly_parts_commitments.length; i = i.uncheckedInc()) {
                tp = proof.quotient_poly_parts_commitments[i].copy_g1();
                tp.point_mul_assign(current_z);
                quotient_result.point_add_assign(tp);

                current_z.mul_assign(z_in_domain_size);
            }
        }

        Queries memory queries = prepare_queries(vk, proof, state);
        queries.commitments_at_z[0] = quotient_result;
        queries.values_at_z[0] = proof.quotient_poly_opening_at_z;
        queries.commitments_at_z[1] = aggregated_linearization_commitment(vk, proof, state);
        queries.values_at_z[1] = proof.linearization_poly_opening_at_z;

        require(queries.commitments_at_z.length == queries.values_at_z.length);

        PairingsBn254.G1Point memory aggregated_commitment_at_z = queries.commitments_at_z[0];

        PairingsBn254.Fr memory aggregated_opening_at_z = queries.values_at_z[0];
        PairingsBn254.Fr memory aggregation_challenge = PairingsBn254.new_fr(1);
        PairingsBn254.G1Point memory scaled;
        for (uint256 i = 1; i < queries.commitments_at_z.length; i = i.uncheckedInc()) {
            aggregation_challenge.mul_assign(state.v);
            scaled = queries.commitments_at_z[i].point_mul(aggregation_challenge);
            aggregated_commitment_at_z.point_add_assign(scaled);

            state.t = queries.values_at_z[i];
            state.t.mul_assign(aggregation_challenge);
            aggregated_opening_at_z.add_assign(state.t);
        }

        aggregation_challenge.mul_assign(state.v);

        PairingsBn254.G1Point memory aggregated_commitment_at_z_omega = queries.commitments_at_z_omega[0].point_mul(
            aggregation_challenge
        );
        PairingsBn254.Fr memory aggregated_opening_at_z_omega = queries.values_at_z_omega[0];
        aggregated_opening_at_z_omega.mul_assign(aggregation_challenge);
        for (uint256 i = 1; i < queries.commitments_at_z_omega.length; i = i.uncheckedInc()) {
            aggregation_challenge.mul_assign(state.v);

            scaled = queries.commitments_at_z_omega[i].point_mul(aggregation_challenge);
            aggregated_commitment_at_z_omega.point_add_assign(scaled);

            state.t = queries.values_at_z_omega[i];
            state.t.mul_assign(aggregation_challenge);
            aggregated_opening_at_z_omega.add_assign(state.t);
        }

        return
            final_pairing(
                vk.g2_elements,
                proof,
                state,
                aggregated_commitment_at_z,
                aggregated_commitment_at_z_omega,
                aggregated_opening_at_z,
                aggregated_opening_at_z_omega
            );
    }

    function verify_quotient_evaluation(
        VerificationKey memory vk,
        Proof memory proof,
        PartialVerifierState memory state
    ) internal view returns (bool) {
        uint256[] memory lagrange_poly_numbers = new uint256[](vk.num_inputs);
        for (uint256 i = 0; i < lagrange_poly_numbers.length; i = i.uncheckedInc()) {
            lagrange_poly_numbers[i] = i;
        }
        require(vk.num_inputs > 0);

        PairingsBn254.Fr memory inputs_term = PairingsBn254.new_fr(0);
        for (uint256 i = 0; i < vk.num_inputs; i = i.uncheckedInc()) {
            state.t = evaluate_lagrange_poly_out_of_domain(i, vk.domain_size, vk.omega, state.z);
            state.t.mul_assign(PairingsBn254.new_fr(proof.input_values[i]));
            inputs_term.add_assign(state.t);
        }
        inputs_term.mul_assign(proof.gate_selectors_openings_at_z[0]);
        PairingsBn254.Fr memory result = proof.linearization_poly_opening_at_z.copy();
        result.add_assign(inputs_term);

        // compute powers of alpha
        compute_powers_of_alpha(state);
        PairingsBn254.Fr memory factor = state.alpha_values[4].copy();
        factor.mul_assign(proof.copy_permutation_grand_product_opening_at_z_omega);

        // - alpha_0 * (a + perm(z) * beta + gamma)*()*(d + gamma) * z(z*omega)
        require(proof.copy_permutation_polys_openings_at_z.length == STATE_WIDTH - 1);
        PairingsBn254.Fr memory t; // TMP;
        for (uint256 i = 0; i < proof.copy_permutation_polys_openings_at_z.length; i = i.uncheckedInc()) {
            t = proof.copy_permutation_polys_openings_at_z[i].copy();
            t.mul_assign(state.beta);
            t.add_assign(proof.state_polys_openings_at_z[i]);
            t.add_assign(state.gamma);

            factor.mul_assign(t);
        }

        t = proof.state_polys_openings_at_z[3].copy();
        t.add_assign(state.gamma);
        factor.mul_assign(t);
        result.sub_assign(factor);

        // - L_0(z) * alpha_1
        PairingsBn254.Fr memory l_0_at_z = evaluate_l0_at_point(vk.domain_size, state.z);
        l_0_at_z.mul_assign(state.alpha_values[4 + 1]);
        result.sub_assign(l_0_at_z);

        PairingsBn254.Fr memory lookup_quotient_contrib = lookup_quotient_contribution(vk, proof, state);
        result.add_assign(lookup_quotient_contrib);

        PairingsBn254.Fr memory lhs = proof.quotient_poly_opening_at_z.copy();
        lhs.mul_assign(evaluate_vanishing(vk.domain_size, state.z));
        return lhs.value == result.value;
    }

    function lookup_quotient_contribution(
        VerificationKey memory vk,
        Proof memory proof,
        PartialVerifierState memory state
    ) internal view returns (PairingsBn254.Fr memory result) {
        PairingsBn254.Fr memory t;

        PairingsBn254.Fr memory one = PairingsBn254.new_fr(1);
        state.beta_plus_one = state.beta_lookup.copy();
        state.beta_plus_one.add_assign(one);
        state.beta_gamma = state.beta_plus_one.copy();
        state.beta_gamma.mul_assign(state.gamma_lookup);

        // (s'*beta + gamma)*(zw')*alpha
        t = proof.lookup_s_poly_opening_at_z_omega.copy();
        t.mul_assign(state.beta_lookup);
        t.add_assign(state.beta_gamma);
        t.mul_assign(proof.lookup_grand_product_opening_at_z_omega);
        t.mul_assign(state.alpha_values[6]);

        // (z - omega^{n-1}) for this part
        PairingsBn254.Fr memory last_omega = vk.omega.pow(vk.domain_size - 1);
        state.z_minus_last_omega = state.z.copy();
        state.z_minus_last_omega.sub_assign(last_omega);
        t.mul_assign(state.z_minus_last_omega);
        result.add_assign(t);

        // - alpha_1 * L_{0}(z)
        state.l_0_at_z = evaluate_lagrange_poly_out_of_domain(0, vk.domain_size, vk.omega, state.z);
        t = state.l_0_at_z.copy();
        t.mul_assign(state.alpha_values[6 + 1]);
        result.sub_assign(t);

        // - alpha_2 * beta_gamma_powered L_{n-1}(z)
        PairingsBn254.Fr memory beta_gamma_powered = state.beta_gamma.pow(vk.domain_size - 1);
        state.l_n_minus_one_at_z = evaluate_lagrange_poly_out_of_domain(
            vk.domain_size - 1,
            vk.domain_size,
            vk.omega,
            state.z
        );
        t = state.l_n_minus_one_at_z.copy();
        t.mul_assign(beta_gamma_powered);
        t.mul_assign(state.alpha_values[6 + 2]);

        result.sub_assign(t);
    }

    function aggregated_linearization_commitment(
        VerificationKey memory vk,
        Proof memory proof,
        PartialVerifierState memory state
    ) internal view returns (PairingsBn254.G1Point memory result) {
        // qMain*(Q_a * A + Q_b * B + Q_c * C + Q_d * D + Q_m * A*B + Q_const + Q_dNext * D_next)
        result = PairingsBn254.new_g1(0, 0);
        // Q_a * A
        PairingsBn254.G1Point memory scaled = vk.gate_setup_commitments[0].point_mul(
            proof.state_polys_openings_at_z[0]
        );
        result.point_add_assign(scaled);
        // Q_b * B
        scaled = vk.gate_setup_commitments[1].point_mul(proof.state_polys_openings_at_z[1]);
        result.point_add_assign(scaled);
        // Q_c * C
        scaled = vk.gate_setup_commitments[2].point_mul(proof.state_polys_openings_at_z[2]);
        result.point_add_assign(scaled);
        // Q_d * D
        scaled = vk.gate_setup_commitments[3].point_mul(proof.state_polys_openings_at_z[3]);
        result.point_add_assign(scaled);
        // Q_m* A*B or Q_ab*A*B
        PairingsBn254.Fr memory t = proof.state_polys_openings_at_z[0].copy();
        t.mul_assign(proof.state_polys_openings_at_z[1]);
        scaled = vk.gate_setup_commitments[4].point_mul(t);
        result.point_add_assign(scaled);
        // Q_AC* A*C
        t = proof.state_polys_openings_at_z[0].copy();
        t.mul_assign(proof.state_polys_openings_at_z[2]);
        scaled = vk.gate_setup_commitments[5].point_mul(t);
        result.point_add_assign(scaled);
        // Q_const
        result.point_add_assign(vk.gate_setup_commitments[6]);
        // Q_dNext * D_next
        scaled = vk.gate_setup_commitments[7].point_mul(proof.state_polys_openings_at_z_omega[0]);
        result.point_add_assign(scaled);
        result.point_mul_assign(proof.gate_selectors_openings_at_z[0]);

        PairingsBn254.G1Point
            memory rescue_custom_gate_linearization_contrib = rescue_custom_gate_linearization_contribution(
                vk,
                proof,
                state
            );
        result.point_add_assign(rescue_custom_gate_linearization_contrib);
        require(vk.non_residues.length == STATE_WIDTH - 1);

        PairingsBn254.Fr memory one = PairingsBn254.new_fr(1);
        PairingsBn254.Fr memory factor = state.alpha_values[4].copy();
        for (uint256 i = 0; i < proof.state_polys_openings_at_z.length; ) {
            t = state.z.copy();
            if (i == 0) {
                t.mul_assign(one);
            } else {
                t.mul_assign(vk.non_residues[i - 1]);
            }
            t.mul_assign(state.beta);
            t.add_assign(state.gamma);
            t.add_assign(proof.state_polys_openings_at_z[i]);

            factor.mul_assign(t);
            unchecked {
                ++i;
            }
        }

        scaled = proof.copy_permutation_grand_product_commitment.point_mul(factor);
        result.point_add_assign(scaled);

        // - (a(z) + beta*perm_a + gamma)*()*()*z(z*omega) * beta * perm_d(X)
        factor = state.alpha_values[4].copy();
        factor.mul_assign(state.beta);
        factor.mul_assign(proof.copy_permutation_grand_product_opening_at_z_omega);
        for (uint256 i = 0; i < STATE_WIDTH - 1; i = i.uncheckedInc()) {
            t = proof.copy_permutation_polys_openings_at_z[i].copy();
            t.mul_assign(state.beta);
            t.add_assign(state.gamma);
            t.add_assign(proof.state_polys_openings_at_z[i]);

            factor.mul_assign(t);
        }
        scaled = vk.permutation_commitments[3].point_mul(factor);
        result.point_sub_assign(scaled);

        // + L_0(z) * Z(x)
        state.l_0_at_z = evaluate_lagrange_poly_out_of_domain(0, vk.domain_size, vk.omega, state.z);
        require(state.l_0_at_z.value != 0);
        factor = state.l_0_at_z.copy();
        factor.mul_assign(state.alpha_values[4 + 1]);
        scaled = proof.copy_permutation_grand_product_commitment.point_mul(factor);
        result.point_add_assign(scaled);

        PairingsBn254.G1Point memory lookup_linearization_contrib = lookup_linearization_contribution(proof, state);
        result.point_add_assign(lookup_linearization_contrib);
    }

    function rescue_custom_gate_linearization_contribution(
        VerificationKey memory vk,
        Proof memory proof,
        PartialVerifierState memory state
    ) public view returns (PairingsBn254.G1Point memory result) {
        PairingsBn254.Fr memory t;
        PairingsBn254.Fr memory intermediate_result;

        // a^2 - b = 0
        t = proof.state_polys_openings_at_z[0].copy();
        t.mul_assign(t);
        t.sub_assign(proof.state_polys_openings_at_z[1]);
        // t.mul_assign(challenge1);
        t.mul_assign(state.alpha_values[1]);
        intermediate_result.add_assign(t);

        // b^2 - c = 0
        t = proof.state_polys_openings_at_z[1].copy();
        t.mul_assign(t);
        t.sub_assign(proof.state_polys_openings_at_z[2]);
        t.mul_assign(state.alpha_values[1 + 1]);
        intermediate_result.add_assign(t);

        // c*a - d = 0;
        t = proof.state_polys_openings_at_z[2].copy();
        t.mul_assign(proof.state_polys_openings_at_z[0]);
        t.sub_assign(proof.state_polys_openings_at_z[3]);
        t.mul_assign(state.alpha_values[1 + 2]);
        intermediate_result.add_assign(t);

        result = vk.gate_selectors_commitments[1].point_mul(intermediate_result);
    }

    function lookup_linearization_contribution(Proof memory proof, PartialVerifierState memory state)
        internal
        view
        returns (PairingsBn254.G1Point memory result)
    {
        PairingsBn254.Fr memory zero = PairingsBn254.new_fr(0);

        PairingsBn254.Fr memory t;
        PairingsBn254.Fr memory factor;
        // s(x) from the Z(x*omega)*(\gamma*(1 + \beta) + s(x) + \beta * s(x*omega)))
        factor = proof.lookup_grand_product_opening_at_z_omega.copy();
        factor.mul_assign(state.alpha_values[6]);
        factor.mul_assign(state.z_minus_last_omega);

        PairingsBn254.G1Point memory scaled = proof.lookup_s_poly_commitment.point_mul(factor);
        result.point_add_assign(scaled);

        // Z(x) from - alpha_0 * Z(x) * (\beta + 1) * (\gamma + f(x)) * (\gamma(1 + \beta) + t(x) + \beta * t(x*omega))
        // + alpha_1 * Z(x) * L_{0}(z) + alpha_2 * Z(x) * L_{n-1}(z)

        // accumulate coefficient
        factor = proof.lookup_t_poly_opening_at_z_omega.copy();
        factor.mul_assign(state.beta_lookup);
        factor.add_assign(proof.lookup_t_poly_opening_at_z);
        factor.add_assign(state.beta_gamma);

        // (\gamma + f(x))
        PairingsBn254.Fr memory f_reconstructed;
        PairingsBn254.Fr memory current = PairingsBn254.new_fr(1);
        PairingsBn254.Fr memory tmp0;
        for (uint256 i = 0; i < STATE_WIDTH - 1; i = i.uncheckedInc()) {
            tmp0 = proof.state_polys_openings_at_z[i].copy();
            tmp0.mul_assign(current);
            f_reconstructed.add_assign(tmp0);

            current.mul_assign(state.eta);
        }

        // add type of table
        t = proof.lookup_table_type_poly_opening_at_z.copy();
        t.mul_assign(current);
        f_reconstructed.add_assign(t);

        f_reconstructed.mul_assign(proof.lookup_selector_poly_opening_at_z);
        f_reconstructed.add_assign(state.gamma_lookup);

        // end of (\gamma + f(x)) part
        factor.mul_assign(f_reconstructed);
        factor.mul_assign(state.beta_plus_one);
        t = zero.copy();
        t.sub_assign(factor);
        factor = t;
        factor.mul_assign(state.alpha_values[6]);

        // Multiply by (z - omega^{n-1})
        factor.mul_assign(state.z_minus_last_omega);

        // L_{0}(z) in front of Z(x)
        t = state.l_0_at_z.copy();
        t.mul_assign(state.alpha_values[6 + 1]);
        factor.add_assign(t);

        // L_{n-1}(z) in front of Z(x)
        t = state.l_n_minus_one_at_z.copy();
        t.mul_assign(state.alpha_values[6 + 2]);
        factor.add_assign(t);

        scaled = proof.lookup_grand_product_commitment.point_mul(factor);
        result.point_add_assign(scaled);
    }

    struct Queries {
        PairingsBn254.G1Point[13] commitments_at_z;
        PairingsBn254.Fr[13] values_at_z;
        PairingsBn254.G1Point[6] commitments_at_z_omega;
        PairingsBn254.Fr[6] values_at_z_omega;
    }

    function prepare_queries(
        VerificationKey memory vk,
        Proof memory proof,
        PartialVerifierState memory state
    ) public view returns (Queries memory queries) {
        // we set first two items in calee side so start idx from 2
        uint256 idx = 2;
        for (uint256 i = 0; i < STATE_WIDTH; i = i.uncheckedInc()) {
            queries.commitments_at_z[idx] = proof.state_polys_commitments[i];
            queries.values_at_z[idx] = proof.state_polys_openings_at_z[i];
            idx = idx.uncheckedInc();
        }
        require(proof.gate_selectors_openings_at_z.length == 1);
        queries.commitments_at_z[idx] = vk.gate_selectors_commitments[0];
        queries.values_at_z[idx] = proof.gate_selectors_openings_at_z[0];
        idx = idx.uncheckedInc();
        for (uint256 i = 0; i < STATE_WIDTH - 1; i = i.uncheckedInc()) {
            queries.commitments_at_z[idx] = vk.permutation_commitments[i];
            queries.values_at_z[idx] = proof.copy_permutation_polys_openings_at_z[i];
            idx = idx.uncheckedInc();
        }

        queries.commitments_at_z_omega[0] = proof.copy_permutation_grand_product_commitment;
        queries.commitments_at_z_omega[1] = proof.state_polys_commitments[STATE_WIDTH - 1];

        queries.values_at_z_omega[0] = proof.copy_permutation_grand_product_opening_at_z_omega;
        queries.values_at_z_omega[1] = proof.state_polys_openings_at_z_omega[0];

        PairingsBn254.G1Point memory lookup_t_poly_commitment_aggregated = vk.lookup_tables_commitments[0];
        PairingsBn254.Fr memory current_eta = state.eta.copy();
        for (uint256 i = 1; i < vk.lookup_tables_commitments.length; i = i.uncheckedInc()) {
            state.tp = vk.lookup_tables_commitments[i].point_mul(current_eta);
            lookup_t_poly_commitment_aggregated.point_add_assign(state.tp);

            current_eta.mul_assign(state.eta);
        }
        queries.commitments_at_z[idx] = lookup_t_poly_commitment_aggregated;
        queries.values_at_z[idx] = proof.lookup_t_poly_opening_at_z;
        idx = idx.uncheckedInc();
        queries.commitments_at_z[idx] = vk.lookup_selector_commitment;
        queries.values_at_z[idx] = proof.lookup_selector_poly_opening_at_z;
        idx = idx.uncheckedInc();
        queries.commitments_at_z[idx] = vk.lookup_table_type_commitment;
        queries.values_at_z[idx] = proof.lookup_table_type_poly_opening_at_z;
        queries.commitments_at_z_omega[2] = proof.lookup_s_poly_commitment;
        queries.values_at_z_omega[2] = proof.lookup_s_poly_opening_at_z_omega;
        queries.commitments_at_z_omega[3] = proof.lookup_grand_product_commitment;
        queries.values_at_z_omega[3] = proof.lookup_grand_product_opening_at_z_omega;
        queries.commitments_at_z_omega[4] = lookup_t_poly_commitment_aggregated;
        queries.values_at_z_omega[4] = proof.lookup_t_poly_opening_at_z_omega;
    }

    function final_pairing(
        // VerificationKey memory vk,
        PairingsBn254.G2Point[NUM_G2_ELS] memory g2_elements,
        Proof memory proof,
        PartialVerifierState memory state,
        PairingsBn254.G1Point memory aggregated_commitment_at_z,
        PairingsBn254.G1Point memory aggregated_commitment_at_z_omega,
        PairingsBn254.Fr memory aggregated_opening_at_z,
        PairingsBn254.Fr memory aggregated_opening_at_z_omega
    ) internal view returns (bool) {
        // q(x) = f(x) - f(z) / (x - z)
        // q(x) * (x-z)  = f(x) - f(z)

        // f(x)
        PairingsBn254.G1Point memory pair_with_generator = aggregated_commitment_at_z.copy_g1();
        aggregated_commitment_at_z_omega.point_mul_assign(state.u);
        pair_with_generator.point_add_assign(aggregated_commitment_at_z_omega);

        // - f(z)*g
        PairingsBn254.Fr memory aggregated_value = aggregated_opening_at_z_omega.copy();
        aggregated_value.mul_assign(state.u);
        aggregated_value.add_assign(aggregated_opening_at_z);
        PairingsBn254.G1Point memory tp = PairingsBn254.P1().point_mul(aggregated_value);
        pair_with_generator.point_sub_assign(tp);

        // +z * q(x)
        tp = proof.opening_proof_at_z.point_mul(state.z);
        PairingsBn254.Fr memory t = state.z_omega.copy();
        t.mul_assign(state.u);
        PairingsBn254.G1Point memory t1 = proof.opening_proof_at_z_omega.point_mul(t);
        tp.point_add_assign(t1);
        pair_with_generator.point_add_assign(tp);

        // rhs
        PairingsBn254.G1Point memory pair_with_x = proof.opening_proof_at_z_omega.point_mul(state.u);
        pair_with_x.point_add_assign(proof.opening_proof_at_z);
        pair_with_x.negate();
        // Pairing precompile expects points to be in a `i*x[1] + x[0]` form instead of `x[0] + i*x[1]`
        // so we handle it in code generation step
        PairingsBn254.G2Point memory first_g2 = g2_elements[0];
        PairingsBn254.G2Point memory second_g2 = g2_elements[1];

        return PairingsBn254.pairingProd2(pair_with_generator, first_g2, pair_with_x, second_g2);
    }
}

pragma solidity ^0.8.13;

// SPDX-License-Identifier: MIT



import "./PairingsBn254.sol";

library TranscriptLib {
    // flip                    0xe000000000000000000000000000000000000000000000000000000000000000;
    uint256 constant FR_MASK = 0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff;

    uint32 constant DST_0 = 0;
    uint32 constant DST_1 = 1;
    uint32 constant DST_CHALLENGE = 2;

    struct Transcript {
        bytes32 state_0;
        bytes32 state_1;
        uint32 challenge_counter;
    }

    function new_transcript() internal pure returns (Transcript memory t) {
        t.state_0 = bytes32(0);
        t.state_1 = bytes32(0);
        t.challenge_counter = 0;
    }

    function update_with_u256(Transcript memory self, uint256 value) internal pure {
        bytes32 old_state_0 = self.state_0;
        self.state_0 = keccak256(abi.encodePacked(DST_0, old_state_0, self.state_1, value));
        self.state_1 = keccak256(abi.encodePacked(DST_1, old_state_0, self.state_1, value));
    }

    function update_with_fr(Transcript memory self, PairingsBn254.Fr memory value) internal pure {
        update_with_u256(self, value.value);
    }

    function update_with_g1(Transcript memory self, PairingsBn254.G1Point memory p) internal pure {
        update_with_u256(self, p.X);
        update_with_u256(self, p.Y);
    }

    function get_challenge(Transcript memory self) internal pure returns (PairingsBn254.Fr memory challenge) {
        bytes32 query = keccak256(abi.encodePacked(DST_CHALLENGE, self.state_0, self.state_1, self.challenge_counter));
        self.challenge_counter += 1;
        challenge = PairingsBn254.Fr({value: uint256(query) & FR_MASK});
    }
}

pragma solidity ^0.8.13;

// SPDX-License-Identifier: MIT



library PairingsBn254 {
    uint256 constant q_mod = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
    uint256 constant r_mod = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
    uint256 constant bn254_b_coeff = 3;

    struct G1Point {
        uint256 X;
        uint256 Y;
    }

    struct Fr {
        uint256 value;
    }

    function new_fr(uint256 fr) internal pure returns (Fr memory) {
        require(fr < r_mod);
        return Fr({value: fr});
    }

    function copy(Fr memory self) internal pure returns (Fr memory n) {
        n.value = self.value;
    }

    function assign(Fr memory self, Fr memory other) internal pure {
        self.value = other.value;
    }

    function inverse(Fr memory fr) internal view returns (Fr memory) {
        require(fr.value != 0);
        return pow(fr, r_mod - 2);
    }

    function add_assign(Fr memory self, Fr memory other) internal pure {
        self.value = addmod(self.value, other.value, r_mod);
    }

    function sub_assign(Fr memory self, Fr memory other) internal pure {
        self.value = addmod(self.value, r_mod - other.value, r_mod);
    }

    function mul_assign(Fr memory self, Fr memory other) internal pure {
        self.value = mulmod(self.value, other.value, r_mod);
    }

    function pow(Fr memory self, uint256 power) internal view returns (Fr memory) {
        uint256[6] memory input = [32, 32, 32, self.value, power, r_mod];
        uint256[1] memory result;
        bool success;
        assembly {
            success := staticcall(gas(), 0x05, input, 0xc0, result, 0x20)
        }
        require(success);
        return Fr({value: result[0]});
    }

    // Encoding of field elements is: X[0] * z + X[1]
    struct G2Point {
        uint256[2] X;
        uint256[2] Y;
    }

    function P1() internal pure returns (G1Point memory) {
        return G1Point(1, 2);
    }

    function new_g1(uint256 x, uint256 y) internal pure returns (G1Point memory) {
        return G1Point(x, y);
    }

    // function new_g1_checked(uint256 x, uint256 y) internal pure returns (G1Point memory) {
    function new_g1_checked(uint256 x, uint256 y) internal pure returns (G1Point memory) {
        if (x == 0 && y == 0) {
            // point of infinity is (0,0)
            return G1Point(x, y);
        }

        // check encoding
        require(x < q_mod, "x axis isn't valid");
        require(y < q_mod, "y axis isn't valid");
        // check on curve
        uint256 lhs = mulmod(y, y, q_mod); // y^2

        uint256 rhs = mulmod(x, x, q_mod); // x^2
        rhs = mulmod(rhs, x, q_mod); // x^3
        rhs = addmod(rhs, bn254_b_coeff, q_mod); // x^3 + b
        require(lhs == rhs, "is not on curve");

        return G1Point(x, y);
    }

    function new_g2(uint256[2] memory x, uint256[2] memory y) internal pure returns (G2Point memory) {
        return G2Point(x, y);
    }

    function copy_g1(G1Point memory self) internal pure returns (G1Point memory result) {
        result.X = self.X;
        result.Y = self.Y;
    }

    function P2() internal pure returns (G2Point memory) {
        // for some reason ethereum expects to have c1*v + c0 form

        return
            G2Point(
                [
                    0x198e9393920d483a7260bfb731fb5d25f1aa493335a9e71297e485b7aef312c2,
                    0x1800deef121f1e76426a00665e5c4479674322d4f75edadd46debd5cd992f6ed
                ],
                [
                    0x090689d0585ff075ec9e99ad690c3395bc4b313370b38ef355acdadcd122975b,
                    0x12c85ea5db8c6deb4aab71808dcb408fe3d1e7690c43d37b4ce6cc0166fa7daa
                ]
            );
    }

    function negate(G1Point memory self) internal pure {
        // The prime q in the base field F_q for G1
        if (self.Y == 0) {
            require(self.X == 0);
            return;
        }

        self.Y = q_mod - self.Y;
    }

    function point_add(G1Point memory p1, G1Point memory p2) internal view returns (G1Point memory r) {
        point_add_into_dest(p1, p2, r);
        return r;
    }

    function point_add_assign(G1Point memory p1, G1Point memory p2) internal view {
        point_add_into_dest(p1, p2, p1);
    }

    function point_add_into_dest(
        G1Point memory p1,
        G1Point memory p2,
        G1Point memory dest
    ) internal view {
        if (p2.X == 0 && p2.Y == 0) {
            // we add zero, nothing happens
            dest.X = p1.X;
            dest.Y = p1.Y;
            return;
        } else if (p1.X == 0 && p1.Y == 0) {
            // we add into zero, and we add non-zero point
            dest.X = p2.X;
            dest.Y = p2.Y;
            return;
        } else {
            uint256[4] memory input;

            input[0] = p1.X;
            input[1] = p1.Y;
            input[2] = p2.X;
            input[3] = p2.Y;

            bool success;
            assembly {
                success := staticcall(gas(), 6, input, 0x80, dest, 0x40)
            }
            require(success);
        }
    }

    function point_sub_assign(G1Point memory p1, G1Point memory p2) internal view {
        point_sub_into_dest(p1, p2, p1);
    }

    function point_sub_into_dest(
        G1Point memory p1,
        G1Point memory p2,
        G1Point memory dest
    ) internal view {
        if (p2.X == 0 && p2.Y == 0) {
            // we subtracted zero, nothing happens
            dest.X = p1.X;
            dest.Y = p1.Y;
            return;
        } else if (p1.X == 0 && p1.Y == 0) {
            // we subtract from zero, and we subtract non-zero point
            dest.X = p2.X;
            dest.Y = q_mod - p2.Y;
            return;
        } else {
            uint256[4] memory input;

            input[0] = p1.X;
            input[1] = p1.Y;
            input[2] = p2.X;
            input[3] = q_mod - p2.Y;

            bool success = false;
            assembly {
                success := staticcall(gas(), 6, input, 0x80, dest, 0x40)
            }
            require(success);
        }
    }

    function point_mul(G1Point memory p, Fr memory s) internal view returns (G1Point memory r) {
        // https://eips.ethereum.org/EIPS/eip-197
        // Elliptic curve points are encoded as a Jacobian pair (X, Y) where the point at infinity is encoded as (0, 0)
        if (p.X == 0 && p.Y == 1) {
            p.Y = 0;
        }
        point_mul_into_dest(p, s, r);
        return r;
    }

    function point_mul_assign(G1Point memory p, Fr memory s) internal view {
        point_mul_into_dest(p, s, p);
    }

    function point_mul_into_dest(
        G1Point memory p,
        Fr memory s,
        G1Point memory dest
    ) internal view {
        uint256[3] memory input;
        input[0] = p.X;
        input[1] = p.Y;
        input[2] = s.value;
        bool success;
        assembly {
            success := staticcall(gas(), 7, input, 0x60, dest, 0x40)
        }
        require(success);
    }

    function pairing(G1Point[] memory p1, G2Point[] memory p2) internal view returns (bool) {
        require(p1.length == p2.length);
        uint256 elements = p1.length;
        uint256 inputSize = elements * 6;
        uint256[] memory input = new uint256[](inputSize);
        for (uint256 i = 0; i < elements; ) {
            input[i * 6 + 0] = p1[i].X;
            input[i * 6 + 1] = p1[i].Y;
            input[i * 6 + 2] = p2[i].X[0];
            input[i * 6 + 3] = p2[i].X[1];
            input[i * 6 + 4] = p2[i].Y[0];
            input[i * 6 + 5] = p2[i].Y[1];
            unchecked {
                ++i;
            }
        }
        uint256[1] memory out;
        bool success;
        assembly {
            success := staticcall(gas(), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20)
        }
        require(success);
        return out[0] != 0;
    }

    /// Convenience method for a pairing check for two pairs.
    function pairingProd2(
        G1Point memory a1,
        G2Point memory a2,
        G1Point memory b1,
        G2Point memory b2
    ) internal view returns (bool) {
        G1Point[] memory p1 = new G1Point[](2);
        G2Point[] memory p2 = new G2Point[](2);
        p1[0] = a1;
        p1[1] = b1;
        p2[0] = a2;
        p2[1] = b2;
        return pairing(p1, p2);
    }
}

{
  "optimizer": {
    "enabled": true,
    "runs": 9999999
  },
  "outputSelection": {
    "*": {
      "*": [
        "evm.bytecode",
        "evm.deployedBytecode",
        "devdoc",
        "userdoc",
        "metadata",
        "abi"
      ]
    }
  }
}

• No Contract Security Audit Submitted- Submit Audit Here

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