homework5.sol

gistfile1.txt

// SPDX-License-Identifier: GPL-3.0

import "hardhat/console.sol";

pragma solidity >=0.8.2 <0.9.0;

contract Homework5 {

    uint256 constant SNARK_SCALAR_FIELD = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
    uint256 constant PRIME_Q = 21888242871839275222246405745257275088696311157297823662689037894645226208583;

    struct G1Point {
        uint256 X;
        uint256 Y;
    }

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

    G1Point G1Gen = G1Point(1,2);

    /*
    * @return The negation of p, i.e. p.plus(p.negate()) should be zero.
    */
    function negate(G1Point memory p) internal pure returns (G1Point memory) {
        // The prime q in the base field F_q for G1
        if (p.X == 0 && p.Y == 0) {
        return G1Point(0, 0);
        } else {
        return G1Point(p.X, PRIME_Q - (p.Y % PRIME_Q));
        }
    }

   /*
    * @return the sum of two points of G1
    */
    function plus(
        G1Point memory p1,
        G1Point memory p2
    ) internal view returns (G1Point memory r) {
        uint256[4] memory input;
        input[0] = p1.X;
        input[1] = p1.Y;
        input[2] = p2.X;
        input[3] = p2.Y;
        bool success;

        // solium-disable-next-line security/no-inline-assembly
        assembly {
        success := staticcall(sub(gas(), 2000), 6, input, 0xc0, r, 0x60)
        // Use "invalid" to make gas estimation work
        switch success case 0 { invalid() }
        }

        require(success, "pairing-add-failed");
    }

    /*
    * @return r the product of a point on G1 and a scalar, i.e.
    *         p == p.scalar_mul(1) and p.plus(p) == p.scalar_mul(2) for all
    *         points p.
    */
    function scalar_mul(G1Point memory p, uint256 s) internal view returns (G1Point memory r) {
        uint256[3] memory input;
        input[0] = p.X;
        input[1] = p.Y;
        input[2] = s;
        bool success;
        // solium-disable-next-line security/no-inline-assembly
        assembly {
        success := staticcall(sub(gas(), 2000), 7, input, 0x80, r, 0x60)
        // Use "invalid" to make gas estimation work
        switch success case 0 { invalid() }
        }
        require(success, "pairing-mul-failed");
    }


    function pairing(
        G1Point memory a1,
        G2Point memory a2,
        G1Point memory b1,
        G2Point memory b2,
        G1Point memory c1,
        G2Point memory c2,
        G1Point memory d1,
        G2Point memory d2
    ) internal view returns (bool) {
        G1Point[4] memory p1 = [a1, b1, c1, d1];
        G2Point[4] memory p2 = [a2, b2, c2, d2];

        uint256 inputSize = 24;
        uint256[] memory input = new uint256[](inputSize);

        for (uint256 i = 0; i < 4; i++) {
        uint256 j = i * 6;
            input[j + 0] = p1[i].X;
            input[j + 1] = p1[i].Y;
            input[j + 2] = p2[i].X[0];
            input[j + 3] = p2[i].X[1];
            input[j + 4] = p2[i].Y[0];
            input[j + 5] = p2[i].Y[1];
        }

        /*
        for(uint256 i = 0; i < 24; i++ ) {
            console.log(input[i]);
        }
        */

        uint256[1] memory out;
        bool success;

        // solium-disable-next-line security/no-inline-assembly
        assembly {
        success := staticcall(gas(), 8, add(input, 0x20), mul(inputSize, 0x20), out, 0x20)
        // Use "invalid" to make gas estimation work
        switch success case 0 { invalid() }
        }

        require(success, "pairing-opcode-failed");

        return out[0] != 0;
    }

    // Hardcoded EC points

    // α1 = 5 * G1
    G1Point alpha_1 = G1Point(10744596414106452074759370245733544594153395043370666422502510773307029471145, 848677436511517736191562425154572367705380862894644942948681172815252343932);
    // β2 = 6 * G2
    G2Point beta_2 = G2Point(
        [10191129150170504690859455063377241352678147020731325090942140630855943625622, 12345624066896925082600651626583520268054356403303305150512393106955803260718],
        [16727484375212017249697795760885267597317766655549468217180521378213906474374, 13790151551682513054696583104432356791070435696840691503641536676885931241944]
    );
    // γ2 = 7 * G2
    G2Point gamma_2 = G2Point(
        [15512671280233143720612069991584289591749188907863576513414377951116606878472, 18551411094430470096460536606940536822990217226529861227533666875800903099477],
        [13376798835316611669264291046140500151806347092962367781523498857425536295743, 1711576522631428957817575436337311654689480489843856945284031697403898093784]
    );
    //  δ2 = 8 * G2
    G2Point delta_2 = G2Point(
        [11166086885672626473267565287145132336823242144708474818695443831501089511977, 1513450333913810775282357068930057790874607011341873340507105465411024430745],
        [10576778712883087908382530888778326306865681986179249638025895353796469496812, 20245151454212206884108313452940569906396451322269011731680309881579291004202]
    );

    /*
        Function takes the following arguments:
        A1, B2, C1, x1, x2, x3
    */
    function pairing_check (
        G1Point memory A1,
        G2Point memory B2,
        G1Point memory C1,
        uint256 x1,
        uint256 x2,
        uint256 x3
    ) public view returns (bool) {

        // X1 = x1 * G1 + x2 * G1 + x3 * G1

        G1Point memory X1 = plus(
            plus(
                scalar_mul(G1Gen, x1),
                scalar_mul(G1Gen, x2)
            ),
            scalar_mul(G1Gen, x3)
        );

        return pairing(
            negate(A1),
            B2,
            alpha_1,
            beta_2,
            X1,
            gamma_2,
            C1,
            delta_2
        );
    }

    function test_pairing() external view returns (bool) {

        // A1 = 22 * G1
        G1Point memory A1 = G1Point(15727213640762128376977790067421582934261473041285176203873887513123693207669,19144605879150273414601776380457513460094228635793066771119021730299648624873);
        // B2 = 11 * G2
        G2Point memory B2 = G2Point([8472151341754925747860535367990505955708751825377817860727104273184244800723, 15624790064206502667756020446826209080711344272800176518784649088946231692936],[1196137947243150610106053819405501111182787323156221967342356892090037828244, 19488077321171448217727198730828487286865984357780136663388739985720647978898]);
        // C1 = 16 * G1
        G1Point memory C1 = G1Point(10835225521862395592687560951453385602895512958032257955899877380493200080708, 2623520004791921319615054428233368525468155544765295675952919303096698181037);

        /*
        We should get:

        - 22 * 11 + 5 * 6 + 12 * 7 + 16 * 8 = 0

        */

        return pairing_check(A1, B2, C1, 3, 4, 5);
    }
}