solidity上实现BLS签名机制

 原文地址：https://ethereum.stackexchange.com/questions/59293/does-ethereum-support-pairing-operations

BLS签名机制说明：http://www.ymcall.com/artinfo/698628886830280666.html

 

pragma solidity ^0.4.14;

/*
Example of how to verify BLS signatures and BGLS aggregate signatures in Ethereum.

Signatures are generated using https://github.com/Project-Arda/bgls
Code is based on https://github.com/jstoxrocky/zksnarks_example
*/

contract BLSExample {
    struct G1Point {
        uint X;
        uint Y;
    }
    // Encoding of field elements is: X[0] * z + X[1]
    struct G2Point {
        uint[2] X;
        uint[2] Y;
    }
    //P1,P2根据 https://github.com/ethereum/EIPs/blob/df132cd37efb3986f9cd3ef4922b15a767d2c54a/EIPS/eip-197.md#specification
    /// @return the generator of G1
    function P1() internal returns (G1Point) {
        return G1Point(1, 2);
    }
    /// @return the generator of G2
    function P2() internal returns (G2Point) {
        return G2Point(
            [11559732032986387107991004021392285783925812861821192530917403151452391805634,
            10857046999023057135944570762232829481370756359578518086990519993285655852781],

            [4082367875863433681332203403145435568316851327593401208105741076214120093531,
            8495653923123431417604973247489272438418190587263600148770280649306958101930]
        );
    }
    //Example of BLS signature verification
    function verifyBLSTest() returns (bool) {

        bytes memory message = hex"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";

        G1Point memory signature = G1Point(11181692345848957662074290878138344227085597134981019040735323471731897153462, 6479746447046570360435714249272776082787932146211764251347798668447381926167);

        G2Point memory v = G2Point(
            [18523194229674161632574346342370534213928970227736813349975332190798837787897, 5725452645840548248571879966249653216818629536104756116202892528545334967238],
            [3816656720215352836236372430537606984911914992659540439626020770732736710924, 677280212051826798882467475639465784259337739185938192379192340908771705870]
        );

        G1Point memory h = hashToG1(message);

        return pairing2(negate(signature), P2(), h, v);
    }

    //Example of BGLS signature verification with 2 signers
    //Note that the messages differ in their last character.
    function verifyBGLS2() returns (bool) {

        uint numberOfSigners = 2;

        G1Point memory signature = G1Point(7985250684665362734034207174567341000146996823387166378141631317099216977152, 5471024627060516972461571110176333017668072838695251726406965080926450112048);

        bytes memory message0 = hex"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";
        bytes memory message1 = hex"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";

        G2Point memory v0 = G2Point(
            [15516709285352539082439213720585739724329002971882390582209636960597958801449, 19324541677661060388134143597417835654030498723817274130329567224531700170734],
            [16550775633156536193089672538964908973667410921848053632462693002610771214528, 10154483139478025296468271477739414260393126999813603835827647034319242387010]
        );

        G2Point memory v1 = G2Point(
            [14125383697019450293340447180826714775062600193406387386692146468060627933203, 10886345395648455940547500614900453787797209052692168129177801883734751834552],
            [13494666809312056575532152175382485778895768300692817869062640713829304801648, 10580958449683540742032499469496205826101096579572266360455646078388895706251]
        );

        G1Point memory h0 = hashToG1(message0);
        G1Point memory h1 = hashToG1(message1);

        G1Point[] memory a = new G1Point[](numberOfSigners + 1);
        G2Point[] memory b = new G2Point[](numberOfSigners + 1);
        a[0] = negate(signature);
        a[1] = h0;
        a[2] = h1;
        b[0] = P2();
        b[1] = v0;
        b[2] = v1;

        return pairing(a, b);
    }

    //Example of BGLS signature verification with 3 signers
    //Note that the messages differ in their last character.
    function verifyBGLS3() returns (bool) {

        uint numberOfSigners = 3;

        G1Point memory signature = G1Point(385846518441062319503502284295243290270560187383398932887791670182362540842, 19731933537428695151702009864745685458233056709189425720845387511061953267292);

        bytes memory message0 = hex"7b0a2020226f70656e223a207b0a20202020227072696365223a2039353931372c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333134323430302c0a2020202020202269736f223a2022323031362d31322d33315430303a30303a30302e3030305a220a202020207d0a20207d2c0a202022636c6f7365223a207b0a20202020227072696365223a2039363736302c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333232383830302c0a2020202020202269736f223a2022323031372d30312d30315430303a30303a30302e3030305a220a202020207d0a20207d2c0a2020226c6f6f6b7570223a207b0a20202020227072696365223a2039363736302c0a20202020226b223a20312c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333232383830302c0a2020202020202269736f223a2022323031372d30312d30315430303a30303a30302e3030305a220a202020207d0a20207d0a7d0a6578616d706c652e636f6d2f6170692f30";
        bytes memory message1 = hex"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";
        bytes memory message2 = hex"7b0a2020226f70656e223a207b0a20202020227072696365223a2039353931372c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333134323430302c0a2020202020202269736f223a2022323031362d31322d33315430303a30303a30302e3030305a220a202020207d0a20207d2c0a202022636c6f7365223a207b0a20202020227072696365223a2039363736302c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333232383830302c0a2020202020202269736f223a2022323031372d30312d30315430303a30303a30302e3030305a220a202020207d0a20207d2c0a2020226c6f6f6b7570223a207b0a20202020227072696365223a2039363736302c0a20202020226b223a20312c0a202020202274696d65223a207b0a20202020202022756e6978223a20313438333232383830302c0a2020202020202269736f223a2022323031372d30312d30315430303a30303a30302e3030305a220a202020207d0a20207d0a7d0a6578616d706c652e636f6d2f6170692f32";

        G2Point memory v0 = G2Point(
            [1787282038370667094324364195810339512415273589223814213215040505578200405366, 414568866548933554513940840943382696902163788831396286279770126458218272940],
            [6560020551439455112781785895092032589010633560844445112872109862153018855017, 19411093226570397520343120724285433000937737461010544490862811136406407315543]
        );

        G2Point memory v1 = G2Point(
            [14831125462625540363404323739936082597729714855858291605999144010730542058037, 8342129546329626371616639780890580451066604883761980695690870205390518348707],
            [808186590373043742842665711030588185456231663895663328011864547134240543671, 1856705676948889458735296604372981546875220644939188415241687241562401814459]
        );

        G2Point memory v2 = G2Point(
            [12507030828714819990408995725310388936101611986473926829733453468215798265704, 16402225253711577242710704509153100189802817297679524801952098990526969620006],
            [18717845356690477533392378472300056893077745517009561191866660997312973511514, 20124563173642533900823905467925868861151292863229012000403558815142682516349]
        );

        G1Point memory h0 = hashToG1(message0);
        G1Point memory h1 = hashToG1(message1);
        G1Point memory h2 = hashToG1(message2);

        G1Point[] memory a = new G1Point[](numberOfSigners + 1);
        G2Point[] memory b = new G2Point[](numberOfSigners + 1);
        a[0] = negate(signature);
        a[1] = h0;
        a[2] = h1;
        a[3] = h2;
        b[0] = P2();
        b[1] = v0;
        b[2] = v1;
        b[3] = v2;

        return pairing(a, b);
    }

    /// @return the result of computing the pairing check
    /// e(p1[0], p2[0]) *  .... * e(p1[n], p2[n]) == 1
    /// For example pairing([P1(), P1().negate()], [P2(), P2()]) should
    /// return true.
    function pairing(G1Point[] p1, G2Point[] p2) internal returns (bool) {
        require(p1.length == p2.length);
        uint elements = p1.length;
        uint inputSize = elements * 6;
        uint[] memory input = new uint[](inputSize);

        for (uint i = 0; i < elements; i++)
        {
            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];
        }

        uint[1] memory out;
        bool success;

        assembly {
            success := call(sub(gas, 2000), 8, 0, add(input, 0x20), mul(inputSize, 0x20), out, 0x20)
        // Use "invalid" to make gas estimation work
            switch success case 0 {invalid}
        }
        require(success);
        return out[0] != 0;
    }

    /// Convenience method for a pairing check for two pairs.
    function pairing2(G1Point a1, G2Point a2, G1Point b1, G2Point b2) internal 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);
    }

    function hashToG1(bytes message) internal returns (G1Point) {
        uint256 h = uint256(keccak256(message));
        return mul(P1(), h);
    }

    function modPow(uint256 base, uint256 exponent, uint256 modulus) internal returns (uint256) {
        uint256[6] memory input = [32, 32, 32, base, exponent, modulus];
        uint256[1] memory result;
        assembly {
            if iszero(call(not(0), 0x05, 0, input, 0xc0, result, 0x20)) {
                revert(0, 0)
            }
        }
        return result[0];
    }

    /// @return the negation of p, i.e. p.add(p.negate()) should be zero.
    function negate(G1Point p) internal returns (G1Point) {
        // The prime q in the base field F_q for G1
        uint q = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
        if (p.X == 0 && p.Y == 0)
            return G1Point(0, 0);
        return G1Point(p.X, q - (p.Y % q));
    }

    /// @return the sum of two points of G1
    function add(G1Point p1, G1Point p2) internal returns (G1Point r) {
        uint[4] memory input;
        input[0] = p1.X;
        input[1] = p1.Y;
        input[2] = p2.X;
        input[3] = p2.Y;
        bool success;
        assembly {
            success := call(sub(gas, 2000), 6, 0, input, 0xc0, r, 0x60)
        // Use "invalid" to make gas estimation work
            switch success case 0 {invalid}
        }
        require(success);
    }

    /*
     common.BytesToAddress([]byte{1}): &ecrecover{},
    common.BytesToAddress([]byte{2}): &sha256hash{},
    common.BytesToAddress([]byte{3}): &ripemd160hash{},
    common.BytesToAddress([]byte{4}): &dataCopy{},
    common.BytesToAddress([]byte{5}): &bigModExp{},
    common.BytesToAddress([]byte{6}): &bn256Add{},
    common.BytesToAddress([]byte{7}): &bn256ScalarMul{},
    common.BytesToAddress([]byte{8}): &bn256Pairing{}, 
     */
    /// @return the product of a point on G1 and a scalar, i.e.
    /// p == p.mul(1) and p.add(p) == p.mul(2) for all points p.
    function mul(G1Point p, uint s) internal returns (G1Point r) {
        uint[3] memory input;
        input[0] = p.X;
        input[1] = p.Y;
        input[2] = s;
        bool success;
        assembly {
        	//call(g, a, v, in, insize, out, outsize)
        	/*call contract at address a with input mem[in…(in+insize)) providing g gas and v wei and 
        	output area mem[out…(out+outsize)) returning 0 on error (eg. out of gas) and 1 on success*/
        	//gas: still available to execution
            success := call(sub(gas, 2000), 7, 0, input, 0x80, r, 0x60)
        // Use "invalid" to make gas estimation work
            switch success case 0 {invalid}  //end execution with invalid instruction
        }
        require(success);
    }

}