Necesito crear una aplicación que use operaciones de emparejamiento bilineal para generar firmas. Si envío un mensaje con su firma a Ethereum, ¿puede Ethereum verificar este mensaje? ¿El EVM admite operaciones de emparejamiento?
Este es un ejemplo de verificación de firma utilizando la firma BLS:
Dada una firma S y una clave pública g^{x}, verificamos que e(S ,g)=e(H(m),g^{x}).
Sí , en la dirección 0x8 el EVM tiene un contrato precompilado para verificar el emparejamiento óptimo en la curva elíptica alt_bn128 descrita en EIP 197 .
¿Cómo podemos verificar las firmas agregadas de BGLS en Solidity? tiene una esencia que contiene el siguiente código que puede ser útil:
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;
}
/// @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"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";
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);
}
/// @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 {
success := call(sub(gas, 2000), 7, 0, input, 0x80, r, 0x60)
// Use "invalid" to make gas estimation work
switch success case 0 {invalid}
}
require(success);
}
}
Todo el archivo de Solidity se incluye arriba para ayudar a evitar enlaces muertos.
La biblioteca solcrypto mencionada en cómo implementar algoritmos criptográficos en contratos inteligentes puede ser útil, incluidas las notas en https://ethresear.ch/t/precompiled-snark-pairing-for-bls-signatures/3196/5
Para usar el equivalente de ECPAIRING, entonces haría:
c = pairing(G2, neg(S)) assert a * c == FQ12.one()Para agregarlos:
y = randint(1, p-1) # second secret key Q = multiply(G2, y) # second public key T = multiply(H_m, y) # second signature d = pairing(add(P, Q), double(H_m)) e = pairing(double(G2, add(S,T)) assert d == ePara verificar los agregados en estilo ECPAIRING:
d * pairing(double(G2) neg(add(S,T))) == FQ12.one()
unction 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) Obtuve errores browser/Pairing.sol:187:13: ParserError: Literal, identificador o instrucción esperada. si es cero (llamada (no (0), 0x05, 0, entrada, 0xc0, resultado, 0x20)PG be a pairing group generator that on input 1^k outputs descriptions of multiplicative groups G_1 and G_T of prime order p where |p| =k. let g \in G_1^{*} and G_{1}^{*}=G_{1} \{1}.The generated groups are such that there exists a bilinear map e : G_1 × G_1 → G_T, meaning for all a, b ∈ Z_p it holds that e (g^a,g^b )=e(g,g)^{ab}. ¿El contrato es capaz de verificar BLS con las curvas elípticas descritas anteriormente?
CriptaInvierno