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| // SPDX-License-Identifier: MIT
pragma solidity ^0.8.0;
// TODO: update doc
/// @title Pairing
library Pairing {
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;
}
/*
* @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
Iif (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()
}
}
Erequire(success, 'pairing-add-failed');
}
/*
* @return 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()
}
}
Erequire(success, 'pairing-mul-failed');
}
/* @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 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];
}
uint256[1] memory out;
bool success;
// solium-disable-next-line security/no-inline-assembly
assembly {
success := staticcall(
sub(gas(), 2000),
8,
add(input, 0x20),
mul(inputSize, 0x20),
out,
0x20
)
// Use "invalid" to make gas estimation work
switch success
case 0 {
invalid()
}
}
Erequire(success, 'pairing-opcode-failed');
return out[0] != 0;
}
}
|