Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Move snark test from SolidityEndToEnd #7941

Merged
merged 1 commit into from
Dec 10, 2019
+297 −304
Merged

Move snark test from SolidityEndToEnd #7941

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
304 changes: 0 additions & 304 deletions test/libsolidity/SolidityEndToEndTest.cpp
View file
Original file line number Diff line number Diff line change
@@ -12887,310 +12887,6 @@ BOOST_AUTO_TEST_CASE(address_overload_resolution)
BOOST_CHECK(callContractFunction("g()") == encodeArgs(u256(5)));
}

BOOST_AUTO_TEST_CASE(snark)
{
if (dev::test::Options::get().evmVersion() <= EVMVersion::byzantium())
return;

char const* sourceCode = R"(
library Pairing {
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 memory) {
return G1Point(1, 2);
}

/// @return the generator of G2
function P2() internal returns (G2Point memory) {
return G2Point(
[11559732032986387107991004021392285783925812861821192530917403151452391805634,
10857046999023057135944570762232829481370756359578518086990519993285655852781],
[4082367875863433681332203403145435568316851327593401208105741076214120093531,
8495653923123431417604973247489272438418190587263600148770280649306958101930]
);
}

/// @return the negation of p, i.e. p.add(p.negate()) should be zero.
function negate(G1Point memory p) internal returns (G1Point memory) {
// 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 memory p1, G1Point memory p2) internal returns (G1Point memory 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 memory p, uint s) internal returns (G1Point memory 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);
}

/// @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 p1, G2Point[] memory p2) internal returns (bool) {
require(p1.length == p2.length);
uint elements = p1.length;
uint inputSize = p1.length * 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;
}
function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory 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 pairingProd3(
G1Point memory a1, G2Point memory a2,
G1Point memory b1, G2Point memory b2,
G1Point memory c1, G2Point memory c2
) internal returns (bool) {
G1Point[] memory p1 = new G1Point[](3);
G2Point[] memory p2 = new G2Point[](3);
p1[0] = a1;
p1[1] = b1;
p1[2] = c1;
p2[0] = a2;
p2[1] = b2;
p2[2] = c2;
return pairing(p1, p2);
}
function pairingProd4(
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 returns (bool) {
G1Point[] memory p1 = new G1Point[](4);
G2Point[] memory p2 = new G2Point[](4);
p1[0] = a1;
p1[1] = b1;
p1[2] = c1;
p1[3] = d1;
p2[0] = a2;
p2[1] = b2;
p2[2] = c2;
p2[3] = d2;
return pairing(p1, p2);
}
}

contract Test {
using Pairing for *;
struct VerifyingKey {
Pairing.G2Point A;
Pairing.G1Point B;
Pairing.G2Point C;
Pairing.G2Point gamma;
Pairing.G1Point gammaBeta1;
Pairing.G2Point gammaBeta2;
Pairing.G2Point Z;
Pairing.G1Point[] IC;
}
struct Proof {
Pairing.G1Point A;
Pairing.G1Point A_p;
Pairing.G2Point B;
Pairing.G1Point B_p;
Pairing.G1Point C;
Pairing.G1Point C_p;
Pairing.G1Point K;
Pairing.G1Point H;
}
function f() public returns (bool) {
Pairing.G1Point memory p1;
Pairing.G1Point memory p2;
p1.X = 1; p1.Y = 2;
p2.X = 1; p2.Y = 2;
Pairing.G1Point memory explict_sum = Pairing.add(p1, p2);
Pairing.G1Point memory scalar_prod = Pairing.mul(p1, 2);
return (explict_sum.X == scalar_prod.X &&
explict_sum.Y == scalar_prod.Y);
}
function g() public returns (bool) {
Pairing.G1Point memory x = Pairing.add(Pairing.P1(), Pairing.negate(Pairing.P1()));
// should be zero
return (x.X == 0 && x.Y == 0);
}
function testMul() public returns (bool) {
Pairing.G1Point memory p;
// @TODO The points here are reported to be not well-formed
p.X = 14125296762497065001182820090155008161146766663259912659363835465243039841726;
p.Y = 16229134936871442251132173501211935676986397196799085184804749187146857848057;
p = Pairing.mul(p, 13986731495506593864492662381614386532349950841221768152838255933892789078521);
return
p.X == 18256332256630856740336504687838346961237861778318632856900758565550522381207 &&
p.Y == 6976682127058094634733239494758371323697222088503263230319702770853579280803;
}
function pair() public returns (bool) {
Pairing.G2Point memory fiveTimesP2 = Pairing.G2Point(
[4540444681147253467785307942530223364530218361853237193970751657229138047649, 20954117799226682825035885491234530437475518021362091509513177301640194298072],
[11631839690097995216017572651900167465857396346217730511548857041925508482915, 21508930868448350162258892668132814424284302804699005394342512102884055673846]
);
// The prime p in the base field F_p for G1
uint p = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
Pairing.G1Point[] memory g1points = new Pairing.G1Point[](2);
Pairing.G2Point[] memory g2points = new Pairing.G2Point[](2);
// check e(5 P1, P2)e(-P1, 5 P2) == 1
g1points[0] = Pairing.P1().mul(5);
g1points[1] = Pairing.P1().negate();
g2points[0] = Pairing.P2();
g2points[1] = fiveTimesP2;
if (!Pairing.pairing(g1points, g2points))
return false;
// check e(P1, P2)e(-P1, P2) == 1
g1points[0] = Pairing.P1();
g1points[1] = Pairing.P1();
g1points[1].Y = p - g1points[1].Y;
g2points[0] = Pairing.P2();
g2points[1] = Pairing.P2();
if (!Pairing.pairing(g1points, g2points))
return false;
return true;
}
function verifyingKey() internal returns (VerifyingKey memory vk) {
vk.A = Pairing.G2Point([0x209dd15ebff5d46c4bd888e51a93cf99a7329636c63514396b4a452003a35bf7, 0x04bf11ca01483bfa8b34b43561848d28905960114c8ac04049af4b6315a41678], [0x2bb8324af6cfc93537a2ad1a445cfd0ca2a71acd7ac41fadbf933c2a51be344d, 0x120a2a4cf30c1bf9845f20c6fe39e07ea2cce61f0c9bb048165fe5e4de877550]);
vk.B = Pairing.G1Point(0x2eca0c7238bf16e83e7a1e6c5d49540685ff51380f309842a98561558019fc02, 0x03d3260361bb8451de5ff5ecd17f010ff22f5c31cdf184e9020b06fa5997db84);
vk.C = Pairing.G2Point([0x2e89718ad33c8bed92e210e81d1853435399a271913a6520736a4729cf0d51eb, 0x01a9e2ffa2e92599b68e44de5bcf354fa2642bd4f26b259daa6f7ce3ed57aeb3], [0x14a9a87b789a58af499b314e13c3d65bede56c07ea2d418d6874857b70763713, 0x178fb49a2d6cd347dc58973ff49613a20757d0fcc22079f9abd10c3baee24590]);
vk.gamma = Pairing.G2Point([0x25f83c8b6ab9de74e7da488ef02645c5a16a6652c3c71a15dc37fe3a5dcb7cb1, 0x22acdedd6308e3bb230d226d16a105295f523a8a02bfc5e8bd2da135ac4c245d], [0x065bbad92e7c4e31bf3757f1fe7362a63fbfee50e7dc68da116e67d600d9bf68, 0x06d302580dc0661002994e7cd3a7f224e7ddc27802777486bf80f40e4ca3cfdb]);
vk.gammaBeta1 = Pairing.G1Point(0x15794ab061441e51d01e94640b7e3084a07e02c78cf3103c542bc5b298669f21, 0x14db745c6780e9df549864cec19c2daf4531f6ec0c89cc1c7436cc4d8d300c6d);
vk.gammaBeta2 = Pairing.G2Point([0x1f39e4e4afc4bc74790a4a028aff2c3d2538731fb755edefd8cb48d6ea589b5e, 0x283f150794b6736f670d6a1033f9b46c6f5204f50813eb85c8dc4b59db1c5d39], [0x140d97ee4d2b36d99bc49974d18ecca3e7ad51011956051b464d9e27d46cc25e, 0x0764bb98575bd466d32db7b15f582b2d5c452b36aa394b789366e5e3ca5aabd4]);
vk.Z = Pairing.G2Point([0x217cee0a9ad79a4493b5253e2e4e3a39fc2df38419f230d341f60cb064a0ac29, 0x0a3d76f140db8418ba512272381446eb73958670f00cf46f1d9e64cba057b53c], [0x26f64a8ec70387a13e41430ed3ee4a7db2059cc5fc13c067194bcc0cb49a9855, 0x2fd72bd9edb657346127da132e5b82ab908f5816c826acb499e22f2412d1a2d7]);
vk.IC = new Pairing.G1Point[](10);
vk.IC[0] = Pairing.G1Point(0x0aee46a7ea6e80a3675026dfa84019deee2a2dedb1bbe11d7fe124cb3efb4b5a, 0x044747b6e9176e13ede3a4dfd0d33ccca6321b9acd23bf3683a60adc0366ebaf);
vk.IC[1] = Pairing.G1Point(0x1e39e9f0f91fa7ff8047ffd90de08785777fe61c0e3434e728fce4cf35047ddc, 0x2e0b64d75ebfa86d7f8f8e08abbe2e7ae6e0a1c0b34d028f19fa56e9450527cb);
vk.IC[2] = Pairing.G1Point(0x1c36e713d4d54e3a9644dffca1fc524be4868f66572516025a61ca542539d43f, 0x042dcc4525b82dfb242b09cb21909d5c22643dcdbe98c4d082cc2877e96b24db);
vk.IC[3] = Pairing.G1Point(0x17d5d09b4146424bff7e6fb01487c477bbfcd0cdbbc92d5d6457aae0b6717cc5, 0x02b5636903efbf46db9235bbe74045d21c138897fda32e079040db1a16c1a7a1);
vk.IC[4] = Pairing.G1Point(0x0f103f14a584d4203c27c26155b2c955f8dfa816980b24ba824e1972d6486a5d, 0x0c4165133b9f5be17c804203af781bcf168da7386620479f9b885ecbcd27b17b);
vk.IC[5] = Pairing.G1Point(0x232063b584fb76c8d07995bee3a38fa7565405f3549c6a918ddaa90ab971e7f8, 0x2ac9b135a81d96425c92d02296322ad56ffb16299633233e4880f95aafa7fda7);
vk.IC[6] = Pairing.G1Point(0x09b54f111d3b2d1b2fe1ae9669b3db3d7bf93b70f00647e65c849275de6dc7fe, 0x18b2e77c63a3e400d6d1f1fbc6e1a1167bbca603d34d03edea231eb0ab7b14b4);
vk.IC[7] = Pairing.G1Point(0x0c54b42137b67cc268cbb53ac62b00ecead23984092b494a88befe58445a244a, 0x18e3723d37fae9262d58b548a0575f59d9c3266db7afb4d5739555837f6b8b3e);
vk.IC[8] = Pairing.G1Point(0x0a6de0e2240aa253f46ce0da883b61976e3588146e01c9d8976548c145fe6e4a, 0x04fbaa3a4aed4bb77f30ebb07a3ec1c7d77a7f2edd75636babfeff97b1ea686e);
vk.IC[9] = Pairing.G1Point(0x111e2e2a5f8828f80ddad08f9f74db56dac1cc16c1cb278036f79a84cf7a116f, 0x1d7d62e192b219b9808faa906c5ced871788f6339e8d91b83ac1343e20a16b30);
}
function verify(uint[] memory input, Proof memory proof) internal returns (uint) {
VerifyingKey memory vk = verifyingKey();
require(input.length + 1 == vk.IC.length);
// Compute the linear combination vk_x
Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0);
for (uint i = 0; i < input.length; i++)
vk_x = Pairing.add(vk_x, Pairing.mul(vk.IC[i + 1], input[i]));
vk_x = Pairing.add(vk_x, vk.IC[0]);
if (!Pairing.pairingProd2(proof.A, vk.A, Pairing.negate(proof.A_p), Pairing.P2())) return 1;
if (!Pairing.pairingProd2(vk.B, proof.B, Pairing.negate(proof.B_p), Pairing.P2())) return 2;
if (!Pairing.pairingProd2(proof.C, vk.C, Pairing.negate(proof.C_p), Pairing.P2())) return 3;
if (!Pairing.pairingProd3(
proof.K, vk.gamma,
Pairing.negate(Pairing.add(vk_x, Pairing.add(proof.A, proof.C))), vk.gammaBeta2,
Pairing.negate(vk.gammaBeta1), proof.B
)) return 4;
if (!Pairing.pairingProd3(
Pairing.add(vk_x, proof.A), proof.B,
Pairing.negate(proof.H), vk.Z,
Pairing.negate(proof.C), Pairing.P2()
)) return 5;
return 0;
}
event Verified(string);
function verifyTx() public returns (bool) {
uint[] memory input = new uint[](9);
Proof memory proof;
proof.A = Pairing.G1Point(12873740738727497448187997291915224677121726020054032516825496230827252793177, 21804419174137094775122804775419507726154084057848719988004616848382402162497);
proof.A_p = Pairing.G1Point(7742452358972543465462254569134860944739929848367563713587808717088650354556, 7324522103398787664095385319014038380128814213034709026832529060148225837366);
proof.B = Pairing.G2Point(
[8176651290984905087450403379100573157708110416512446269839297438960217797614, 15588556568726919713003060429893850972163943674590384915350025440408631945055],
[15347511022514187557142999444367533883366476794364262773195059233657571533367, 4265071979090628150845437155927259896060451682253086069461962693761322642015]);
proof.B_p = Pairing.G1Point(2979746655438963305714517285593753729335852012083057917022078236006592638393, 6470627481646078059765266161088786576504622012540639992486470834383274712950);
proof.C = Pairing.G1Point(6851077925310461602867742977619883934042581405263014789956638244065803308498, 10336382210592135525880811046708757754106524561907815205241508542912494488506);
proof.C_p = Pairing.G1Point(12491625890066296859584468664467427202390981822868257437245835716136010795448, 13818492518017455361318553880921248537817650587494176379915981090396574171686);
proof.H = Pairing.G1Point(12091046215835229523641173286701717671667447745509192321596954139357866668225, 14446807589950902476683545679847436767890904443411534435294953056557941441758);
proof.K = Pairing.G1Point(21341087976609916409401737322664290631992568431163400450267978471171152600502, 2942165230690572858696920423896381470344658299915828986338281196715687693170);
input[0] = 13986731495506593864492662381614386532349950841221768152838255933892789078521;
input[1] = 622860516154313070522697309645122400675542217310916019527100517240519630053;
input[2] = 11094488463398718754251685950409355128550342438297986977413505294941943071569;
input[3] = 6627643779954497813586310325594578844876646808666478625705401786271515864467;
input[4] = 2957286918163151606545409668133310005545945782087581890025685458369200827463;
input[5] = 1384290496819542862903939282897996566903332587607290986044945365745128311081;
input[6] = 5613571677741714971687805233468747950848449704454346829971683826953541367271;
input[7] = 9643208548031422463313148630985736896287522941726746581856185889848792022807;
input[8] = 18066496933330839731877828156604;
if (verify(input, proof) == 0) {
emit Verified("Transaction successfully verified.");
return true;
} else {
return false;
}
}

}
)";
compileAndRun(sourceCode, 0, "Pairing");
compileAndRun(sourceCode, 0, "Test", bytes(), map<string, Address>{{"Pairing", m_contractAddress}});
// Disabled because the point seems to be not well-formed, we need to find another example.
//BOOST_CHECK(callContractFunction("testMul()") == encodeArgs(true));
BOOST_CHECK(callContractFunction("f()") == encodeArgs(true));
BOOST_CHECK(callContractFunction("g()") == encodeArgs(true));
BOOST_CHECK(callContractFunction("pair()") == encodeArgs(true));
BOOST_CHECK(callContractFunction("verifyTx()") == encodeArgs(true));
}

BOOST_AUTO_TEST_CASE(abi_encode)
{
char const* sourceCode = R"(
297 changes: 297 additions & 0 deletions test/libsolidity/semanticTests/snark.sol
View file
Original file line number Diff line number Diff line change
@@ -0,0 +1,297 @@
library Pairing {
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 memory) {
return G1Point(1, 2);
}

/// @return the generator of G2
function P2() internal returns (G2Point memory) {
return G2Point(
[11559732032986387107991004021392285783925812861821192530917403151452391805634,
10857046999023057135944570762232829481370756359578518086990519993285655852781],
[4082367875863433681332203403145435568316851327593401208105741076214120093531,
8495653923123431417604973247489272438418190587263600148770280649306958101930]
);
}

/// @return the negation of p, i.e. p.add(p.negate()) should be zero.
function negate(G1Point memory p) internal returns (G1Point memory) {
// 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 memory p1, G1Point memory p2) internal returns (G1Point memory 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 memory p, uint s) internal returns (G1Point memory 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);
}

/// @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 p1, G2Point[] memory p2) internal returns (bool) {
require(p1.length == p2.length);
uint elements = p1.length;
uint inputSize = p1.length * 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;
}
function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory 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 pairingProd3(
G1Point memory a1, G2Point memory a2,
G1Point memory b1, G2Point memory b2,
G1Point memory c1, G2Point memory c2
) internal returns (bool) {
G1Point[] memory p1 = new G1Point[](3);
G2Point[] memory p2 = new G2Point[](3);
p1[0] = a1;
p1[1] = b1;
p1[2] = c1;
p2[0] = a2;
p2[1] = b2;
p2[2] = c2;
return pairing(p1, p2);
}
function pairingProd4(
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 returns (bool) {
G1Point[] memory p1 = new G1Point[](4);
G2Point[] memory p2 = new G2Point[](4);
p1[0] = a1;
p1[1] = b1;
p1[2] = c1;
p1[3] = d1;
p2[0] = a2;
p2[1] = b2;
p2[2] = c2;
p2[3] = d2;
return pairing(p1, p2);
}
}

contract Test {
using Pairing for *;
struct VerifyingKey {
Pairing.G2Point A;
Pairing.G1Point B;
Pairing.G2Point C;
Pairing.G2Point gamma;
Pairing.G1Point gammaBeta1;
Pairing.G2Point gammaBeta2;
Pairing.G2Point Z;
Pairing.G1Point[] IC;
}
struct Proof {
Pairing.G1Point A;
Pairing.G1Point A_p;
Pairing.G2Point B;
Pairing.G1Point B_p;
Pairing.G1Point C;
Pairing.G1Point C_p;
Pairing.G1Point K;
Pairing.G1Point H;
}
function f() public returns (bool) {
Pairing.G1Point memory p1;
Pairing.G1Point memory p2;
p1.X = 1; p1.Y = 2;
p2.X = 1; p2.Y = 2;
Pairing.G1Point memory explict_sum = Pairing.add(p1, p2);
Pairing.G1Point memory scalar_prod = Pairing.mul(p1, 2);
return (explict_sum.X == scalar_prod.X &&
explict_sum.Y == scalar_prod.Y);
}
function g() public returns (bool) {
Pairing.G1Point memory x = Pairing.add(Pairing.P1(), Pairing.negate(Pairing.P1()));
// should be zero
return (x.X == 0 && x.Y == 0);
}
function testMul() public returns (bool) {
Pairing.G1Point memory p;
// @TODO The points here are reported to be not well-formed
p.X = 14125296762497065001182820090155008161146766663259912659363835465243039841726;
p.Y = 16229134936871442251132173501211935676986397196799085184804749187146857848057;
p = Pairing.mul(p, 13986731495506593864492662381614386532349950841221768152838255933892789078521);
return
p.X == 18256332256630856740336504687838346961237861778318632856900758565550522381207 &&
p.Y == 6976682127058094634733239494758371323697222088503263230319702770853579280803;
}
function pair() public returns (bool) {
Pairing.G2Point memory fiveTimesP2 = Pairing.G2Point(
[4540444681147253467785307942530223364530218361853237193970751657229138047649, 20954117799226682825035885491234530437475518021362091509513177301640194298072],
[11631839690097995216017572651900167465857396346217730511548857041925508482915, 21508930868448350162258892668132814424284302804699005394342512102884055673846]
);
// The prime p in the base field F_p for G1
uint p = 21888242871839275222246405745257275088696311157297823662689037894645226208583;
Pairing.G1Point[] memory g1points = new Pairing.G1Point[](2);
Pairing.G2Point[] memory g2points = new Pairing.G2Point[](2);
// check e(5 P1, P2)e(-P1, 5 P2) == 1
g1points[0] = Pairing.P1().mul(5);
g1points[1] = Pairing.P1().negate();
g2points[0] = Pairing.P2();
g2points[1] = fiveTimesP2;
if (!Pairing.pairing(g1points, g2points))
return false;
// check e(P1, P2)e(-P1, P2) == 1
g1points[0] = Pairing.P1();
g1points[1] = Pairing.P1();
g1points[1].Y = p - g1points[1].Y;
g2points[0] = Pairing.P2();
g2points[1] = Pairing.P2();
if (!Pairing.pairing(g1points, g2points))
return false;
return true;
}
function verifyingKey() internal returns (VerifyingKey memory vk) {
vk.A = Pairing.G2Point([0x209dd15ebff5d46c4bd888e51a93cf99a7329636c63514396b4a452003a35bf7, 0x04bf11ca01483bfa8b34b43561848d28905960114c8ac04049af4b6315a41678], [0x2bb8324af6cfc93537a2ad1a445cfd0ca2a71acd7ac41fadbf933c2a51be344d, 0x120a2a4cf30c1bf9845f20c6fe39e07ea2cce61f0c9bb048165fe5e4de877550]);
vk.B = Pairing.G1Point(0x2eca0c7238bf16e83e7a1e6c5d49540685ff51380f309842a98561558019fc02, 0x03d3260361bb8451de5ff5ecd17f010ff22f5c31cdf184e9020b06fa5997db84);
vk.C = Pairing.G2Point([0x2e89718ad33c8bed92e210e81d1853435399a271913a6520736a4729cf0d51eb, 0x01a9e2ffa2e92599b68e44de5bcf354fa2642bd4f26b259daa6f7ce3ed57aeb3], [0x14a9a87b789a58af499b314e13c3d65bede56c07ea2d418d6874857b70763713, 0x178fb49a2d6cd347dc58973ff49613a20757d0fcc22079f9abd10c3baee24590]);
vk.gamma = Pairing.G2Point([0x25f83c8b6ab9de74e7da488ef02645c5a16a6652c3c71a15dc37fe3a5dcb7cb1, 0x22acdedd6308e3bb230d226d16a105295f523a8a02bfc5e8bd2da135ac4c245d], [0x065bbad92e7c4e31bf3757f1fe7362a63fbfee50e7dc68da116e67d600d9bf68, 0x06d302580dc0661002994e7cd3a7f224e7ddc27802777486bf80f40e4ca3cfdb]);
vk.gammaBeta1 = Pairing.G1Point(0x15794ab061441e51d01e94640b7e3084a07e02c78cf3103c542bc5b298669f21, 0x14db745c6780e9df549864cec19c2daf4531f6ec0c89cc1c7436cc4d8d300c6d);
vk.gammaBeta2 = Pairing.G2Point([0x1f39e4e4afc4bc74790a4a028aff2c3d2538731fb755edefd8cb48d6ea589b5e, 0x283f150794b6736f670d6a1033f9b46c6f5204f50813eb85c8dc4b59db1c5d39], [0x140d97ee4d2b36d99bc49974d18ecca3e7ad51011956051b464d9e27d46cc25e, 0x0764bb98575bd466d32db7b15f582b2d5c452b36aa394b789366e5e3ca5aabd4]);
vk.Z = Pairing.G2Point([0x217cee0a9ad79a4493b5253e2e4e3a39fc2df38419f230d341f60cb064a0ac29, 0x0a3d76f140db8418ba512272381446eb73958670f00cf46f1d9e64cba057b53c], [0x26f64a8ec70387a13e41430ed3ee4a7db2059cc5fc13c067194bcc0cb49a9855, 0x2fd72bd9edb657346127da132e5b82ab908f5816c826acb499e22f2412d1a2d7]);
vk.IC = new Pairing.G1Point[](10);
vk.IC[0] = Pairing.G1Point(0x0aee46a7ea6e80a3675026dfa84019deee2a2dedb1bbe11d7fe124cb3efb4b5a, 0x044747b6e9176e13ede3a4dfd0d33ccca6321b9acd23bf3683a60adc0366ebaf);
vk.IC[1] = Pairing.G1Point(0x1e39e9f0f91fa7ff8047ffd90de08785777fe61c0e3434e728fce4cf35047ddc, 0x2e0b64d75ebfa86d7f8f8e08abbe2e7ae6e0a1c0b34d028f19fa56e9450527cb);
vk.IC[2] = Pairing.G1Point(0x1c36e713d4d54e3a9644dffca1fc524be4868f66572516025a61ca542539d43f, 0x042dcc4525b82dfb242b09cb21909d5c22643dcdbe98c4d082cc2877e96b24db);
vk.IC[3] = Pairing.G1Point(0x17d5d09b4146424bff7e6fb01487c477bbfcd0cdbbc92d5d6457aae0b6717cc5, 0x02b5636903efbf46db9235bbe74045d21c138897fda32e079040db1a16c1a7a1);
vk.IC[4] = Pairing.G1Point(0x0f103f14a584d4203c27c26155b2c955f8dfa816980b24ba824e1972d6486a5d, 0x0c4165133b9f5be17c804203af781bcf168da7386620479f9b885ecbcd27b17b);
vk.IC[5] = Pairing.G1Point(0x232063b584fb76c8d07995bee3a38fa7565405f3549c6a918ddaa90ab971e7f8, 0x2ac9b135a81d96425c92d02296322ad56ffb16299633233e4880f95aafa7fda7);
vk.IC[6] = Pairing.G1Point(0x09b54f111d3b2d1b2fe1ae9669b3db3d7bf93b70f00647e65c849275de6dc7fe, 0x18b2e77c63a3e400d6d1f1fbc6e1a1167bbca603d34d03edea231eb0ab7b14b4);
vk.IC[7] = Pairing.G1Point(0x0c54b42137b67cc268cbb53ac62b00ecead23984092b494a88befe58445a244a, 0x18e3723d37fae9262d58b548a0575f59d9c3266db7afb4d5739555837f6b8b3e);
vk.IC[8] = Pairing.G1Point(0x0a6de0e2240aa253f46ce0da883b61976e3588146e01c9d8976548c145fe6e4a, 0x04fbaa3a4aed4bb77f30ebb07a3ec1c7d77a7f2edd75636babfeff97b1ea686e);
vk.IC[9] = Pairing.G1Point(0x111e2e2a5f8828f80ddad08f9f74db56dac1cc16c1cb278036f79a84cf7a116f, 0x1d7d62e192b219b9808faa906c5ced871788f6339e8d91b83ac1343e20a16b30);
}
function verify(uint[] memory input, Proof memory proof) internal returns (uint) {
VerifyingKey memory vk = verifyingKey();
require(input.length + 1 == vk.IC.length);
// Compute the linear combination vk_x
Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0);
for (uint i = 0; i < input.length; i++)
vk_x = Pairing.add(vk_x, Pairing.mul(vk.IC[i + 1], input[i]));
vk_x = Pairing.add(vk_x, vk.IC[0]);
if (!Pairing.pairingProd2(proof.A, vk.A, Pairing.negate(proof.A_p), Pairing.P2())) return 1;
if (!Pairing.pairingProd2(vk.B, proof.B, Pairing.negate(proof.B_p), Pairing.P2())) return 2;
if (!Pairing.pairingProd2(proof.C, vk.C, Pairing.negate(proof.C_p), Pairing.P2())) return 3;
if (!Pairing.pairingProd3(
proof.K, vk.gamma,
Pairing.negate(Pairing.add(vk_x, Pairing.add(proof.A, proof.C))), vk.gammaBeta2,
Pairing.negate(vk.gammaBeta1), proof.B
)) return 4;
if (!Pairing.pairingProd3(
Pairing.add(vk_x, proof.A), proof.B,
Pairing.negate(proof.H), vk.Z,
Pairing.negate(proof.C), Pairing.P2()
)) return 5;
return 0;
}
event Verified(string);
function verifyTx() public returns (bool) {
uint[] memory input = new uint[](9);
Proof memory proof;
proof.A = Pairing.G1Point(12873740738727497448187997291915224677121726020054032516825496230827252793177, 21804419174137094775122804775419507726154084057848719988004616848382402162497);
proof.A_p = Pairing.G1Point(7742452358972543465462254569134860944739929848367563713587808717088650354556, 7324522103398787664095385319014038380128814213034709026832529060148225837366);
proof.B = Pairing.G2Point(
[8176651290984905087450403379100573157708110416512446269839297438960217797614, 15588556568726919713003060429893850972163943674590384915350025440408631945055],
[15347511022514187557142999444367533883366476794364262773195059233657571533367, 4265071979090628150845437155927259896060451682253086069461962693761322642015]);
proof.B_p = Pairing.G1Point(2979746655438963305714517285593753729335852012083057917022078236006592638393, 6470627481646078059765266161088786576504622012540639992486470834383274712950);
proof.C = Pairing.G1Point(6851077925310461602867742977619883934042581405263014789956638244065803308498, 10336382210592135525880811046708757754106524561907815205241508542912494488506);
proof.C_p = Pairing.G1Point(12491625890066296859584468664467427202390981822868257437245835716136010795448, 13818492518017455361318553880921248537817650587494176379915981090396574171686);
proof.H = Pairing.G1Point(12091046215835229523641173286701717671667447745509192321596954139357866668225, 14446807589950902476683545679847436767890904443411534435294953056557941441758);
proof.K = Pairing.G1Point(21341087976609916409401737322664290631992568431163400450267978471171152600502, 2942165230690572858696920423896381470344658299915828986338281196715687693170);
input[0] = 13986731495506593864492662381614386532349950841221768152838255933892789078521;
input[1] = 622860516154313070522697309645122400675542217310916019527100517240519630053;
input[2] = 11094488463398718754251685950409355128550342438297986977413505294941943071569;
input[3] = 6627643779954497813586310325594578844876646808666478625705401786271515864467;
input[4] = 2957286918163151606545409668133310005545945782087581890025685458369200827463;
input[5] = 1384290496819542862903939282897996566903332587607290986044945365745128311081;
input[6] = 5613571677741714971687805233468747950848449704454346829971683826953541367271;
input[7] = 9643208548031422463313148630985736896287522941726746581856185889848792022807;
input[8] = 18066496933330839731877828156604;
if (verify(input, proof) == 0) {
emit Verified("Transaction successfully verified.");
return true;
} else {
return false;
}
}
}
/// Disabled because the point seems to be not well-formed, we need to find another example.
/// testMul() -> true
//
// ====
// EVMVersion: >=constantinople
// ----
// library: Pairing
// f() -> true
// g() -> true
// pair() -> true
// verifyTx() -> true