Skip to content

Instantly share code, notes, and snippets.

What would you like to do?
zkSNARKs test code
// This file is MIT Licensed.
// Copyright 2017 Christian Reitwiessner
// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
pragma solidity ^0.4.14;
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) {
return G1Point(1, 2);
/// @return the generator of G2
function P2() internal returns (G2Point) {
return G2Point(
/// @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 }
/// @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);
/// @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 }
return out[0] != 0;
/// Convenience method for a pairing check for two pairs.
function pairingProd2(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);
/// Convenience method for a pairing check for three pairs.
function pairingProd3(
G1Point a1, G2Point a2,
G1Point b1, G2Point b2,
G1Point c1, G2Point 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);
/// Convenience method for a pairing check for four pairs.
function pairingProd4(
G1Point a1, G2Point a2,
G1Point b1, G2Point b2,
G1Point c1, G2Point c2,
G1Point d1, G2Point 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() returns (bool) {
Pairing.G1Point memory p1;
Pairing.G1Point memory p2;
p1.X = 1; p1.Y = 2;
p2.X = 1; p2.Y = 2;
var explict_sum = Pairing.add(p1, p2);
var scalar_prod = Pairing.mul(p1, 2);
return (explict_sum.X == scalar_prod.X &&
explict_sum.Y == scalar_prod.Y);
function g() 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() 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);
p.X == 18256332256630856740336504687838346961237861778318632856900758565550522381207 &&
p.Y == 6976682127058094634733239494758371323697222088503263230319702770853579280803;
function pair() 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();
g1points[1].Y = p - g1points[1].Y;
g2points[0] = Pairing.P2();
g2points[1] = fiveTimesP2;
if (!Pairing.pairing(g1points, g2points))
return false;
// check e(P1, P2)e(-P1, P2) == 0
g1points[0] = Pairing.P1();
g1points[1] = Pairing.P1().negate();
g2points[0] = Pairing.P2();
g2points[1] = Pairing.P2();
if (!Pairing.pairing(g1points, g2points))
return false;
return true;
function verifyingKey() internal returns (VerifyingKey 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[] input, Proof 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() returns (bool r) {
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) {
Verified("Transaction successfully verified.");
return true;
} else {
return false;
Copy link

vjuge commented Oct 3, 2017

Can you describe how to use it ? thx

Copy link

saitam1 commented Oct 4, 2017

Any explanation on how to use this?

Copy link

georgek146 commented Oct 12, 2017

yeah this looks awesome, but have no idea where to even start.

Copy link

devonwesley commented Oct 15, 2017

So awesome Thank you so much

Copy link

chriseth commented Oct 16, 2017

@vjuge @saitam1 @georgek146 @jusdev89 we are working on tools to make this easier:
They will probably be released at devcon.

Copy link

kumavis commented Oct 26, 2017

@chriseth - is verifyTx using a real world zcash tx?
EDIT: i saw on reddit that it is. was hoping to get the tx hash but i suppose you dont have it anymore.

What is verified here is the zkSNARK part of some real transaction on the real zCash network. I pulled the data out of the chain some time around January, I think. I have no idea who created the transaction or how much money is sent inside it, but now the Ethereum network knows it is correct :-)

Copy link

kumavis commented Oct 26, 2017

@chriseth - curious why vk.B and proof.B are swapped here (maybe the order doesnt matter)

		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;

Copy link

vjuge commented Nov 2, 2017

@chriseth : saw the presentation at devcon (mainstage one - remotely), happy to get the github repo, and will check it out :)

Copy link

marmengol commented Nov 22, 2017

I have a doubt about this line: success := call(sub(gas, 2000), 8, 0, add(input, 0x20), mul(inputSize, 0x20), out, 0x20)
what does the address param (8) means? As I see in Solidity documentation, this opcode has the following description: "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"

One more doubt. Could you explain me (cause I'm quite noob) why, in pairing function, position 0 of out param always is 0? It makes that verifyTx function always returns false.

Thank you!

Copy link

marmengol commented Nov 23, 2017

Hi again @chriseth,
I deployed the contract and tried verifyTx() function but transaction always fails. Do you know why?
Thank you!

Copy link

jackieWhn commented Nov 25, 2017

hi @chriseth
I have the same question with marmengol.
What does the addree param(8) means? thanks

Copy link

matthieu-merlyn commented Nov 28, 2017

@marmengol I was able to test the verifyTx() function on a private network using this exact code. Make sure your geth client is greater than 1.7.0 and that you are using Byzantium (for a private network: include "ByzantiumBlock": 0 in your genesis.json)

@jackieWhn if I'm not mistaken the addr 8 refers to the precompiled bn256Pairing contract

Copy link

jackieWhn commented Dec 27, 2017

@matthieu-merlyn, i test the verifyTx() function on a private network, return false. f() function, return true. why?

Copy link

renchenchang commented Sep 28, 2018

could you show the ZoKrates code to generate this verification code?

Copy link

alexpArtos commented Jan 7, 2019

@marmengol @jackieWhn @matthieu-merlyn
Indeed, it is the 8th precompiled Ethereum contract, as explained here.
The specification of this particular contract is in here.

Precompiled contracts are not written in EVM bytecode, they are directly implemented by the client. The Geth implementation for the precompiled contracts is here:

var PrecompiledContractsByzantium = map[common.Address]PrecompiledContract{
	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{},

Contract 8 is actually implemented by the last function in the file: it extracts two sets of points and computes the product of their pairings. The actual work is done by function bn256.PairingCheck(cs, ts), which is implemented here.

Copy link

DaniyarSarasenov commented Jan 14, 2022

I wanna see full source code using sz-SNARK.
Who could you give me a way how can find the samples of sz-SANRK?

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment