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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+                            Preamble
+
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+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) {year}  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    {project}  Copyright (C) {year}  {fullname}
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

README.md

@@ -0,0 +1,133 @@
+# snarkjs: JavaScript implementation of zkSNARKs.
+
+This is a JavaScript implementation of zkSNARK schemes. It allows the original 8points protocol
+and the Groth Protocol (3 point only and 3 pairings)
+
+This library allows to do the trusted setup, generate proofs and verify the proofs.
+
+This library uses the compiled circuits generated by the jaz compiler.
+
+### Tutorial.
+
+A good starting point [is this tutorial](https://github.com/iden3/circom/blob/master/TUTORIAL.md)
+
+Also this [video](https://www.youtube.com/watch?v=-9TJa1hVsKA) is a good starting point.
+
+## Install.
+
+```sh
+npm install snarkjs
+```
+
+## Usage from command line.
+
+
+```sh
+snarkjs --help
+```
+
+Will show all the info in how to use the cli.
+
+## Usage from javascript
+
+
+### Import.
+
+```js
+const zkSnark = require("snarkjs");
+```
+
+### Load a circuit.
+
+```js
+// "myCircuit.cir" is the output of the jaz compiler
+
+const circuitDef = JSON.parse(fs.readFileSync("myCircuit.cir", "utf8"));
+const circuit = new zkSnark.Circuit(circuitDef);
+```
+
+### Inspect the circuit.
+
+```js
+    // `signalId` can always be a number or an alias string
+
+    circuit.nConstraints; // number of constraints
+    circuit.nSignals; // number of signals
+    circuit.nPublic; // number of public signals (nOutputs + nPublicInputs)
+
+    // The array of signals is always sorted in this order:
+    // [ 1, outputs, publicInputs, privateInputs, internalSignals, constants]
+
+    // returns a,b and c coeficients of the `signalId` on a given `constraint`
+    circuit.a(constraint, signalId)
+    circuit.b(constraint, signalId)
+    circuit.c(constraint, signalId)
+
+    circuit.nOutputs           // number of public outputs
+    circuit.pubInputs          // number of public inputs
+    circuit.nPrvInputs         // number of private inputs
+    circuit.nInputs            // number of inputs ( nPublicInputs + nPrivateInputs)
+    circuit.nVars              // number of variables ( not including constants (one is a variable) )
+    circuit.nSignals           // number of signals ( including constants )
+
+    circuit.outputIdx(i)       // returns the index of the i'th output
+    circuit.inputIdx(i)        // returns the index of the i'th input
+    circuit.pubInputIdx(i)     // returns the index of the i'th public input
+    circuit.prvInputIdx(i)     // returns the index of the i'th private input
+    circuit.varIdx(i)          // returns the index of the i'th variable
+    circuit.constantIdx(i)     // returns the index of the i'th constant
+    circuit.signalIdx(i)       // returns the index of the i'th signal
+
+    // returns signal Idx given a signalId
+    // if the idx >= n , it is a constant
+    // if the idx == -1, the signal does not exist
+    circuit.getSignalIdx(name);
+
+    // returns an array aliases names of the i'th signal
+    circuit.signalNames(i)
+
+    // input is a key value object where keys are the signal names
+    //   of all the inputs (public and private)
+    // returns an array of values representing the witness
+    circuit.calculateWitness(input)
+```
+
+### Trusted setup.
+
+```js
+const setup = zkSnark.setup(circuit);
+fs.writeFileSync("myCircuit.vk_proof", JSON.stringify(setup.vk_proof), "utf8");
+fs.writeFileSync("myCircuit.vk_verifier", JSON.stringify(setup.vk_verifier), "utf8");
+setup.toxic  // Must be discarded.
+```
+
+### Generate proof.
+
+```js
+const circuitDef = JSON.parse(fs.readFileSync("myCircuit.cir", "utf8"));
+const circuit = new zkSnark.Circuit(circuitDef);
+const input = {
+    "main.pubIn1": "123",
+    "main.out1": "456"
+}
+const witness = circuit.calculateWitness(input);
+const vk_proof = JSON.parse(fs.readFileSync("myCircuit.vk_proof", "utf8"));
+
+const {proof, publicSignals} = zkSnark.genProof(vk_proof, witness);
+```
+
+### Verifier.
+
+```js
+const vk_verifier = JSON.parse(fs.readFileSync("myCircuit.vk_verifier", "utf8"));
+
+if (zkSnark.isValid(vk_verifier, proof, publicSignals)) {
+    console.log("The proof is valid");
+} else {
+    console.log("The proof is not valid");
+}
+```
+
+## License
+
+snarkjs is part of the iden3 project copyright 2018 0KIMS association and published with GPL-3 license. Please check the COPYING file for more details.

cli.js

@@ -0,0 +1,544 @@
+#!/usr/bin/env node
+
+/*
+    Copyright 2018 0KIMS association.
+
+    This file is part of jaz (Zero Knowledge Circuit Compiler).
+
+    jaz is a free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    jaz is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
+    License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with jaz. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* eslint-disable no-console */
+
+const fs = require("fs");
+const path = require("path");
+
+const zkSnark = require("./index.js");
+const {stringifyBigInts, unstringifyBigInts} = require("./src/stringifybigint.js");
+
+
+const version = require("./package").version;
+
+const argv = require("yargs")
+    .version(version)
+    .usage(`snarkjs <command> <options>
+
+setup command
+=============
+
+    snarkjs setup <option>
+
+    Runs a setup for a circuit generating the proving and the verification key.
+
+    -c or --circuit <circuitFile>
+
+        Filename of the compiled circuit file generated by circom.
+
+        Default: circuit.json
+
+    --pk or --provingkey <provingKeyFile>
+
+        Output filename where the proving key will be stored.
+
+        Default: proving_key.json
+
+    --vk or --verificationkey <verificationKeyFile>
+
+        Output Filename where the verification key will be stored.
+
+        Default: verification_key.json
+
+    --protocol [original|groth|kimleeoh]
+
+        Defines which variant of snark you want to use
+
+        Default: original
+
+calculate witness command
+=========================
+
+    snarkjs calculatewitness <options>
+
+    Calculate the witness of a circuit given an input.
+
+    -c or --circuit <circuitFile>
+
+        Filename of the compiled circuit file generated by circom.
+
+        Default: circuit.json
+
+    -i or --input <inputFile>
+
+        JSON file with the inputs of the circuit.
+
+        Default: input.json
+
+        Example of a circuit with two inputs a and b:
+
+            {"a": "22", "b": "33"}
+
+    -w or --witness
+
+        Output filename with the generated witness.
+
+        Default: witness.json
+
+    --lo or --logoutput
+
+        Output all the Output signals
+
+    --lg or --logget
+
+        Output GET access to the signals
+
+    --ls or --logset
+
+        Output SET access to the signal
+
+    --lt or --logtrigger
+
+        Output when a subcomponent is triggered and when finished
+
+
+generate a proof command
+========================
+
+    snarkjs proof <options>
+
+    -w or --witness
+
+        Input filename used to calculate the proof.
+
+        Default: witness.json
+
+    --pk or --provingkey <provingKeyFile>
+
+        Input filename with the proving key (generated during the setup).
+
+        Default: proving_key.json
+
+    -p or --proof
+
+        Output filenam with the zero knowlage proof.
+
+        Default: proof.json
+
+    --pub or --public <publicFilename>
+
+        Output filename with the value of the public wires/signals.
+        This info will be needed to verify the proof.
+
+        Default: public.json
+
+verify command
+==============
+
+    snarkjs verify <options>
+
+    The command returns "OK" if the proof is valid
+    and  "INVALID" in case it is not a valid proof.
+
+    --vk or --verificationkey <verificationKeyFile>
+
+        Input Filename with the verification key (generated during the setup).
+
+        Default: verification_key.json
+
+    -p or --proof
+
+        Input filenam with the zero knowlage proof you want to verify
+
+        Default: proof.json
+
+    --pub or --public <publicFilename>
+
+        Input filename with the public wires/signals.
+
+        Default: public.json
+
+
+generate solidity verifier command
+==================================
+
+    snarkjs generateverifier <options>
+
+    Generates a solidity smart contract that verifies the zero knowlage proof.
+
+    --vk or --verificationkey <verificationKeyFile>
+
+        Input Filename with the verification key (generated during the setup).
+
+        Default: verification_key.json
+
+    -v or --verifier
+
+        Output file with a solidity smart contract that verifies a zero knowlage proof.
+
+        Default: verifier.sol
+
+
+generate call parameters
+========================
+
+    snarkjs generatecall <options>
+
+    Outputs into the console the raw parameters to be used in 'verifyProof'
+    method of the solidity verifier function.
+
+    -p or --proof
+
+        Input filename with the zero knowlage proof you want to use
+
+        Default: proof.json
+
+    --pub or --public <publicFilename>
+
+        Input filename with the public wires/signals.
+
+        Default: public.json
+
+circuit info
+============
+
+    snarkjs info <options>
+
+    Print statistics of a circuit
+
+    -c or --circuit <circuitFile>
+
+        Filename of the compiled circuit file generated by circom.
+
+        Default: circuit.json
+
+print constraints
+=================
+
+    snarkjs printconstraints <options>
+
+    Print all the constraints of a given circuit
+
+    -c or --circuit <circuitFile>
+
+        Filename of the compiled circuit file generated by circom.
+
+        Default: circuit.json
+        `)
+    .alias("c", "circuit")
+    .alias("pk", "provingkey")
+    .alias("vk", "verificationkey")
+    .alias("w", "witness")
+    .alias("p", "proof")
+    .alias("i", "input")
+    .alias("pub", "public")
+    .alias("v", "verifier")
+    .alias("lo", "logoutput")
+    .alias("lg", "logget")
+    .alias("ls", "logset")
+    .alias("lt", "logtrigger")
+    .help("h")
+    .alias("h", "help")
+
+    .epilogue(`Copyright (C) 2018  0kims association
+    This program comes with ABSOLUTELY NO WARRANTY;
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; see the COPYING file in the official
+    repo directory at  https://github.com/iden3/circom `)
+    .argv;
+
+const circuitName = (argv.circuit) ? argv.circuit : "circuit.json";
+const provingKeyName = (argv.provingkey) ? argv.provingkey : "proving_key.json";
+const verificationKeyName = (argv.verificationkey) ? argv.verificationkey : "verification_key.json";
+const inputName = (argv.input) ? argv.input : "input.json";
+const witnessName = (argv.witness) ? argv.witness : "witness.json";
+const proofName = (argv.proof) ? argv.proof : "proof.json";
+const publicName = (argv.public) ? argv.public : "public.json";
+const verifierName = (argv.verifier) ? argv.verifier : "verifier.sol";
+const protocol = (argv.protocol) ? argv.protocol : "original";
+
+function p256(n) {
+    let nstr = n.toString(16);
+    while (nstr.length < 64) nstr = "0"+nstr;
+    nstr = `"0x${nstr}"`;
+    return nstr;
+}
+
+try {
+    if (argv._[0].toUpperCase() == "INFO") {
+        const cirDef = JSON.parse(fs.readFileSync(circuitName, "utf8"));
+        const cir = new zkSnark.Circuit(cirDef);
+
+        console.log(`# Wires: ${cir.nVars}`);
+        console.log(`# Constraints: ${cir.nConstraints}`);
+        console.log(`# Private Inputs: ${cir.nPrvInputs}`);
+        console.log(`# Public Inputs: ${cir.nPubInputs}`);
+        console.log(`# Outputs: ${cir.nOutputs}`);
+
+    } else if (argv._[0].toUpperCase() == "PRINTCONSTRAINTS") {
+        const cirDef = JSON.parse(fs.readFileSync(circuitName, "utf8"));
+        const cir = new zkSnark.Circuit(cirDef);
+
+        cir.printConstraints();
+
+    } else if (argv._[0].toUpperCase() == "SETUP") {
+        const cirDef = JSON.parse(fs.readFileSync(circuitName, "utf8"));
+        const cir = new zkSnark.Circuit(cirDef);
+
+        if (!zkSnark[protocol]) throw new Error("Invalid protocol");
+        const setup = zkSnark[protocol].setup(cir);
+
+        fs.writeFileSync(provingKeyName, JSON.stringify(stringifyBigInts(setup.vk_proof), null, 1), "utf-8");
+        fs.writeFileSync(verificationKeyName, JSON.stringify(stringifyBigInts(setup.vk_verifier), null, 1), "utf-8");
+        process.exit(0);
+    } else if (argv._[0].toUpperCase() == "CALCULATEWITNESS") {
+        const cirDef = JSON.parse(fs.readFileSync(circuitName, "utf8"));
+        const cir = new zkSnark.Circuit(cirDef);
+        const input = unstringifyBigInts(JSON.parse(fs.readFileSync(inputName, "utf8")));
+
+        const witness = cir.calculateWitness(input, {
+            logOutput: argv.logoutput,
+            logSet: argv.logset,
+            logGet: argv.logget,
+            logTrigger: argv.logtrigger
+        });
+
+        fs.writeFileSync(witnessName, JSON.stringify(stringifyBigInts(witness), null, 1), "utf-8");
+        process.exit(0);
+    } else if (argv._[0].toUpperCase() == "PROOF") {
+        const witness = unstringifyBigInts(JSON.parse(fs.readFileSync(witnessName, "utf8")));
+        const provingKey = unstringifyBigInts(JSON.parse(fs.readFileSync(provingKeyName, "utf8")));
+
+        const protocol = provingKey.protocol;
+        if (!zkSnark[protocol]) throw new Error("Invalid protocol");
+        const {proof, publicSignals} = zkSnark[protocol].genProof(provingKey, witness);
+
+        fs.writeFileSync(proofName, JSON.stringify(stringifyBigInts(proof), null, 1), "utf-8");
+        fs.writeFileSync(publicName, JSON.stringify(stringifyBigInts(publicSignals), null, 1), "utf-8");
+        process.exit(0);
+    } else if (argv._[0].toUpperCase() == "VERIFY") {
+        const public = unstringifyBigInts(JSON.parse(fs.readFileSync(publicName, "utf8")));
+        const verificationKey = unstringifyBigInts(JSON.parse(fs.readFileSync(verificationKeyName, "utf8")));
+        const proof = unstringifyBigInts(JSON.parse(fs.readFileSync(proofName, "utf8")));
+
+        const protocol = verificationKey.protocol;
+        if (!zkSnark[protocol]) throw new Error("Invalid protocol");
+
+        const isValid = zkSnark[protocol].isValid(verificationKey, proof, public);
+
+        if (isValid) {
+            console.log("OK");
+            process.exit(0);
+        } else {
+            console.log("INVALID");
+            process.exit(1);
+        }
+    } else if (argv._[0].toUpperCase() == "GENERATEVERIFIER") {
+
+        const verificationKey = unstringifyBigInts(JSON.parse(fs.readFileSync(verificationKeyName, "utf8")));
+
+        let verifierCode;
+        if (verificationKey.protocol == "original") {
+            verifierCode = generateVerifier_original(verificationKey);
+        } else if (verificationKey.protocol == "groth") {
+            verifierCode = generateVerifier_groth(verificationKey);
+        } else if (verificationKey.protocol == "kimleeoh") {
+            verifierCode = generateVerifier_kimleeoh(verificationKey);
+        } else {
+            throw new Error("InvalidProof");
+        }
+
+        fs.writeFileSync(verifierName, verifierCode, "utf-8");
+        process.exit(0);
+
+    } else if (argv._[0].toUpperCase() == "GENERATECALL") {
+
+        const public = unstringifyBigInts(JSON.parse(fs.readFileSync(publicName, "utf8")));
+        const proof = unstringifyBigInts(JSON.parse(fs.readFileSync(proofName, "utf8")));
+
+        let inputs = "";
+        for (let i=0; i<public.length; i++) {
+            if (inputs != "") inputs = inputs + ",";
+            inputs = inputs + p256(public[i]);
+        }
+
+        let S;
+        if ((typeof proof.protocol === "undefined") || (proof.protocol == "original")) {
+            S=`[${p256(proof.pi_a[0])}, ${p256(proof.pi_a[1])}],` +
+              `[${p256(proof.pi_ap[0])}, ${p256(proof.pi_ap[1])}],` +
+              `[[${p256(proof.pi_b[0][1])}, ${p256(proof.pi_b[0][0])}],[${p256(proof.pi_b[1][1])}, ${p256(proof.pi_b[1][0])}]],` +
+              `[${p256(proof.pi_bp[0])}, ${p256(proof.pi_bp[1])}],` +
+              `[${p256(proof.pi_c[0])}, ${p256(proof.pi_c[1])}],` +
+              `[${p256(proof.pi_cp[0])}, ${p256(proof.pi_cp[1])}],` +
+              `[${p256(proof.pi_h[0])}, ${p256(proof.pi_h[1])}],` +
+              `[${p256(proof.pi_kp[0])}, ${p256(proof.pi_kp[1])}],` +
+              `[${inputs}]`;
+        } else if ((proof.protocol == "groth")||(proof.protocol == "kimleeoh")) {
+            S=`[${p256(proof.pi_a[0])}, ${p256(proof.pi_a[1])}],` +
+              `[[${p256(proof.pi_b[0][1])}, ${p256(proof.pi_b[0][0])}],[${p256(proof.pi_b[1][1])}, ${p256(proof.pi_b[1][0])}]],` +
+              `[${p256(proof.pi_c[0])}, ${p256(proof.pi_c[1])}],` +
+              `[${inputs}]`;
+        } else {
+            throw new Error("InvalidProof");
+        }
+
+        console.log(S);
+        process.exit(0);
+    } else {
+        throw new Error("Invalid Command");
+    }
+} catch(err) {
+    console.log(err.stack);
+    console.log("ERROR: " + err);
+    process.exit(1);
+}
+
+
+function generateVerifier_original(verificationKey) {
+    let template = fs.readFileSync(path.join( __dirname,  "templates", "verifier_original.sol"), "utf-8");
+
+    const vka_str = `[${verificationKey.vk_a[0][1].toString()},`+
+                     `${verificationKey.vk_a[0][0].toString()}], `+
+                    `[${verificationKey.vk_a[1][1].toString()},` +
+                     `${verificationKey.vk_a[1][0].toString()}]`;
+    template = template.replace("<%vk_a%>", vka_str);
+
+    const vkb_str = `${verificationKey.vk_b[0].toString()},`+
+                    `${verificationKey.vk_b[1].toString()}`;
+    template = template.replace("<%vk_b%>", vkb_str);
+
+    const vkc_str = `[${verificationKey.vk_c[0][1].toString()},`+
+                     `${verificationKey.vk_c[0][0].toString()}], `+
+                    `[${verificationKey.vk_c[1][1].toString()},` +
+                     `${verificationKey.vk_c[1][0].toString()}]`;
+    template = template.replace("<%vk_c%>", vkc_str);
+
+    const vkg_str = `[${verificationKey.vk_g[0][1].toString()},`+
+                      `${verificationKey.vk_g[0][0].toString()}], `+
+                    `[${verificationKey.vk_g[1][1].toString()},` +
+                     `${verificationKey.vk_g[1][0].toString()}]`;
+    template = template.replace("<%vk_g%>", vkg_str);
+
+    const vkgb1_str = `${verificationKey.vk_gb_1[0].toString()},`+
+                      `${verificationKey.vk_gb_1[1].toString()}`;
+    template = template.replace("<%vk_gb1%>", vkgb1_str);
+
+    const vkgb2_str = `[${verificationKey.vk_gb_2[0][1].toString()},`+
+                       `${verificationKey.vk_gb_2[0][0].toString()}], `+
+                      `[${verificationKey.vk_gb_2[1][1].toString()},` +
+                       `${verificationKey.vk_gb_2[1][0].toString()}]`;
+    template = template.replace("<%vk_gb2%>", vkgb2_str);
+
+    const vkz_str = `[${verificationKey.vk_z[0][1].toString()},`+
+                     `${verificationKey.vk_z[0][0].toString()}], `+
+                    `[${verificationKey.vk_z[1][1].toString()},` +
+                     `${verificationKey.vk_z[1][0].toString()}]`;
+    template = template.replace("<%vk_z%>", vkz_str);
+
+    // The points
+
+    template = template.replace(/<%vk_input_length%>/g, (verificationKey.IC.length-1).toString());
+    template = template.replace("<%vk_ic_length%>", verificationKey.IC.length.toString());
+    let vi = "";
+    for (let i=0; i<verificationKey.IC.length; i++) {
+        if (vi != "") vi = vi + "        ";
+        vi = vi + `vk.IC[${i}] = Pairing.G1Point(${verificationKey.IC[i][0].toString()},`+
+                                                `${verificationKey.IC[i][1].toString()});\n`;
+    }
+    template = template.replace("<%vk_ic_pts%>", vi);
+
+    return template;
+}
+
+
+function generateVerifier_groth(verificationKey) {
+    let template = fs.readFileSync(path.join( __dirname,  "templates", "verifier_groth.sol"), "utf-8");
+
+
+    const vkalfa1_str = `${verificationKey.vk_alfa_1[0].toString()},`+
+                        `${verificationKey.vk_alfa_1[1].toString()}`;
+    template = template.replace("<%vk_alfa1%>", vkalfa1_str);
+
+    const vkbeta2_str = `[${verificationKey.vk_beta_2[0][1].toString()},`+
+                         `${verificationKey.vk_beta_2[0][0].toString()}], `+
+                        `[${verificationKey.vk_beta_2[1][1].toString()},` +
+                         `${verificationKey.vk_beta_2[1][0].toString()}]`;
+    template = template.replace("<%vk_beta2%>", vkbeta2_str);
+
+    const vkgamma2_str = `[${verificationKey.vk_gamma_2[0][1].toString()},`+
+                          `${verificationKey.vk_gamma_2[0][0].toString()}], `+
+                         `[${verificationKey.vk_gamma_2[1][1].toString()},` +
+                          `${verificationKey.vk_gamma_2[1][0].toString()}]`;
+    template = template.replace("<%vk_gamma2%>", vkgamma2_str);
+
+    const vkdelta2_str = `[${verificationKey.vk_delta_2[0][1].toString()},`+
+                          `${verificationKey.vk_delta_2[0][0].toString()}], `+
+                         `[${verificationKey.vk_delta_2[1][1].toString()},` +
+                          `${verificationKey.vk_delta_2[1][0].toString()}]`;
+    template = template.replace("<%vk_delta2%>", vkdelta2_str);
+
+    // The points
+
+    template = template.replace(/<%vk_input_length%>/g, (verificationKey.IC.length-1).toString());
+    template = template.replace("<%vk_ic_length%>", verificationKey.IC.length.toString());
+    let vi = "";
+    for (let i=0; i<verificationKey.IC.length; i++) {
+        if (vi != "") vi = vi + "        ";
+        vi = vi + `vk.IC[${i}] = Pairing.G1Point(${verificationKey.IC[i][0].toString()},`+
+                                                `${verificationKey.IC[i][1].toString()});\n`;
+    }
+    template = template.replace("<%vk_ic_pts%>", vi);
+
+    return template;
+}
+
+function generateVerifier_kimleeoh(verificationKey) {
+    let template = fs.readFileSync(path.join( __dirname,  "templates", "verifier_groth.sol"), "utf-8");
+
+
+    const vkalfa1_str = `${verificationKey.vk_alfa_1[0].toString()},`+
+                        `${verificationKey.vk_alfa_1[1].toString()}`;
+    template = template.replace("<%vk_alfa1%>", vkalfa1_str);
+
+    const vkbeta2_str = `[${verificationKey.vk_beta_2[0][1].toString()},`+
+                         `${verificationKey.vk_beta_2[0][0].toString()}], `+
+                        `[${verificationKey.vk_beta_2[1][1].toString()},` +
+                         `${verificationKey.vk_beta_2[1][0].toString()}]`;
+    template = template.replace("<%vk_beta2%>", vkbeta2_str);
+
+    const vkgamma2_str = `[${verificationKey.vk_gamma_2[0][1].toString()},`+
+                          `${verificationKey.vk_gamma_2[0][0].toString()}], `+
+                         `[${verificationKey.vk_gamma_2[1][1].toString()},` +
+                          `${verificationKey.vk_gamma_2[1][0].toString()}]`;
+    template = template.replace("<%vk_gamma2%>", vkgamma2_str);
+
+    const vkdelta2_str = `[${verificationKey.vk_delta_2[0][1].toString()},`+
+                          `${verificationKey.vk_delta_2[0][0].toString()}], `+
+                         `[${verificationKey.vk_delta_2[1][1].toString()},` +
+                          `${verificationKey.vk_delta_2[1][0].toString()}]`;
+    template = template.replace("<%vk_delta2%>", vkdelta2_str);
+
+    // The points
+
+    template = template.replace(/<%vk_input_length%>/g, (verificationKey.IC.length-1).toString());
+    template = template.replace("<%vk_ic_length%>", verificationKey.IC.length.toString());
+    let vi = "";
+    for (let i=0; i<verificationKey.IC.length; i++) {
+        if (vi != "") vi = vi + "        ";
+        vi = vi + `vk.IC[${i}] = Pairing.G1Point(${verificationKey.IC[i][0].toString()},`+
+                                                `${verificationKey.IC[i][1].toString()});\n`;
+    }
+    template = template.replace("<%vk_ic_pts%>", vi);
+
+    return template;
+}
+

index.js

@@ -0,0 +1,44 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+exports.Circuit = require("./src/circuit.js");
+exports.original = {
+    setup: require("./src/setup_original.js"),
+    genProof: require("./src/prover_original.js"),
+    isValid: require("./src/verifier_original.js")
+};
+exports.groth = {
+    setup: require("./src/setup_groth.js"),
+    genProof: require("./src/prover_groth.js"),
+    isValid: require("./src/verifier_groth.js")
+};
+exports.kimleeoh = {
+    setup: require("./src/setup_kimleeoh.js"),
+    genProof: require("./src/prover_kimleeoh.js"),
+    isValid: require("./src/verifier_kimleeoh.js")
+};
+exports.bigInt = require("./src/bigint.js");
+exports.ZqField = require("./src/zqfield.js");
+
+exports.stringifyBigInts = require("./src/stringifybigint.js").stringifyBigInts;
+exports.unstringifyBigInts = require("./src/stringifybigint.js").unstringifyBigInts;
+
+
+const Bn128 = require("./src/bn128.js");
+exports.bn128 = new Bn128();

package.json

@@ -0,0 +1,42 @@
+{
+  "name": "snarkjs",
+  "version": "0.1.20",
+  "description": "zkSNARKs implementation in JavaScript",
+  "main": "index.js",
+  "scripts": {
+    "test": "mocha"
+  },
+  "bin": {
+    "snarkjs": "cli.js"
+  },
+  "directories": {
+    "templates": "templates"
+  },
+  "keywords": [
+    "zksnark",
+    "zcash",
+    "ethereum",
+    "zero",
+    "knowlage",
+    "cryptography",
+    "circuit"
+  ],
+  "author": "Jordi Baylina",
+  "license": "GPL-3.0",
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/iden3/snarkjs.git"
+  },
+  "dependencies": {
+    "big-integer": "^1.6.43",
+    "chai": "^4.2.0",
+    "escape-string-regexp": "^1.0.5",
+    "eslint": "^5.16.0",
+    "keccak": "^2.0.0",
+    "yargs": "^12.0.5"
+  },
+  "devDependencies": {
+    "eslint-plugin-mocha": "^5.3.0",
+    "mocha": "^5.2.0"
+  }
+}

src/bigint.js

@@ -0,0 +1,522 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* global BigInt */
+const bigInt = require("big-integer");
+
+let wBigInt;
+
+if (typeof(BigInt) != "undefined") {
+    wBigInt  = BigInt;
+    wBigInt.one = wBigInt(1);
+    wBigInt.zero = wBigInt(0);
+
+    // Affine
+    wBigInt.genAffine = (q) => {
+        const nq = -q;
+        return (a) => {
+            let aux = a;
+            if (aux < 0) {
+                if (aux <= nq) {
+                    aux = aux % q;
+                }
+                if (aux < wBigInt.zero) {
+                    aux = aux + q;
+                }
+            } else {
+                if (aux >= q) {
+                    aux = aux % q;
+                }
+            }
+            return aux.valueOf();
+        };
+    };
+
+
+    // Inverse
+    wBigInt.genInverse = (q) => {
+        return (a) => {
+            let t = wBigInt.zero;
+            let r = q;
+            let newt = wBigInt.one;
+            let newr = wBigInt.affine(a, q);
+            while (newr!=wBigInt.zero) {
+                let q = r/newr;
+                [t, newt] = [newt, t-q*newt];
+                [r, newr] = [newr, r-q*newr];
+            }
+            if (t<wBigInt.zero) t += q;
+            return t;
+        };
+    };
+
+
+    // Add
+    wBigInt.genAdd = (q) => {
+        if (q) {
+            return (a,b) => (a+b) % q;
+        } else {
+            return (a,b) => a+b;
+        }
+    };
+
+    // Sub
+    wBigInt.genSub = (q) => {
+        if (q) {
+            return (a,b) => (a-b) % q;
+        } else {
+            return (a,b) => a-b;
+        }
+    };
+
+
+    // Neg
+    wBigInt.genNeg = (q) => {
+        if (q) {
+            return (a) => (-a) % q;
+        } else {
+            return (a) => -a;
+        }
+    };
+
+    // Mul
+    wBigInt.genMul = (q) => {
+        if (q) {
+            return (a,b) => (a*b) % q;
+        } else {
+            return (a,b) => a*b;
+        }
+    };
+
+    // Shr
+    wBigInt.genShr = () => {
+        return (a,b) => a >> wBigInt(b);
+    };
+
+    // Shl
+    wBigInt.genShl = (q) => {
+        if (q) {
+            return (a,b) => (a << wBigInt(b)) % q;
+        } else {
+            return (a,b) => a << wBigInt(b);
+        }
+    };
+
+    // Equals
+    wBigInt.genEquals = (q) => {
+        if (q) {
+            return (a,b) => (a.affine(q) == b.affine(q));
+        } else {
+            return (a,b) => a == b;
+        }
+    };
+
+    // Square
+    wBigInt.genSquare = (q) => {
+        if (q) {
+            return (a) => (a*a) %q;
+        } else {
+            return (a) => a*a;
+        }
+    };
+
+
+    // Double
+    wBigInt.genDouble = (q) => {
+        if (q) {
+            return (a) => (a+a) %q;
+        } else {
+            return (a) => a+a;
+        }
+    };
+
+    // IsZero
+    wBigInt.genIsZero = (q) => {
+        if (q) {
+            return (a) => (a.affine(q) == wBigInt.zero);
+        } else {
+            return (a) =>  a == wBigInt.zero;
+        }
+    };
+
+
+    // Other minor functions
+    wBigInt.prototype.isOdd = function() {
+        return (this & wBigInt.one) == wBigInt(1);
+    };
+
+    wBigInt.prototype.isNegative = function() {
+        return this < wBigInt.zero;
+    };
+
+    wBigInt.prototype.and = function(m) {
+        return this & m;
+    };
+
+    wBigInt.prototype.div = function(c) {
+        return this / c;
+    };
+
+    wBigInt.prototype.mod = function(c) {
+        return this % c;
+    };
+
+    wBigInt.prototype.pow = function(c) {
+        return this ** c;
+    };
+
+    wBigInt.prototype.abs = function() {
+        return (this > wBigInt.zero) ? this : -this;
+    };
+
+    wBigInt.prototype.modPow = function(e, m) {
+        let acc = wBigInt.one;
+        let exp = this;
+        let rem = e;
+        while (rem) {
+            if (rem & wBigInt.one) {
+                acc = (acc * exp) %m;
+            }
+            exp = (exp * exp) % m;
+            rem = rem >> wBigInt.one;
+        }
+        return acc;
+    };
+
+    wBigInt.prototype.greaterOrEquals = function(b) {
+        return this >= b;
+    };
+
+    wBigInt.prototype.greater = function(b) {
+        return this > b;
+    };
+    wBigInt.prototype.gt = wBigInt.prototype.greater;
+
+    wBigInt.prototype.lesserOrEquals = function(b) {
+        return this <= b;
+    };
+
+    wBigInt.prototype.lesser = function(b) {
+        return this < b;
+    };
+    wBigInt.prototype.lt = wBigInt.prototype.lesser;
+
+    wBigInt.prototype.equals = function(b) {
+        return this == b;
+    };
+    wBigInt.prototype.eq = wBigInt.prototype.equals;
+
+    wBigInt.prototype.neq = function(b) {
+        return this != b;
+    };
+
+    wBigInt.prototype.toJSNumber = function() {
+        return Number(this);
+    };
+
+
+} else {
+
+    var oldProto = bigInt.prototype;
+    wBigInt = function(a) {
+        if ((typeof a == "string") && (a.slice(0,2) == "0x")) {
+            return bigInt(a.slice(2), 16);
+        } else {
+            return bigInt(a);
+        }
+    };
+    wBigInt.one = bigInt.one;
+    wBigInt.zero = bigInt.zero;
+    wBigInt.prototype = oldProto;
+
+    wBigInt.prototype.div = function(c) {
+        return this.divide(c);
+    };
+
+    // Affine
+    wBigInt.genAffine = (q) => {
+        const nq = wBigInt.zero.minus(q);
+        return (a) => {
+            let aux = a;
+            if (aux.isNegative()) {
+                if (aux.lesserOrEquals(nq)) {
+                    aux = aux.mod(q);
+                }
+                if (aux.isNegative()) {
+                    aux = aux.add(q);
+                }
+            } else {
+                if (aux.greaterOrEquals(q)) {
+                    aux = aux.mod(q);
+                }
+            }
+            return aux;
+        };
+    };
+
+
+    // Inverse
+    wBigInt.genInverse = (q) => {
+        return (a) => a.affine(q).modInv(q);
+    };
+
+    // Add
+    wBigInt.genAdd = (q) => {
+        if (q) {
+            return (a,b) => {
+                const r = a.add(b);
+                return r.greaterOrEquals(q) ? r.minus(q) : r;
+            };
+        } else {
+            return (a,b) => a.add(b);
+        }
+    };
+
+    // Sub
+    wBigInt.genSub = (q) => {
+        if (q) {
+            return (a,b) => a.greaterOrEquals(b) ? a.minus(b) : a.minus(b).add(q);
+        } else {
+            return (a,b) => a.minus(b);
+        }
+    };
+
+    wBigInt.genNeg = (q) => {
+        if (q) {
+            return (a) => a.isZero() ? a : q.minus(a);
+        } else {
+            return (a) => wBigInt.zero.minus(a);
+        }
+    };
+
+    // Mul
+    wBigInt.genMul = (q) => {
+        if (q) {
+            return (a,b) => a.times(b).mod(q);
+        } else {
+            return (a,b) => a.times(b);
+        }
+    };
+
+    // Shr
+    wBigInt.genShr = () => {
+        return (a,b) => a.shiftRight(wBigInt(b).value);
+    };
+
+    // Shr
+    wBigInt.genShl = (q) => {
+        if (q) {
+            return (a,b) => a.shiftLeft(wBigInt(b).value).mod(q);
+        } else {
+            return (a,b) => a.shiftLeft(wBigInt(b).value);
+        }
+    };
+
+    // Square
+    wBigInt.genSquare = (q) => {
+        if (q) {
+            return (a) => a.square().mod(q);
+        } else {
+            return (a) => a.square();
+        }
+    };
+
+    // Double
+    wBigInt.genDouble = (q) => {
+        if (q) {
+            return (a) => a.add(a).mod(q);
+        } else {
+            return (a) => a.add(a);
+        }
+    };
+
+    // Equals
+    wBigInt.genEquals = (q) => {
+        if (q) {
+            return (a,b) => a.affine(q).equals(b.affine(q));
+        } else {
+            return (a,b) => a.equals(b);
+        }
+    };
+
+    // IsZero
+    wBigInt.genIsZero = (q) => {
+        if (q) {
+            return (a) => (a.affine(q).isZero());
+        } else {
+            return (a) =>  a.isZero();
+        }
+    };
+}
+
+
+
+wBigInt.affine = function(a, q) {
+    return wBigInt.genAffine(q)(a);
+};
+
+wBigInt.prototype.affine = function (q) {
+    return wBigInt.affine(this, q);
+};
+
+wBigInt.inverse = function(a, q) {
+    return wBigInt.genInverse(q)(a);
+};
+
+wBigInt.prototype.inverse = function (q) {
+    return wBigInt.genInverse(q)(this);
+};
+
+wBigInt.add = function(a, b, q) {
+    return wBigInt.genAdd(q)(a,b);
+};
+
+wBigInt.prototype.add = function (a, q) {
+    return wBigInt.genAdd(q)(this, a);
+};
+
+wBigInt.sub = function(a, b, q) {
+    return wBigInt.genSub(q)(a,b);
+};
+
+wBigInt.prototype.sub = function (a, q) {
+    return wBigInt.genSub(q)(this, a);
+};
+
+wBigInt.neg = function(a, q) {
+    return wBigInt.genNeg(q)(a);
+};
+
+wBigInt.prototype.neg = function (q) {
+    return wBigInt.genNeg(q)(this);
+};
+
+wBigInt.mul = function(a, b, q) {
+    return wBigInt.genMul(q)(a,b);
+};
+
+wBigInt.prototype.mul = function (a, q) {
+    return wBigInt.genMul(q)(this, a);
+};
+
+wBigInt.shr = function(a, b, q) {
+    return wBigInt.genShr(q)(a,b);
+};
+
+wBigInt.prototype.shr = function (a, q) {
+    return wBigInt.genShr(q)(this, a);
+};
+
+wBigInt.shl = function(a, b, q) {
+    return wBigInt.genShl(q)(a,b);
+};
+
+wBigInt.prototype.shl = function (a, q) {
+    return wBigInt.genShl(q)(this, a);
+};
+
+wBigInt.equals = function(a, b, q) {
+    return wBigInt.genEquals(q)(a,b);
+};
+
+wBigInt.prototype.equals = function (a, q) {
+    return wBigInt.genEquals(q)(this, a);
+};
+
+wBigInt.square = function(a, q) {
+    return wBigInt.genSquare(q)(a);
+};
+
+wBigInt.prototype.square = function (q) {
+    return wBigInt.genSquare(q)(this);
+};
+
+wBigInt.double = function(a, q) {
+    return wBigInt.genDouble(q)(a);
+};
+
+wBigInt.prototype.double = function (q) {
+    return wBigInt.genDouble(q)(this);
+};
+
+wBigInt.isZero = function(a, q) {
+    return wBigInt.genIsZero(q)(a);
+};
+
+wBigInt.prototype.isZero = function (q) {
+    return wBigInt.genIsZero(q)(this);
+};
+
+wBigInt.leBuff2int = function(buff) {
+    let res = wBigInt.zero;
+    for (let i=0; i<buff.length; i++) {
+        const n = wBigInt(buff[i]);
+        res = res.add(n.shl(i*8));
+    }
+    return res;
+};
+
+wBigInt.leInt2Buff = function(n, len) {
+    let r = n;
+    let o =0;
+    const buff = Buffer.alloc(len);
+    while ((r.greater(wBigInt.zero))&&(o<buff.length)) {
+        let c = Number(r.and(wBigInt("255")));
+        buff[o] = c;
+        o++;
+        r = r.shr(8);
+    }
+    if (r.greater(wBigInt.zero)) throw new Error("Number does not feed in buffer");
+    return buff;
+};
+
+wBigInt.prototype.leInt2Buff = function (len) {
+    return wBigInt.leInt2Buff(this,len);
+};
+
+
+wBigInt.beBuff2int = function(buff) {
+    let res = wBigInt.zero;
+    for (let i=0; i<buff.length; i++) {
+        const n = wBigInt(buff[buff.length - i - 1]);
+        res = res.add(n.shl(i*8));
+    }
+    return res;
+};
+
+wBigInt.beInt2Buff = function(n, len) {
+    let r = n;
+    let o =len-1;
+    const buff = Buffer.alloc(len);
+    while ((r.greater(wBigInt.zero))&&(o>=0)) {
+        let c = Number(r.and(wBigInt("255")));
+        buff[o] = c;
+        o--;
+        r = r.shr(8);
+    }
+    if (r.greater(wBigInt.zero)) throw new Error("Number does not feed in buffer");
+    return buff;
+};
+
+wBigInt.prototype.beInt2Buff = function (len) {
+    return wBigInt.beInt2Buff(this,len);
+};
+
+module.exports = wBigInt;
+

src/bn128.js

@@ -0,0 +1,445 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint.js");
+
+const F1Field = require("./zqfield.js");
+const F2Field = require("./f2field.js");
+const F3Field = require("./f3field.js");
+const GCurve = require("./gcurve.js");
+
+class BN128 {
+
+    constructor() {
+
+        this.q = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
+        this.r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+        this.g1 = [ bigInt(1), bigInt(2), bigInt(1)];
+        this.g2 = [
+            [
+                bigInt("10857046999023057135944570762232829481370756359578518086990519993285655852781"),
+                bigInt("11559732032986387107991004021392285783925812861821192530917403151452391805634")
+            ],
+            [
+                bigInt("8495653923123431417604973247489272438418190587263600148770280649306958101930"),
+                bigInt("4082367875863433681332203403145435568316851327593401208105741076214120093531")
+            ],
+            [
+                bigInt("1"),
+                bigInt("0")
+            ]
+        ];
+
+        this.nonResidueF2 = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582");
+        this.nonResidueF6 = [ bigInt("9"), bigInt("1") ];
+
+        this.F1 = new F1Field(this.q);
+        this.F2 = new F2Field(this.F1, this.nonResidueF2);
+        this.G1 = new GCurve(this.F1, this.g1);
+        this.G2 = new GCurve(this.F2, this.g2);
+        this.F6 = new F3Field(this.F2, this.nonResidueF6);
+        this.F12 = new F2Field(this.F6, this.nonResidueF6);
+        this.Fr = new F1Field(this.r);
+        const self = this;
+        this.F12._mulByNonResidue = function(a) {
+            return [self.F2.mul(this.nonResidue, a[2]), a[0], a[1]];
+        };
+
+        this._preparePairing();
+
+    }
+
+    _preparePairing() {
+        this.loopCount = bigInt("29793968203157093288");// CONSTANT
+
+        // Set loopCountNeg
+        if (this.loopCount.isNegative()) {
+            this.loopCount = this.loopCount.neg();
+            this.loopCountNeg = true;
+        } else {
+            this.loopCountNeg = false;
+        }
+
+        // Set loop_count_bits
+        let lc = this.loopCount;
+        this.loop_count_bits = []; // Constant
+        while (!lc.isZero()) {
+            this.loop_count_bits.push( lc.isOdd() );
+            lc = lc.shr(1);
+        }
+
+        this.two_inv = this.F1.inverse(bigInt(2));
+
+        this.coef_b = bigInt(3);
+        this.twist = [bigInt(9) , bigInt(1)];
+        this.twist_coeff_b = this.F2.mulScalar(  this.F2.inverse(this.twist), this.coef_b  );
+
+        this.frobenius_coeffs_c1_1 = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582");
+        this.twist_mul_by_q_X =
+            [
+                bigInt("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
+                bigInt("10307601595873709700152284273816112264069230130616436755625194854815875713954")
+            ];
+        this.twist_mul_by_q_Y =
+            [
+                bigInt("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
+                bigInt("3505843767911556378687030309984248845540243509899259641013678093033130930403")
+            ];
+
+        this.final_exponent = bigInt("552484233613224096312617126783173147097382103762957654188882734314196910839907541213974502761540629817009608548654680343627701153829446747810907373256841551006201639677726139946029199968412598804882391702273019083653272047566316584365559776493027495458238373902875937659943504873220554161550525926302303331747463515644711876653177129578303191095900909191624817826566688241804408081892785725967931714097716709526092261278071952560171111444072049229123565057483750161460024353346284167282452756217662335528813519139808291170539072125381230815729071544861602750936964829313608137325426383735122175229541155376346436093930287402089517426973178917569713384748081827255472576937471496195752727188261435633271238710131736096299798168852925540549342330775279877006784354801422249722573783561685179618816480037695005515426162362431072245638324744480");
+
+    }
+
+
+    pairing(p1, p2) {
+
+        const pre1 = this.precomputeG1(p1);
+        const pre2 = this.precomputeG2(p2);
+
+        const r1 = this.millerLoop(pre1, pre2);
+
+        const res = this.finalExponentiation(r1);
+
+        return res;
+    }
+
+
+    precomputeG1(p) {
+        const Pcopy = this.G1.affine(p);
+
+        const res = {};
+        res.PX = Pcopy[0];
+        res.PY = Pcopy[1];
+
+        return res;
+    }
+
+    precomputeG2(p) {
+
+        const Qcopy = this.G2.affine(p);
+
+        const res = {
+            QX: Qcopy[0],
+            QY: Qcopy[1],
+            coeffs: []
+        };
+
+        const R = {
+            X: Qcopy[0],
+            Y: Qcopy[1],
+            Z: this.F2.one
+        };
+
+        let c;
+
+        for (let i = this.loop_count_bits.length-2; i >= 0; --i)
+        {
+            const bit = this.loop_count_bits[i];
+
+            c = this._doubleStep(R);
+            res.coeffs.push(c);
+
+            if (bit)
+            {
+                c = this._addStep(Qcopy, R);
+                res.coeffs.push(c);
+            }
+        }
+
+        const Q1 = this.G2.affine(this._g2MulByQ(Qcopy));
+        if (!this.F2.equals(Q1[2], this.F2.one))
+        {
+            throw new Error("Expected values are not equal");
+        }
+        const Q2 = this.G2.affine(this._g2MulByQ(Q1));
+        if (!this.F2.equals(Q2[2], this.F2.one))
+        {
+            throw new Error("Expected values are not equal");
+        }
+
+        if (this.loopCountNeg)
+        {
+            R.Y = this.F2.neg(R.Y);
+        }
+        Q2[1] = this.F2.neg(Q2[1]);
+
+        c = this._addStep(Q1, R);
+        res.coeffs.push(c);
+
+        c = this._addStep(Q2, R);
+        res.coeffs.push(c);
+
+        return res;
+    }
+
+    millerLoop(pre1, pre2) {
+        let f = this.F12.one;
+
+        let idx = 0;
+
+        let c;
+
+        for (let i = this.loop_count_bits.length-2; i >= 0; --i)
+        {
+            const bit = this.loop_count_bits[i];
+
+            /* code below gets executed for all bits (EXCEPT the MSB itself) of
+               alt_bn128_param_p (skipping leading zeros) in MSB to LSB
+               order */
+
+            c = pre2.coeffs[idx++];
+            f = this.F12.square(f);
+            f = this._mul_by_024(
+                f,
+                c.ell_0,
+                this.F2.mulScalar(c.ell_VW , pre1.PY),
+                this.F2.mulScalar(c.ell_VV , pre1.PX));
+
+            if (bit)
+            {
+                c = pre2.coeffs[idx++];
+                f = this._mul_by_024(
+                    f,
+                    c.ell_0,
+                    this.F2.mulScalar(c.ell_VW, pre1.PY),
+                    this.F2.mulScalar(c.ell_VV, pre1.PX));
+            }
+
+        }
+
+        if (this.loopCountNeg)
+        {
+            f = this.F12.inverse(f);
+        }
+
+        c = pre2.coeffs[idx++];
+        f = this._mul_by_024(
+            f,
+            c.ell_0,
+            this.F2.mulScalar(c.ell_VW, pre1.PY),
+            this.F2.mulScalar(c.ell_VV, pre1.PX));
+
+        c = pre2.coeffs[idx++];
+        f = this._mul_by_024(
+            f,
+            c.ell_0,
+            this.F2.mulScalar(c.ell_VW, pre1.PY),
+            this.F2.mulScalar(c.ell_VV, pre1.PX));
+
+        return f;
+    }
+
+    finalExponentiation(elt) {
+        // TODO: There is an optimization in FF
+
+        const res = this.F12.exp(elt,this.final_exponent);
+
+        return res;
+    }
+
+    _doubleStep(current) {
+        const X = current.X;
+        const Y = current.Y;
+        const Z = current.Z;
+
+        const A = this.F2.mulScalar(this.F2.mul(X,Y), this.two_inv);                     // A = X1 * Y1 / 2
+        const B = this.F2.square(Y);                           // B = Y1^2
+        const C = this.F2.square(Z);                           // C = Z1^2
+        const D = this.F2.add(C, this.F2.add(C,C));            // D = 3 * C
+        const E = this.F2.mul(this.twist_coeff_b, D);     // E = twist_b * D
+        const F = this.F2.add(E, this.F2.add(E,E));            // F = 3 * E
+        const G =
+            this.F2.mulScalar(
+                this.F2.add( B , F ),
+                this.two_inv);                            // G = (B+F)/2
+        const H =
+            this.F2.sub(
+                this.F2.square( this.F2.add(Y,Z) ),
+                this.F2.add( B , C));                          // H = (Y1+Z1)^2-(B+C)
+        const I = this.F2.sub(E, B);                           // I = E-B
+        const J = this.F2.square(X);                           // J = X1^2
+        const E_squared = this.F2.square(E);                   // E_squared = E^2
+
+        current.X = this.F2.mul( A, this.F2.sub(B,F) );        // X3 = A * (B-F)
+        current.Y =
+            this.F2.sub(
+                this.F2.sub( this.F2.square(G) , E_squared ),
+                this.F2.add( E_squared , E_squared ));         // Y3 = G^2 - 3*E^2
+        current.Z = this.F2.mul( B, H );                       // Z3 = B * H
+
+        const c = {
+            ell_0 : this.F2.mul( I, this.twist),          // ell_0 = xi * I
+            ell_VW: this.F2.neg( H ),                          // ell_VW = - H (later: * yP)
+            ell_VV: this.F2.add( J , this.F2.add(J,J) )        // ell_VV = 3*J (later: * xP)
+        };
+
+        return c;
+    }
+
+    _addStep(base, current) {
+
+        const X1 = current.X;
+        const Y1 = current.Y;
+        const Z1 = current.Z;
+        const x2 = base[0];
+        const y2 = base[1];
+
+        const D = this.F2.sub( X1, this.F2.mul(x2,Z1) );  // D = X1 - X2*Z1
+
+//        console.log("Y: "+ A[0].affine(this.q).toString(16));
+
+        const E = this.F2.sub( Y1, this.F2.mul(y2,Z1) );  // E = Y1 - Y2*Z1
+        const F = this.F2.square(D);                      // F = D^2
+        const G = this.F2.square(E);                      // G = E^2
+        const H = this.F2.mul(D,F);                       // H = D*F
+        const I = this.F2.mul(X1,F);                      // I = X1 * F
+        const J =
+            this.F2.sub(
+                this.F2.add( H, this.F2.mul(Z1,G) ),
+                this.F2.add( I, I ));                     // J = H + Z1*G - (I+I)
+
+        current.X = this.F2.mul( D , J );                 // X3 = D*J
+        current.Y =
+            this.F2.sub(
+                this.F2.mul( E , this.F2.sub(I,J) ),
+                this.F2.mul( H , Y1));                    // Y3 = E*(I-J)-(H*Y1)
+        current.Z = this.F2.mul(Z1,H);
+        const c = {
+            ell_0 :
+                this.F2.mul(
+                    this.twist,
+                    this.F2.sub(
+                        this.F2.mul(E , x2),
+                        this.F2.mul(D , y2))),            // ell_0 = xi * (E * X2 - D * Y2)
+            ell_VV : this.F2.neg(E),                      // ell_VV = - E (later: * xP)
+            ell_VW : D                                    // ell_VW = D (later: * yP )
+        };
+
+        return c;
+    }
+
+    _mul_by_024(a, ell_0, ell_VW, ell_VV) {
+
+        //  Old implementation
+/*
+        const b = [
+            [ell_0, this.F2.zero, ell_VV],
+            [this.F2.zero, ell_VW, this.F2.zero]
+        ];
+
+        return this.F12.mul(a,b);
+*/
+
+        // This is a new implementation,
+        //  But it does not look worthy
+        //  at least in javascript.
+
+        let z0 = a[0][0];
+        let z1 = a[0][1];
+        let z2 = a[0][2];
+        let z3 = a[1][0];
+        let z4 = a[1][1];
+        let z5 = a[1][2];
+
+        const x0 = ell_0;
+        const x2 = ell_VV;
+        const x4 = ell_VW;
+
+        const D0 = this.F2.mul(z0, x0);
+        const D2 = this.F2.mul(z2, x2);
+        const D4 = this.F2.mul(z4, x4);
+        const t2 = this.F2.add(z0, z4);
+        let t1 = this.F2.add(z0, z2);
+        const s0 = this.F2.add(this.F2.add(z1,z3),z5);
+
+        // For z.a_.a_ = z0.
+        let S1 = this.F2.mul(z1, x2);
+        let T3 = this.F2.add(S1, D4);
+        let T4 = this.F2.add( this.F2.mul(this.nonResidueF6, T3),D0);
+        z0 = T4;
+
+        // For z.a_.b_ = z1
+        T3 = this.F2.mul(z5, x4);
+        S1 = this.F2.add(S1, T3);
+        T3 = this.F2.add(T3, D2);
+        T4 = this.F2.mul(this.nonResidueF6, T3);
+        T3 = this.F2.mul(z1, x0);
+        S1 = this.F2.add(S1, T3);
+        T4 = this.F2.add(T4, T3);
+        z1 = T4;
+
+        // For z.a_.c_ = z2
+        let t0 = this.F2.add(x0, x2);
+        T3 = this.F2.sub(
+            this.F2.mul(t1, t0),
+            this.F2.add(D0, D2));
+        T4 = this.F2.mul(z3, x4);
+        S1 = this.F2.add(S1, T4);
+
+        // For z.b_.a_ = z3 (z3 needs z2)
+        t0 = this.F2.add(z2, z4);
+        z2 = this.F2.add(T3, T4);
+        t1 = this.F2.add(x2, x4);
+        T3 = this.F2.sub(
+            this.F2.mul(t0,t1),
+            this.F2.add(D2, D4));
+
+        T4 = this.F2.mul(this.nonResidueF6,  T3);
+        T3 = this.F2.mul(z3, x0);
+        S1 = this.F2.add(S1, T3);
+        T4 = this.F2.add(T4, T3);
+        z3 = T4;
+
+        // For z.b_.b_ = z4
+        T3 = this.F2.mul(z5, x2);
+        S1 = this.F2.add(S1, T3);
+        T4 = this.F2.mul(this.nonResidueF6, T3);
+        t0 = this.F2.add(x0, x4);
+        T3 = this.F2.sub(
+            this.F2.mul(t2,t0),
+            this.F2.add(D0, D4));
+        T4 = this.F2.add(T4, T3);
+        z4 = T4;
+
+        // For z.b_.c_ = z5.
+        t0 = this.F2.add(this.F2.add(x0, x2), x4);
+        T3 = this.F2.sub(this.F2.mul(s0, t0), S1);
+        z5 = T3;
+
+        return [
+            [z0, z1, z2],
+            [z3, z4, z5]
+        ];
+
+
+    }
+
+    _g2MulByQ(p) {
+        const fmx = [p[0][0], this.F1.mul(p[0][1], this.frobenius_coeffs_c1_1 )];
+        const fmy = [p[1][0], this.F1.mul(p[1][1], this.frobenius_coeffs_c1_1 )];
+        const fmz = [p[2][0], this.F1.mul(p[2][1], this.frobenius_coeffs_c1_1 )];
+        return [
+            this.F2.mul(this.twist_mul_by_q_X , fmx),
+            this.F2.mul(this.twist_mul_by_q_Y , fmy),
+            fmz
+        ];
+    }
+}
+
+module.exports = BN128;

src/calculateWitness.js

@@ -0,0 +1,233 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint");
+
+module.exports = calculateWitness;
+
+function calculateWitness(circuit, inputSignals, options) {
+    options = options || {};
+    if (!options.logFunction) options.logFunction = console.log;
+    const ctx = new RTCtx(circuit, options);
+
+    function iterateSelector(values, sels, cb) {
+        if (!Array.isArray(values)) {
+            return cb(sels, values);
+        }
+        for (let i=0; i<values.length; i++) {
+            sels.push(i);
+            iterateSelector(values[i], sels, cb);
+            sels.pop(i);
+        }
+    }
+
+    ctx.setSignal("one", [], bigInt(1));
+
+    for (let c in ctx.notInitSignals) {
+        if (ctx.notInitSignals[c] == 0) ctx.triggerComponent(c);
+    }
+
+    for (let s in inputSignals) {
+        ctx.currentComponent = "main";
+        iterateSelector(inputSignals[s], [], function(selector, value) {
+            if (typeof(value) == "undefined") throw new Error("Signal not defined:" + s);
+            ctx.setSignal(s, selector, bigInt(value));
+        });
+    }
+
+    for (let i=0; i<circuit.nInputs; i++) {
+        const idx = circuit.inputIdx(i);
+        if (typeof(ctx.witness[idx]) == "undefined") {
+            throw new Error("Input Signal not assigned: " + circuit.signalNames(idx));
+        }
+    }
+
+
+    for (let i=0; i<ctx.witness.length; i++) {
+        if (typeof(ctx.witness[i]) == "undefined") {
+            throw new Error("Signal not assigned: " + circuit.signalNames(i));
+        }
+        if (options.logOutput) options.logFunction(circuit.signalNames(i) + " --> " + ctx.witness[i].toString());
+    }
+    return ctx.witness.slice(0, circuit.nVars);
+//    return ctx.witness;
+}
+
+class RTCtx {
+    constructor(circuit, options) {
+        this.options = options;
+        this.scopes = [];
+        this.circuit = circuit;
+        this.witness = new Array(circuit.nSignals);
+        this.notInitSignals = {};
+        for (let c in this.circuit.components) {
+            this.notInitSignals[c] = this.circuit.components[c].inputSignals;
+        }
+    }
+
+    _sels2str(sels) {
+        let res = "";
+        for (let i=0; i<sels.length; i++) {
+            res += `[${sels[i]}]`;
+        }
+        return res;
+    }
+
+    setPin(componentName, componentSels, signalName, signalSels, value) {
+        let fullName = componentName=="one" ? "one" : this.currentComponent + "." + componentName;
+        fullName += this._sels2str(componentSels) +
+                    "."+
+                    signalName+
+                    this._sels2str(signalSels);
+        this.setSignalFullName(fullName, value);
+    }
+
+    setSignal(name, sels, value) {
+        let fullName = this.currentComponent ? this.currentComponent + "." + name : name;
+        fullName += this._sels2str(sels);
+        this.setSignalFullName(fullName, value);
+    }
+
+    triggerComponent(c) {
+        if (this.options.logTrigger) this.options.logFunction("Component Treiggered: " + this.circuit.components[c].name);
+
+        // Set notInitSignals to -1 to not initialize again
+        this.notInitSignals[c] --;
+        const oldComponent = this.currentComponent;
+        this.currentComponent = this.circuit.components[c].name;
+        const template = this.circuit.components[c].template;
+
+        const newScope = {};
+        for (let p in this.circuit.components[c].params) {
+            newScope[p] = this.circuit.components[c].params[p];
+        }
+
+        const oldScope = this.scopes;
+        this.scopes = [ this.scopes[0], newScope ];
+
+        // TODO set params.
+
+        this.circuit.templates[template](this);
+        this.scopes = oldScope;
+        this.currentComponent = oldComponent;
+
+        if (this.options.logTrigger)  this.options.logFunction("End Component Treiggered: " + this.circuit.components[c].name);
+    }
+
+    callFunction(functionName, params) {
+
+        const newScope = {};
+        for (let p=0; p<this.circuit.functions[functionName].params.length; p++) {
+            const paramName = this.circuit.functions[functionName].params[p];
+            newScope[paramName] = params[p];
+        }
+
+        const oldScope = this.scopes;
+        this.scopes = [ this.scopes[0], newScope ];
+
+        // TODO set params.
+
+        const res = this.circuit.functions[functionName].func(this);
+        this.scopes = oldScope;
+
+        return res;
+    }
+
+    setSignalFullName(fullName, value) {
+        if (this.options.logSet) this.options.logFunction("set " + fullName + " <-- " + value.toString());
+        const sId = this.circuit.getSignalIdx(fullName);
+        let firstInit =false;
+        if (typeof(this.witness[sId]) == "undefined") {
+            firstInit = true;
+        }
+        this.witness[sId] = bigInt(value);
+        const callComponents = [];
+        for (let i=0; i<this.circuit.signals[sId].triggerComponents.length; i++) {
+            var idCmp = this.circuit.signals[sId].triggerComponents[i];
+            if (firstInit) this.notInitSignals[idCmp] --;
+            callComponents.push(idCmp);
+        }
+        callComponents.map( (c) => {
+            if (this.notInitSignals[c] == 0) this.triggerComponent(c);
+        });
+        return this.witness[sId];
+    }
+
+    setVar(name, sels, value) {
+        function setVarArray(a, sels2, value) {
+            if (sels2.length == 1) {
+                a[sels2[0]] = value;
+            } else {
+                if (typeof(a[sels2[0]]) == "undefined") a[sels2[0]] = [];
+                setVarArray(a[sels2[0]], sels2.slice(1), value);
+            }
+        }
+        const scope = this.scopes[this.scopes.length-1];
+        if (sels.length == 0) {
+            scope[name] = value;
+        } else {
+            if (typeof(scope[name]) == "undefined") scope[name] = [];
+            setVarArray(scope[name], sels, value);
+        }
+        return value;
+    }
+
+    getVar(name, sels) {
+        function select(a, sels2) {
+            return  (sels2.length == 0) ? a : select(a[sels2[0]], sels2.slice(1));
+        }
+        for (let i=this.scopes.length-1; i>=0; i--) {
+            if (typeof(this.scopes[i][name]) != "undefined") return select(this.scopes[i][name], sels);
+        }
+        throw new Error("Variable not defined: " + name);
+    }
+
+    getSignal(name, sels) {
+        let fullName = name=="one" ? "one" : this.currentComponent + "." + name;
+        fullName += this._sels2str(sels);
+        return this.getSignalFullName(fullName);
+    }
+
+
+    getPin(componentName, componentSels, signalName, signalSels) {
+        let fullName = componentName=="one" ? "one" : this.currentComponent + "." + componentName;
+        fullName += this._sels2str(componentSels) +
+                    "."+
+                    signalName+
+                    this._sels2str(signalSels);
+        return this.getSignalFullName(fullName);
+    }
+
+    getSignalFullName(fullName) {
+        const sId = this.circuit.getSignalIdx(fullName);
+        if (typeof(this.witness[sId]) == "undefined") {
+            throw new Error("Signal not initialized: "+fullName);
+        }
+        if (this.options.logGet) this.options.logFunction("get --->" + fullName + " = " + this.witness[sId].toString() );
+        return this.witness[sId];
+    }
+
+    assert(a,b,errStr) {
+        const ba = bigInt(a);
+        const bb = bigInt(b);
+        if (!ba.equals(bb)) {
+            throw new Error("Constraint doesn't match "+ this.currentComponent+": "+ errStr + " -> "+ ba.toString() + " != " + bb.toString());
+        }
+    }
+}

src/circuit.js

@@ -0,0 +1,191 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint.js");
+
+const __P__ = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+const __MASK__ = bigInt("28948022309329048855892746252171976963317496166410141009864396001978282409983"); // 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
+const calculateWitness = require("./calculateWitness.js");
+
+module.exports = class Circuit {
+    constructor(circuitDef) {
+        this.nPubInputs = circuitDef.nPubInputs;
+        this.nPrvInputs = circuitDef.nPrvInputs;
+        this.nInputs = circuitDef.nInputs;
+        this.nOutputs = circuitDef.nOutputs;
+        this.nVars = circuitDef.nVars;
+        this.nSignals = circuitDef.nSignals;
+        this.nConstants = circuitDef.nConstants;
+
+        this.nConstraints = circuitDef.constraints.length;
+
+        this.signalName2Idx = circuitDef.signalName2Idx;
+        this.components = circuitDef.components;
+        this.componentName2Idx = circuitDef.componentName2Idx;
+        this.signals = circuitDef.signals;
+        this.constraints = circuitDef.constraints;
+
+        this.templates = {};
+        for (let t in circuitDef.templates) {
+            this.templates[t] = eval(" const __f= " +circuitDef.templates[t] + "\n__f");
+        }
+
+        this.functions = {};
+        for (let f in circuitDef.functions) {
+            this.functions[f] = {
+                params: circuitDef.functions[f].params,
+                func: eval(" const __f= " +circuitDef.functions[f].func + "\n__f;")
+            };
+        }
+    }
+
+    calculateWitness(input, log) {
+        return calculateWitness(this, input, log);
+    }
+
+    checkWitness(w) {
+        const evalLC = (lc, w) => {
+            let acc = bigInt(0);
+            for (let k in lc) {
+                acc=  acc.add(bigInt(w[k]).mul(bigInt(lc[k]))).mod(__P__);
+            }
+            return acc;
+        }
+
+        const checkConstraint = (ct, w) => {
+            const a=evalLC(ct[0],w);
+            const b=evalLC(ct[1],w);
+            const c=evalLC(ct[2],w);
+            const res = (a.mul(b).sub(c)).affine(__P__);
+            if (!res.isZero()) return false;
+            return true;
+        }
+
+
+        for (let i=0; i<this.constraints.length; i++) {
+            if (!checkConstraint(this.constraints[i], w)) {
+                this.printCostraint(this.constraints[i]);
+                return false;
+            }
+        }
+
+        return true;
+
+    }
+
+    printCostraint(c) {
+        const lc2str = (lc) => {
+            let S = "";
+            for (let k in lc) {
+                let name = this.signals[k].names[0];
+                if (name == "one") name = "";
+                let v = bigInt(lc[k]);
+                let vs;
+                if (!v.lesserOrEquals(__P__.shr(bigInt(1)))) {
+                    v = __P__.sub(v);
+                    vs = "-"+v.toString();
+                } else {
+                    if (S!="") {
+                        vs = "+"+v.toString();
+                    } else {
+                        vs = "";
+                    }
+                    if (vs!="1") {
+                        vs = vs + v.toString();;
+                    }
+                }
+
+                S= S + " " + vs + name;
+            }
+            return S;
+        };
+        const S = `[ ${lc2str(c[0])} ] * [ ${lc2str(c[1])} ] - [ ${lc2str(c[2])} ] = 0`;
+        console.log(S);
+    }
+
+    printConstraints() {
+        for (let i=0; i<this.constraints.length; i++) {
+            this.printCostraint(this.constraints[i]);
+        }
+    }
+
+    getSignalIdx(name) {
+        if (typeof(this.signalName2Idx[name]) != "undefined") return this.signalName2Idx[name];
+        if (!isNaN(name)) return Number(name);
+        throw new Error("Invalid signal identifier: "+ name);
+    }
+
+    // returns the index of the i'th output
+    outputIdx(i) {
+        if (i>=this.nOutputs) throw new Error("Accessing an invalid output: "+i);
+        return i+1;
+    }
+
+    // returns the index of the i'th input
+    inputIdx(i) {
+        if (i>=this.nInputs) throw new Error("Accessing an invalid input: "+i);
+        return this.nOutputs + 1 + i;
+    }
+
+    // returns the index of the i'th public input
+    pubInputIdx(i) {
+        if (i>=this.nPubInputs) throw new Error("Accessing an invalid pubInput: "+i);
+        return this.inputIdx(i);
+    }
+
+    // returns the index of the i'th private input
+    prvInputIdx(i) {
+        if (i>=this.nPrvInputs) throw new Error("Accessing an invalid prvInput: "+i);
+        return this.inputIdx(this.nPubInputs + i);
+    }
+
+    // returns the index of the i'th variable
+    varIdx(i) {
+        if (i>=this.nVars) throw new Error("Accessing an invalid variable: "+i);
+        return i;
+    }
+
+    // returns the index of the i'th constant
+    constantIdx(i) {
+        if (i>=this.nConstants) throw new Error("Accessing an invalid constant: "+i);
+        return this.nVars + i;
+    }
+
+    // returns the index of the i'th signal
+    signalIdx(i) {
+        if (i>=this.nSignls) throw new Error("Accessing an invalid signal: "+i);
+        return i;
+    }
+
+    signalNames(i) {
+        return this.signals[ this.getSignalIdx(i) ].names.join(", ");
+    }
+
+    a(constraint, signalIdx) {
+        return bigInt(this.constraints[constraint][0][signalIdx] || 0 );
+    }
+
+    b(constraint, signalIdx) {
+        return bigInt(this.constraints[constraint][1][signalIdx] || 0);
+    }
+
+    c(constraint, signalIdx) {
+        return bigInt(this.constraints[constraint][2][signalIdx] || 0);
+    }
+};

src/f2field.js

@@ -0,0 +1,137 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const fUtils = require("./futils.js");
+
+class F2Field {
+    constructor(F, nonResidue) {
+        this.F = F;
+        this.zero = [this.F.zero, this.F.zero];
+        this.one = [this.F.one, this.F.zero];
+        this.nonResidue = nonResidue;
+    }
+
+    _mulByNonResidue(a) {
+        return this.F.mul(this.nonResidue, a);
+    }
+
+    copy(a) {
+        return [this.F.copy(a[0]), this.F.copy(a[1])];
+    }
+
+    add(a, b) {
+        return [
+            this.F.add(a[0], b[0]),
+            this.F.add(a[1], b[1])
+        ];
+    }
+
+    double(a) {
+        return this.add(a,a);
+    }
+
+    sub(a, b) {
+        return [
+            this.F.sub(a[0], b[0]),
+            this.F.sub(a[1], b[1])
+        ];
+    }
+
+    neg(a) {
+        return this.sub(this.zero, a);
+    }
+
+    mul(a, b) {
+        const aA = this.F.mul(a[0] , b[0]);
+        const bB = this.F.mul(a[1] , b[1]);
+
+        return [
+            this.F.add( aA , this._mulByNonResidue(bB)),
+            this.F.sub(
+                this.F.mul(
+                    this.F.add(a[0], a[1]),
+                    this.F.add(b[0], b[1])),
+                this.F.add(aA, bB))];
+    }
+
+    inverse(a) {
+        const t0 = this.F.square(a[0]);
+        const t1 = this.F.square(a[1]);
+        const t2 = this.F.sub(t0, this._mulByNonResidue(t1));
+        const t3 = this.F.inverse(t2);
+        return [
+            this.F.mul(a[0], t3),
+            this.F.neg(this.F.mul( a[1], t3)) ];
+    }
+
+    div(a, b) {
+        return this.mul(a, this.inverse(b));
+    }
+
+    square(a) {
+        const ab = this.F.mul(a[0] , a[1]);
+
+        /*
+        [
+            (a + b) * (a + non_residue * b) - ab - non_residue * ab,
+            ab + ab
+        ];
+        */
+
+        return [
+            this.F.sub(
+                this.F.mul(
+                    this.F.add(a[0], a[1]) ,
+                    this.F.add(
+                        a[0] ,
+                        this._mulByNonResidue(a[1]))),
+                this.F.add(
+                    ab,
+                    this._mulByNonResidue(ab))),
+            this.F.add(ab, ab)
+        ];
+    }
+
+    isZero(a) {
+        return this.F.isZero(a[0]) && this.F.isZero(a[1]);
+    }
+
+    equals(a, b) {
+        return this.F.equals(a[0], b[0]) && this.F.equals(a[1], b[1]);
+    }
+
+    affine(a) {
+        return [this.F.affine(a[0]), this.F.affine(a[1])];
+    }
+
+    mulScalar(base, e) {
+        return fUtils.mulScalar(this, base, e);
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
+    toString(a) {
+        const cp = this.affine(a);
+        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])} ]`;
+    }
+}
+
+module.exports = F2Field;

src/f3field.js

@@ -0,0 +1,177 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const fUtils = require("./futils.js");
+
+class F3Field {
+    constructor(F, nonResidue) {
+        this.F = F;
+        this.zero = [this.F.zero, this.F.zero, this.F.zero];
+        this.one = [this.F.one, this.F.zero, this.F.zero];
+        this.nonResidue = nonResidue;
+    }
+
+    _mulByNonResidue(a) {
+        return this.F.mul(this.nonResidue, a);
+    }
+
+    copy(a) {
+        return [this.F.copy(a[0]), this.F.copy(a[1]), this.F.copy(a[2])];
+    }
+
+    add(a, b) {
+        return [
+            this.F.add(a[0], b[0]),
+            this.F.add(a[1], b[1]),
+            this.F.add(a[2], b[2])
+        ];
+    }
+
+    double(a) {
+        return this.add(a,a);
+    }
+
+    sub(a, b) {
+        return [
+            this.F.sub(a[0], b[0]),
+            this.F.sub(a[1], b[1]),
+            this.F.sub(a[2], b[2])
+        ];
+    }
+
+    neg(a) {
+        return this.sub(this.zero, a);
+    }
+
+    mul(a, b) {
+
+        const aA = this.F.mul(a[0] , b[0]);
+        const bB = this.F.mul(a[1] , b[1]);
+        const cC = this.F.mul(a[2] , b[2]);
+
+        return [
+            this.F.add(
+                aA,
+                this._mulByNonResidue(
+                    this.F.sub(
+                        this.F.mul(
+                            this.F.add(a[1], a[2]),
+                            this.F.add(b[1], b[2])),
+                        this.F.add(bB, cC)))),    // aA + non_residue*((b+c)*(B+C)-bB-cC),
+
+            this.F.add(
+                this.F.sub(
+                    this.F.mul(
+                        this.F.add(a[0], a[1]),
+                        this.F.add(b[0], b[1])),
+                    this.F.add(aA, bB)),
+                this._mulByNonResidue( cC)),   // (a+b)*(A+B)-aA-bB+non_residue*cC
+
+            this.F.add(
+                this.F.sub(
+                    this.F.mul(
+                        this.F.add(a[0], a[2]),
+                        this.F.add(b[0], b[2])),
+                    this.F.add(aA, cC)),
+                bB)];                           // (a+c)*(A+C)-aA+bB-cC)
+    }
+
+    inverse(a) {
+        const t0 = this.F.square(a[0]);             // t0 = a^2 ;
+        const t1 = this.F.square(a[1]);             // t1 = b^2 ;
+        const t2 = this.F.square(a[2]);             // t2 = c^2;
+        const t3 = this.F.mul(a[0],a[1]);           // t3 = ab
+        const t4 = this.F.mul(a[0],a[2]);           // t4 = ac
+        const t5 = this.F.mul(a[1],a[2]);           // t5 = bc;
+        // c0 = t0 - non_residue * t5;
+        const c0 = this.F.sub(t0, this._mulByNonResidue(t5));
+        // c1 = non_residue * t2 - t3;
+        const c1 = this.F.sub(this._mulByNonResidue(t2), t3);
+        const c2 = this.F.sub(t1, t4);              // c2 = t1-t4
+
+        // t6 = (a * c0 + non_residue * (c * c1 + b * c2)).inverse();
+        const t6 =
+            this.F.inverse(
+                this.F.add(
+                    this.F.mul(a[0], c0),
+                    this._mulByNonResidue(
+                        this.F.add(
+                            this.F.mul(a[2], c1),
+                            this.F.mul(a[1], c2)))));
+
+        return [
+            this.F.mul(t6, c0),         // t6*c0
+            this.F.mul(t6, c1),         // t6*c1
+            this.F.mul(t6, c2)];        // t6*c2
+    }
+
+    div(a, b) {
+        return this.mul(a, this.inverse(b));
+    }
+
+    square(a) {
+        const s0 = this.F.square(a[0]);                   // s0 = a^2
+        const ab = this.F.mul(a[0], a[1]);                // ab = a*b
+        const s1 = this.F.add(ab, ab);                    // s1 = 2ab;
+        const s2 = this.F.square(
+            this.F.add(this.F.sub(a[0],a[1]), a[2]));     // s2 = (a - b + c)^2;
+        const bc = this.F.mul(a[1],a[2]);                 // bc = b*c
+        const s3 = this.F.add(bc, bc);                    // s3 = 2*bc
+        const s4 = this.F.square(a[2]);                   // s4 = c^2
+
+
+        return [
+            this.F.add(
+                s0,
+                this._mulByNonResidue(s3)),           // s0 + non_residue * s3,
+            this.F.add(
+                s1,
+                this._mulByNonResidue(s4)),           // s1 + non_residue * s4,
+            this.F.sub(
+                this.F.add( this.F.add(s1, s2) , s3 ),
+                this.F.add(s0, s4))];                      // s1 + s2 + s3 - s0 - s4
+    }
+
+    isZero(a) {
+        return this.F.isZero(a[0]) && this.F.isZero(a[1]) && this.F.isZero(a[2]);
+    }
+
+    equals(a, b) {
+        return this.F.equals(a[0], b[0]) && this.F.equals(a[1], b[1]) && this.F.equals(a[2], b[2]);
+    }
+
+    affine(a) {
+        return [this.F.affine(a[0]), this.F.affine(a[1]), this.F.affine(a[2])];
+    }
+
+    mulScalar(base, e) {
+        return fUtils.mulScalar(this, base, e);
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
+    toString(a) {
+        const cp = this.affine(a);
+        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])}, ${this.F.toString(cp[2])} ]`;
+    }
+}
+
+module.exports = F3Field;

src/futils.js

@@ -0,0 +1,53 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint.js");
+
+exports.mulScalar = (F, base, e) =>{
+    let res = F.zero;
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = F.add(res, exp);
+        }
+        exp = F.double(exp);
+        rem = rem.shr(1);
+    }
+
+    return res;
+};
+
+
+exports.exp = (F, base, e) =>{
+    let res = F.one;
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = F.mul(res, exp);
+        }
+        exp = F.square(exp);
+        rem = rem.shr(1);
+    }
+
+    return res;
+};

src/gcurve.js

@@ -0,0 +1,190 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const fUtils = require("./futils.js");
+
+class GCurve {
+
+    constructor(F, g) {
+        this.F = F;
+        this.g = [F.copy(g[0]), F.copy(g[1])];
+        if (this.g.length == 2) this.g[2] = this.F.one;
+        this.zero = [this.F.zero, this.F.one, this.F.zero];
+    }
+
+    isZero(p) {
+        return this.F.isZero(p[2]);
+    }
+
+    add(p1, p2) {
+
+        const F = this.F;
+
+        if (this.isZero(p1)) return p2;
+        if (this.isZero(p2)) return p1;
+
+        const res = new Array(3);
+
+        const Z1Z1 = F.square( p1[2] );
+        const Z2Z2 = F.square( p2[2] );
+
+        const U1 = F.mul( p1[0] , Z2Z2 );     // U1 = X1  * Z2Z2
+        const U2 = F.mul( p2[0] , Z1Z1 );     // U2 = X2  * Z1Z1
+
+        const Z1_cubed = F.mul( p1[2] , Z1Z1);
+        const Z2_cubed = F.mul( p2[2] , Z2Z2);
+
+        const S1 = F.mul( p1[1] , Z2_cubed);  // S1 = Y1 * Z2 * Z2Z2
+        const S2 = F.mul( p2[1] , Z1_cubed);  // S2 = Y2 * Z1 * Z1Z1
+
+        if (F.equals(U1,U2) && F.equals(S1,S2)) {
+            return this.double(p1);
+        }
+
+        const H = F.sub( U2 , U1 );                    // H = U2-U1
+
+        const S2_minus_S1 = F.sub( S2 , S1 );
+
+        const I = F.square( F.add(H,H) );         // I = (2 * H)^2
+        const J = F.mul( H , I );                      // J = H * I
+
+        const r = F.add( S2_minus_S1 , S2_minus_S1 );  // r = 2 * (S2-S1)
+        const V = F.mul( U1 , I );                     // V = U1 * I
+
+        res[0] =
+            F.sub(
+                F.sub( F.square(r) , J ),
+                F.add( V , V ));                       // X3 = r^2 - J - 2 * V
+
+        const S1_J = F.mul( S1 , J );
+
+        res[1] =
+            F.sub(
+                F.mul( r , F.sub(V,res[0])),
+                F.add( S1_J,S1_J ));                   // Y3 = r * (V-X3)-2 S1 J
+
+        res[2] =
+            F.mul(
+                H,
+                F.sub(
+                    F.square( F.add(p1[2],p2[2]) ),
+                    F.add( Z1Z1 , Z2Z2 )));            // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
+
+        return res;
+    }
+
+    neg(p) {
+        return [p[0], this.F.neg(p[1]), p[2]];
+    }
+
+    sub(a, b) {
+        return this.add(a, this.neg(b));
+    }
+
+    double(p) {
+        const F = this.F;
+
+        const res = new Array(3);
+
+        if (this.isZero(p)) return p;
+
+        const A = F.square( p[0] );                    // A = X1^2
+        const B = F.square( p[1] );                    // B = Y1^2
+        const C = F.square( B );                       // C = B^2
+
+        let D =
+            F.sub(
+                F.square( F.add(p[0] , B )),
+                F.add( A , C));
+        D = F.add(D,D);                    // D = 2 * ((X1 + B)^2 - A - C)
+
+        const E = F.add( F.add(A,A), A);          // E = 3 * A
+        const FF =F.square( E );                       // F = E^2
+
+        res[0] = F.sub( FF , F.add(D,D) );         // X3 = F - 2 D
+
+        let eightC = F.add( C , C );
+        eightC = F.add( eightC , eightC );
+        eightC = F.add( eightC , eightC );
+
+        res[1] =
+            F.sub(
+                F.mul(
+                    E,
+                    F.sub( D, res[0] )),
+                eightC);                                    // Y3 = E * (D - X3) - 8 * C
+
+        const Y1Z1 = F.mul( p[1] , p[2] );
+        res[2] = F.add( Y1Z1 , Y1Z1 );                 // Z3 = 2 * Y1 * Z1
+
+        return res;
+    }
+
+    mulScalar(base, e) {
+        return fUtils.mulScalar(this, base, e);
+    }
+
+    affine(p) {
+        const F = this.F;
+        if (this.isZero(p)) {
+            return this.zero;
+        } else {
+            const Z_inv = F.inverse(p[2]);
+            const Z2_inv = F.square(Z_inv);
+            const Z3_inv = F.mul(Z2_inv, Z_inv);
+
+            const res = new Array(3);
+            res[0] = F.affine( F.mul(p[0],Z2_inv));
+            res[1] = F.affine( F.mul(p[1],Z3_inv));
+            res[2] = F.one;
+
+            return res;
+        }
+    }
+
+    equals(p1, p2) {
+        const F = this.F;
+
+        if (this.isZero(p1)) return this.isZero(p2);
+        if (this.isZero(p2)) return this.isZero(p1);
+
+        const Z1Z1 = F.square( p1[2] );
+        const Z2Z2 = F.square( p2[2] );
+
+        const U1 = F.mul( p1[0] , Z2Z2 );
+        const U2 = F.mul( p2[0] , Z1Z1 );
+
+        const Z1_cubed = F.mul( p1[2] , Z1Z1);
+        const Z2_cubed = F.mul( p2[2] , Z2Z2);
+
+        const S1 = F.mul( p1[1] , Z2_cubed);
+        const S2 = F.mul( p2[1] , Z1_cubed);
+
+        return (F.equals(U1,U2) && F.equals(S1,S2));
+    }
+
+    toString(p) {
+        const cp = this.affine(p);
+        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])} ]`;
+    }
+
+}
+
+module.exports = GCurve;
+

src/polfield.js

@@ -0,0 +1,534 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/*
+    This library does operations on polynomials with coefficients in a field F.
+
+    A polynomial P(x) = p0 + p1 * x + p2 * x^2 + ... + pn * x^n  is represented
+    by the array [ p0, p1, p2, ... , pn ].
+ */
+
+const bigInt = require("./bigint.js");
+
+class PolField {
+    constructor (F) {
+        this.F = F;
+
+        const q = this.F.q;
+        let rem = q.sub(bigInt(1));
+        let s = 0;
+        while (!rem.isOdd()) {
+            s ++;
+            rem = rem.shr(1);
+        }
+
+        const five = this.F.add(this.F.add(this.F.two, this.F.two), this.F.one);
+
+        this.w = new Array(s+1);
+        this.wi = new Array(s+1);
+        this.w[s] = this.F.exp(five, rem);
+        this.wi[s] = this.F.inverse(this.w[s]);
+
+        let n=s-1;
+        while (n>=0) {
+            this.w[n] = this.F.square(this.w[n+1]);
+            this.wi[n] = this.F.square(this.wi[n+1]);
+            n--;
+        }
+
+
+        this.roots = [];
+/*        for (let i=0; i<16; i++) {
+            let r = this.F.one;
+            n = 1 << i;
+            const rootsi = new Array(n);
+            for (let j=0; j<n; j++) {
+                rootsi[j] = r;
+                r = this.F.mul(r, this.w[i]);
+            }
+
+            this.roots.push(rootsi);
+        }
+    */
+        this._setRoots(15);
+    }
+
+    _setRoots(n) {
+        for (let i=n; (i>=0) && (!this.roots[i]); i--) {
+            let r = this.F.one;
+            const nroots = 1 << i;
+            const rootsi = new Array(nroots);
+            for (let j=0; j<nroots; j++) {
+                rootsi[j] = r;
+                r = this.F.mul(r, this.w[i]);
+            }
+
+            this.roots[i] = rootsi;
+        }
+    }
+
+    add(a, b) {
+        const m = Math.max(a.length, b.length);
+        const res = new Array(m);
+        for (let i=0; i<m; i++) {
+            res[i] = this.F.add(a[i] || this.F.zero, b[i] || this.F.zero);
+        }
+        return this.reduce(res);
+    }
+
+    double(a) {
+        return this.add(a,a);
+    }
+
+    sub(a, b) {
+        const m = Math.max(a.length, b.length);
+        const res = new Array(m);
+        for (let i=0; i<m; i++) {
+            res[i] = this.F.sub(a[i] || this.F.zero, b[i] || this.F.zero);
+        }
+        return this.reduce(res);
+    }
+
+    mulScalar(p, b) {
+        if (this.F.isZero(b)) return [];
+        if (this.F.equals(b, this.F.one)) return p;
+        const res = new Array(p.length);
+        for (let i=0; i<p.length; i++) {
+            res[i] = this.F.mul(p[i], b);
+        }
+        return res;
+    }
+
+
+
+    mul(a, b) {
+        if (a.length == 0) return [];
+        if (b.length == 0) return [];
+        if (a.length == 1) return this.mulScalar(b, a[0]);
+        if (b.length == 1) return this.mulScalar(a, b[0]);
+
+        if (b.length > a.length) {
+            [b, a] = [a, b];
+        }
+
+        if ((b.length <= 2) || (b.length < log2(a.length))) {
+            return this.mulNormal(a,b);
+        } else {
+            return this.mulFFT(a,b);
+        }
+    }
+
+    mulNormal(a, b) {
+        let res = [];
+        b = this.affine(b);
+        for (let i=0; i<b.length; i++) {
+            res = this.add(res, this.scaleX(this.mulScalar(a, b[i]), i) );
+        }
+        return res;
+    }
+
+    mulFFT(a,b) {
+        const longestN = Math.max(a.length, b.length);
+        const bitsResult = log2(longestN-1)+2;
+        this._setRoots(bitsResult);
+
+        const m = 1 << bitsResult;
+        const ea = this.extend(a,m);
+        const eb = this.extend(b,m);
+
+        const ta = __fft(this, ea, bitsResult, 0, 1, false);
+        const tb = __fft(this, eb, bitsResult, 0, 1, false);
+
+        const tres = new Array(m);
+
+        for (let i=0; i<m; i++) {
+            tres[i] = this.F.mul(ta[i], tb[i]);
+        }
+
+        const res = __fft(this, tres, bitsResult, 0, 1, true);
+
+        const twoinvm = this.F.inverse( this.F.mulScalar(this.F.one, m) );
+        const resn = new Array(m);
+        for (let i=0; i<m; i++) {
+            resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
+        }
+
+        return this.reduce(this.affine(resn));
+    }
+
+
+
+    square(a) {
+        return this.mul(a,a);
+    }
+
+    scaleX(p, n) {
+        if (n==0) {
+            return p;
+        } else if (n>0) {
+            const z = new Array(n).fill(this.F.zero);
+            return z.concat(p);
+        } else {
+            if (-n >= p.length) return [];
+            return p.slice(-n);
+        }
+    }
+
+    eval2(p, x) {
+        let v = this.F.zero;
+        let ix = this.F.one;
+        for (let i=0; i<p.length; i++) {
+            v = this.F.add(v, this.F.mul(p[i], ix));
+            ix = this.F.mul(ix, x);
+        }
+        return v;
+    }
+
+    eval(p,x) {
+        const F = this.F;
+        if (p.length == 0) return F.zero;
+        const m = this._next2Power(p.length);
+        const ep = this.extend(p, m);
+
+        return _eval(ep, x, 0, 1, m);
+
+        function _eval(p, x, offset, step, n) {
+            if (n==1) return p[offset];
+            const newX = F.square(x);
+            const res= F.add(
+                _eval(p, newX, offset, step << 1, n >> 1),
+                F.mul(
+                    x,
+                    _eval(p, newX, offset+step , step << 1, n >> 1)));
+            return res;
+        }
+    }
+
+    lagrange(points) {
+        let roots = [this.F.one];
+        for (let i=0; i<points.length; i++) {
+            roots = this.mul(roots, [this.F.neg(points[i][0]), this.F.one]);
+        }
+
+        let sum = [];
+        for (let i=0; i<points.length; i++) {
+            let mpol = this.ruffini(roots, points[i][0]);
+            const factor =
+                this.F.mul(
+                    this.F.inverse(this.eval(mpol, points[i][0])),
+                    points[i][1]);
+            mpol = this.mulScalar(mpol, factor);
+            sum = this.add(sum, mpol);
+        }
+        return sum;
+    }
+
+
+    fft(p) {
+        if (p.length <= 1) return p;
+        const bits = log2(p.length-1)+1;
+        this._setRoots(bits);
+
+        const m = 1 << bits;
+        const ep = this.extend(p, m);
+        const res = __fft(this, ep, bits, 0, 1);
+        return res;
+    }
+
+    ifft(p) {
+
+        if (p.length <= 1) return p;
+        const bits = log2(p.length-1)+1;
+        this._setRoots(bits);
+        const m = 1 << bits;
+        const ep = this.extend(p, m);
+        const res =  __fft(this, ep, bits, 0, 1);
+
+        const twoinvm = this.F.inverse( this.F.mulScalar(this.F.one, m) );
+        const resn = new Array(m);
+        for (let i=0; i<m; i++) {
+            resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
+        }
+
+        return resn;
+
+    }
+
+
+    _fft(pall, bits, offset, step) {
+
+        const n = 1 << bits;
+        if (n==1) {
+            return [ pall[offset] ];
+        }
+
+        const ndiv2 = n >> 1;
+        const p1 = this._fft(pall, bits-1, offset, step*2);
+        const p2 = this._fft(pall, bits-1, offset+step, step*2);
+
+        const out = new Array(n);
+
+        let m= this.F.one;
+        for (let i=0; i<ndiv2; i++) {
+            out[i] = this.F.add(p1[i], this.F.mul(m, p2[i]));
+            out[i+ndiv2] = this.F.sub(p1[i], this.F.mul(m, p2[i]));
+            m = this.F.mul(m, this.w[bits]);
+        }
+
+        return out;
+    }
+
+    extend(p, e) {
+        if (e == p.length) return p;
+        const z = new Array(e-p.length).fill(this.F.zero);
+
+        return p.concat(z);
+    }
+
+    reduce(p) {
+        if (p.length == 0) return p;
+        if (! this.F.isZero(p[p.length-1]) ) return p;
+        let i=p.length-1;
+        while( i>0 && this.F.isZero(p[i]) ) i--;
+        return p.slice(0, i+1);
+    }
+
+    affine(p) {
+        for (let i=0; i<p.length; i++) {
+            p[i] = this.F.affine(p[i]);
+        }
+        return p;
+    }
+
+    equals(a, b) {
+        const pa = this.reduce(this.affine(a));
+        const pb = this.reduce(this.affine(b));
+
+        if (pa.length != pb.length) return false;
+        for (let i=0; i<pb.length; i++) {
+            if (!this.F.equals(pa[i], pb[i])) return false;
+        }
+
+        return true;
+    }
+
+    ruffini(p, r) {
+        const res = new Array(p.length-1);
+        res[res.length-1] = p[p.length-1];
+        for (let i = res.length-2; i>=0; i--) {
+            res[i] = this.F.add(this.F.mul(res[i+1], r), p[i+1]);
+        }
+        return res;
+    }
+
+    _next2Power(v) {
+        v--;
+        v |= v >> 1;
+        v |= v >> 2;
+        v |= v >> 4;
+        v |= v >> 8;
+        v |= v >> 16;
+        v++;
+        return v;
+    }
+
+    toString(p) {
+        const ap = this.affine(p);
+        let S = "";
+        for (let i=ap.length-1; i>=0; i--) {
+            if (!this.F.isZero(p[i])) {
+                if (S!="") S += " + ";
+                S = S + p[i].toString(10);
+                if (i>0) {
+                    S = S + "x";
+                    if (i>1) {
+                        S = S + "^" +i;
+                    }
+                }
+            }
+        }
+        return S;
+    }
+
+
+    _reciprocal(p, bits) {
+        const k = 1 << bits;
+        if (k==1) {
+            return [ this.F.inverse(p[0]) ];
+        }
+        const np = this.scaleX(p, -k/2);
+        const q = this._reciprocal(np, bits-1);
+        const a = this.scaleX(this.double(q), 3*k/2-2);
+        const b = this.mul( this.square(q), p);
+
+        return this.scaleX(this.sub(a,b),   -(k-2));
+    }
+
+    // divides x^m / v
+    _div2(m, v) {
+        const kbits = log2(v.length-1)+1;
+        const k = 1 << kbits;
+
+        const scaleV = k - v.length;
+
+        // rec = x^(k - 2) / v* x^scaleV =>
+        // rec = x^(k-2-scaleV)/ v
+        //
+        // res = x^m/v = x^(m + (2*k-2 - scaleV) - (2*k-2 - scaleV)) /v =>
+        // res = rec * x^(m - (2*k-2 - scaleV)) =>
+        // res = rec * x^(m - 2*k + 2 + scaleV)
+
+        const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
+        const res = this.scaleX(rec, m - 2*k + 2 + scaleV);
+
+        return res;
+    }
+
+    div(_u, _v) {
+        if (_u.length < _v.length) return [];
+        const kbits = log2(_v.length-1)+1;
+        const k = 1 << kbits;
+
+        const u = this.scaleX(_u, k-_v.length);
+        const v = this.scaleX(_v, k-_v.length);
+
+        const n = v.length-1;
+        let m = u.length-1;
+
+        const s = this._reciprocal(v, kbits);
+        let t;
+        if (m>2*n) {
+            t = this.sub(this.scaleX([this.F.one], 2*n), this.mul(s, v));
+        }
+
+        let q = [];
+        let rem = u;
+        let us, ut;
+        let finish = false;
+
+        while (!finish) {
+            us = this.mul(rem, s);
+            q = this.add(q, this.scaleX(us, -2*n));
+
+            if ( m > 2*n ) {
+                ut = this.mul(rem, t);
+                rem = this.scaleX(ut, -2*n);
+                m = rem.length-1;
+            } else {
+                finish = true;
+            }
+        }
+
+        return q;
+    }
+
+
+    // returns the ith nth-root of one
+    oneRoot(n, i) {
+        let nbits = log2(n-1)+1;
+        let res = this.F.one;
+        let r = i;
+
+        if(i>=n) {
+            throw new Error("Given 'i' should be lower than 'n'");
+        }
+        else if (1<<nbits !== n) {
+            throw new Error(`Internal errlr: ${n} should equal ${1<<nbits}`);
+        }
+
+        while (r>0) {
+            if (r & 1 == 1) {
+                res = this.F.mul(res, this.w[nbits]);
+            }
+            r = r >> 1;
+            nbits --;
+        }
+        return res;
+    }
+
+    computeVanishingPolinomial(bits, t) {
+        const m = 1 << bits;
+        return this.F.sub(this.F.exp(t, bigInt(m)), this.F.one);
+    }
+
+    evaluateLagrangePolynomials(bits, t) {
+        const m= 1 << bits;
+        const tm = this.F.exp(t, bigInt(m));
+        const u= new Array(m).fill(this.F.zero);
+        this._setRoots(bits);
+        const omega = this.w[bits];
+
+        if (this.F.equals(tm, this.F.one)) {
+            for (let i = 0; i < m; i++) {
+                if (this.F.equals(this.roots[bits][0],t)) { // i.e., t equals omega^i
+                    u[i] = this.F.one;
+                    return u;
+                }
+            }
+        }
+
+        const z = this.F.sub(tm, this.F.one);
+//        let l = this.F.mul(z,  this.F.exp(this.F.twoinv, m));
+        let l = this.F.mul(z,  this.F.inverse(bigInt(m)));
+        for (let i = 0; i < m; i++) {
+            u[i] = this.F.mul(l, this.F.inverse(this.F.sub(t,this.roots[bits][i])));
+            l = this.F.mul(l, omega);
+        }
+
+        return u;
+    }
+
+    log2(V) {
+        return log2(V);
+    }
+}
+
+function log2( V )
+{
+    return( ( ( V & 0xFFFF0000 ) !== 0 ? ( V &= 0xFFFF0000, 16 ) : 0 ) | ( ( V & 0xFF00FF00 ) !== 0 ? ( V &= 0xFF00FF00, 8 ) : 0 ) | ( ( V & 0xF0F0F0F0 ) !== 0 ? ( V &= 0xF0F0F0F0, 4 ) : 0 ) | ( ( V & 0xCCCCCCCC ) !== 0 ? ( V &= 0xCCCCCCCC, 2 ) : 0 ) | ( ( V & 0xAAAAAAAA ) !== 0 ) );
+}
+
+
+function __fft(PF, pall, bits, offset, step) {
+
+    const n = 1 << bits;
+    if (n==1) {
+        return [ pall[offset] ];
+    } else if (n==2) {
+        return [
+            PF.F.add(pall[offset], pall[offset + step]),
+            PF.F.sub(pall[offset], pall[offset + step])];
+    }
+
+    const ndiv2 = n >> 1;
+    const p1 = __fft(PF, pall, bits-1, offset, step*2);
+    const p2 = __fft(PF, pall, bits-1, offset+step, step*2);
+
+    const out = new Array(n);
+
+    for (let i=0; i<ndiv2; i++) {
+        out[i] = PF.F.add(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
+        out[i+ndiv2] = PF.F.sub(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
+    }
+
+    return out;
+}
+
+
+module.exports = PolField;

src/prover_groth.js

@@ -0,0 +1,141 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+
+const bn128 = new BN128();
+const PolF = new PolField(new ZqField(bn128.r));
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function genProof(vk_proof, witness) {
+
+    const proof = {};
+
+    const r = PolF.F.random();
+    const s = PolF.F.random();
+
+/* Uncomment to generate a deterministic proof to debug
+    const r = PolF.F.zero;
+    const s = PolF.F.zero;
+*/
+
+
+    proof.pi_a = G1.zero;
+    proof.pi_b = G2.zero;
+    proof.pi_c = G1.zero;
+
+    let pib1 = G1.zero;
+
+
+    // Skip public entries and the "1" signal that are forced by the verifier
+
+    for (let s= 0; s< vk_proof.nVars; s++) {
+        // pi_a = pi_a + A[s] * witness[s];
+        proof.pi_a = G1.add( proof.pi_a, G1.mulScalar( vk_proof.A[s], witness[s]));
+
+        // pi_b = pi_b + B[s] * witness[s];
+        proof.pi_b = G2.add( proof.pi_b, G2.mulScalar( vk_proof.B2[s], witness[s]));
+
+        pib1 = G1.add( pib1, G1.mulScalar( vk_proof.B1[s], witness[s]));
+    }
+
+    for (let s= vk_proof.nPublic+1; s< vk_proof.nVars; s++) {
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.C[s], witness[s]));
+    }
+
+    proof.pi_a  = G1.add( proof.pi_a, vk_proof.vk_alfa_1 );
+    proof.pi_a  = G1.add( proof.pi_a, G1.mulScalar( vk_proof.vk_delta_1, r ));
+
+    proof.pi_b  = G2.add( proof.pi_b, vk_proof.vk_beta_2 );
+    proof.pi_b  = G2.add( proof.pi_b, G2.mulScalar( vk_proof.vk_delta_2, s ));
+
+    pib1 = G1.add( pib1, vk_proof.vk_beta_1 );
+    pib1 = G1.add( pib1, G1.mulScalar( vk_proof.vk_delta_1, s ));
+
+    const h = calculateH(vk_proof, witness);
+
+    // proof.pi_c = G1.affine(proof.pi_c);
+    // console.log("pi_onlyc", proof.pi_c);
+
+    for (let i = 0; i < h.length; i++) {
+        // console.log(i + "->" + h[i].toString());
+        proof.pi_c = G1.add( proof.pi_c, G1.mulScalar( vk_proof.hExps[i], h[i]));
+    }
+
+    // proof.pi_c = G1.affine(proof.pi_c);
+    // console.log("pi_candh", proof.pi_c);
+
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( proof.pi_a, s ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( pib1, r ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.vk_delta_1, PolF.F.affine(PolF.F.neg(PolF.F.mul(r,s) ))));
+
+
+    const publicSignals = witness.slice(1, vk_proof.nPublic+1);
+
+    proof.pi_a = G1.affine(proof.pi_a);
+    proof.pi_b = G2.affine(proof.pi_b);
+    proof.pi_c = G1.affine(proof.pi_c);
+
+    proof.protocol = "groth";
+
+    return {proof, publicSignals};
+
+};
+
+
+function calculateH(vk_proof, witness) {
+
+    const F = PolF.F;
+    const m = vk_proof.domainSize;
+    const polA_T = new Array(m).fill(PolF.F.zero);
+    const polB_T = new Array(m).fill(PolF.F.zero);
+    const polC_T = new Array(m).fill(PolF.F.zero);
+
+    for (let s=0; s<vk_proof.nVars; s++) {
+        for (let c in vk_proof.polsA[s]) {
+            polA_T[c] = F.add(polA_T[c], F.mul(witness[s], vk_proof.polsA[s][c]));
+        }
+        for (let c in vk_proof.polsB[s]) {
+            polB_T[c] = F.add(polB_T[c], F.mul(witness[s], vk_proof.polsB[s][c]));
+        }
+        for (let c in vk_proof.polsC[s]) {
+            polC_T[c] = F.add(polC_T[c], F.mul(witness[s], vk_proof.polsC[s][c]));
+        }
+    }
+
+    const polA_S = PolF.ifft(polA_T);
+    const polB_S = PolF.ifft(polB_T);
+
+    const polAB_S = PolF.mul(polA_S, polB_S);
+
+    const polC_S = PolF.ifft(polC_T);
+
+    const polABC_S = PolF.sub(polAB_S, polC_S);
+
+    const H_S = polABC_S.slice(m);
+
+    return H_S;
+}

src/prover_kimleeoh.js

@@ -0,0 +1,177 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+const createKeccakHash = require("keccak");
+const bigInt = require("./bigint");
+
+const bn128 = new BN128();
+const PolF = new PolField(new ZqField(bn128.r));
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function genProof(vk_proof, witness) {
+
+    const proof = {};
+
+    const r = PolF.F.random();
+    const s = PolF.F.random();
+
+//    const r = PolF.F.zero;
+//    const s = PolF.F.zero;
+
+/* Uncomment to generate a deterministic proof to debug
+    const r = PolF.F.zero;
+    const s = PolF.F.zero;
+*/
+
+
+    proof.pi_a = G1.zero;
+    proof.pi_b = G2.zero;
+    proof.pi_c = G1.zero;
+
+    let pib1 = G1.zero;
+    let piadelta = G1.zero;
+
+
+    // Skip public entries and the "1" signal that are forced by the verifier
+
+    for (let s= 0; s< vk_proof.nVars; s++) {
+        // pi_a = pi_a + A[s] * witness[s];
+        proof.pi_a = G1.add( proof.pi_a, G1.mulScalar( vk_proof.A[s], witness[s]));
+
+        // pi_b = pi_b + B[s] * witness[s];
+        proof.pi_b = G2.add( proof.pi_b, G2.mulScalar( vk_proof.B2[s], witness[s]));
+
+        piadelta = G1.add( piadelta, G1.mulScalar( vk_proof.Adelta[s], witness[s]));
+        pib1 = G1.add( pib1, G1.mulScalar( vk_proof.B1[s], witness[s]));
+    }
+
+    for (let s= vk_proof.nPublic+1; s< vk_proof.nVars; s++) {
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.C[s], witness[s]));
+    }
+
+    proof.pi_a  = G1.add( proof.pi_a, vk_proof.vk_alfa_1 );
+    proof.pi_a  = G1.add( proof.pi_a, G1.mulScalar( G1.g, r ));
+
+    piadelta = G1.add( piadelta, vk_proof.vk_alfadelta_1);
+    piadelta = G1.add( piadelta, G1.mulScalar( vk_proof.vk_delta_1, r ));
+
+    proof.pi_b  = G2.add( proof.pi_b, vk_proof.vk_beta_2 );
+    proof.pi_b  = G2.add( proof.pi_b, G2.mulScalar( G2.g, s ));
+
+    pib1 = G1.add( pib1, vk_proof.vk_beta_1 );
+    pib1 = G1.add( pib1, G1.mulScalar( G1.g, s ));
+
+    proof.pi_a = G1.affine(proof.pi_a);
+    proof.pi_b = G2.affine(proof.pi_b);
+
+    const buff = Buffer.concat([
+        proof.pi_a[0].beInt2Buff(32),
+        proof.pi_a[1].beInt2Buff(32),
+        proof.pi_b[0][0].beInt2Buff(32),
+        proof.pi_b[0][1].beInt2Buff(32),
+        proof.pi_b[1][0].beInt2Buff(32),
+        proof.pi_b[1][1].beInt2Buff(32)
+    ]);
+
+    const h1buff = createKeccakHash("keccak256").update(buff).digest();
+    const h2buff = createKeccakHash("keccak256").update(h1buff).digest();
+
+    const h1 = bigInt.beBuff2int(h1buff);
+    const h2 = bigInt.beBuff2int(h2buff);
+
+
+//    const h1 = PolF.F.zero;
+//    const h2 = PolF.F.zero;
+
+    console.log(h1.toString());
+    console.log(h2.toString());
+
+    const h = calculateH(vk_proof, witness);
+
+    // proof.pi_c = G1.affine(proof.pi_c);
+    // console.log("pi_onlyc", proof.pi_c);
+
+    for (let i = 0; i < h.length; i++) {
+        // console.log(i + "->" + h[i].toString());
+        proof.pi_c = G1.add( proof.pi_c, G1.mulScalar( vk_proof.hExps[i], h[i]));
+    }
+
+    // proof.pi_c = G1.affine(proof.pi_c);
+    // console.log("pi_candh", proof.pi_c);
+
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( proof.pi_a, s ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( pib1, r ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( G1.g, PolF.F.affine(PolF.F.neg(PolF.F.mul(r,s) ))));
+
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( piadelta, h2 ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( pib1, h1 ));
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.vk_delta_1, PolF.F.mul(h1,h2)));
+
+    const publicSignals = witness.slice(1, vk_proof.nPublic+1);
+
+    proof.pi_c = G1.affine(proof.pi_c);
+
+    proof.protocol = "kimleeoh";
+
+    return {proof, publicSignals};
+
+};
+
+
+function calculateH(vk_proof, witness) {
+
+    const F = PolF.F;
+    const m = vk_proof.domainSize;
+    const polA_T = new Array(m).fill(PolF.F.zero);
+    const polB_T = new Array(m).fill(PolF.F.zero);
+    const polC_T = new Array(m).fill(PolF.F.zero);
+
+    for (let s=0; s<vk_proof.nVars; s++) {
+        for (let c in vk_proof.polsA[s]) {
+            polA_T[c] = F.add(polA_T[c], F.mul(witness[s], vk_proof.polsA[s][c]));
+        }
+        for (let c in vk_proof.polsB[s]) {
+            polB_T[c] = F.add(polB_T[c], F.mul(witness[s], vk_proof.polsB[s][c]));
+        }
+        for (let c in vk_proof.polsC[s]) {
+            polC_T[c] = F.add(polC_T[c], F.mul(witness[s], vk_proof.polsC[s][c]));
+        }
+    }
+
+    const polA_S = PolF.ifft(polA_T);
+    const polB_S = PolF.ifft(polB_T);
+
+    const polAB_S = PolF.mul(polA_S, polB_S);
+
+    const polC_S = PolF.ifft(polC_T);
+
+    const polABC_S = PolF.sub(polAB_S, polC_S);
+
+    const H_S = polABC_S.slice(m);
+
+    return H_S;
+}

src/prover_original.js

@@ -0,0 +1,210 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+
+const bn128 = new BN128();
+const PolF = new PolField(new ZqField(bn128.r));
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function genProof(vk_proof, witness) {
+
+    const proof = {};
+
+
+    const d1 = PolF.F.random();
+    const d2 = PolF.F.random();
+    const d3 = PolF.F.random();
+
+    proof.pi_a = G1.zero;
+    proof.pi_ap = G1.zero;
+    proof.pi_b = G2.zero;
+    proof.pi_bp = G1.zero;
+    proof.pi_c = G1.zero;
+    proof.pi_cp = G1.zero;
+    proof.pi_kp = G1.zero;
+    proof.pi_h = G1.zero;
+
+
+    // Skip public entries and the "1" signal that are forced by the verifier
+    for (let s= vk_proof.nPublic+1; s< vk_proof.nVars; s++) {
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_a  = G1.add( proof.pi_a, G1.mulScalar( vk_proof.A[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_ap = G1.add( proof.pi_ap, G1.mulScalar( vk_proof.Ap[s], witness[s]));
+    }
+
+    for (let s= 0; s< vk_proof.nVars; s++) {
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_b  = G2.add( proof.pi_b, G2.mulScalar( vk_proof.B[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_bp = G1.add( proof.pi_bp, G1.mulScalar( vk_proof.Bp[s], witness[s]));
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.C[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_cp = G1.add( proof.pi_cp, G1.mulScalar( vk_proof.Cp[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_kp = G1.add( proof.pi_kp, G1.mulScalar( vk_proof.Kp[s], witness[s]));
+    }
+
+    proof.pi_a  = G1.add( proof.pi_a, G1.mulScalar( vk_proof.A[vk_proof.nVars], d1));
+    proof.pi_ap  = G1.add( proof.pi_ap, G1.mulScalar( vk_proof.Ap[vk_proof.nVars], d1));
+
+    proof.pi_b  = G2.add( proof.pi_b, G2.mulScalar( vk_proof.B[vk_proof.nVars], d2));
+    proof.pi_bp  = G1.add( proof.pi_bp, G1.mulScalar( vk_proof.Bp[vk_proof.nVars], d2));
+
+    proof.pi_c  = G1.add( proof.pi_c, G1.mulScalar( vk_proof.C[vk_proof.nVars], d3));
+    proof.pi_cp  = G1.add( proof.pi_cp, G1.mulScalar( vk_proof.Cp[vk_proof.nVars], d3));
+
+    proof.pi_kp  = G1.add( proof.pi_kp, G1.mulScalar( vk_proof.Kp[vk_proof.nVars  ], d1));
+    proof.pi_kp  = G1.add( proof.pi_kp, G1.mulScalar( vk_proof.Kp[vk_proof.nVars+1], d2));
+    proof.pi_kp  = G1.add( proof.pi_kp, G1.mulScalar( vk_proof.Kp[vk_proof.nVars+2], d3));
+
+/*
+    let polA = [];
+    let polB = [];
+    let polC = [];
+
+    for (let s= 0; s< vk_proof.nVars; s++) {
+        polA = PolF.add(
+            polA,
+            PolF.mul(
+                vk_proof.polsA[s],
+                [witness[s]] ));
+
+        polB = PolF.add(
+            polB,
+            PolF.mul(
+                vk_proof.polsB[s],
+                [witness[s]] ));
+
+        polC = PolF.add(
+            polC,
+            PolF.mul(
+                vk_proof.polsC[s],
+                [witness[s]] ));
+    }
+
+
+    let polFull = PolF.sub(PolF.mul( polA, polB), polC);
+
+    const h = PolF.div(polFull, vk_proof.polZ );
+*/
+
+    const h = calculateH(vk_proof, witness, d1, d2, d3);
+
+//    console.log(h.length + "/" + vk_proof.hExps.length);
+
+    for (let i = 0; i < h.length; i++) {
+        proof.pi_h = G1.add( proof.pi_h, G1.mulScalar( vk_proof.hExps[i], h[i]));
+    }
+
+    proof.pi_a = G1.affine(proof.pi_a);
+    proof.pi_b = G2.affine(proof.pi_b);
+    proof.pi_c = G1.affine(proof.pi_c);
+    proof.pi_ap = G1.affine(proof.pi_ap);
+    proof.pi_bp = G1.affine(proof.pi_bp);
+    proof.pi_cp = G1.affine(proof.pi_cp);
+    proof.pi_kp = G1.affine(proof.pi_kp);
+    proof.pi_h = G1.affine(proof.pi_h);
+
+//    proof.h=h;
+
+    proof.protocol = "original";
+
+    const publicSignals = witness.slice(1, vk_proof.nPublic+1);
+
+    return {proof, publicSignals};
+};
+
+
+function calculateH(vk_proof, witness, d1, d2, d3) {
+
+    const F = PolF.F;
+    const m = vk_proof.domainSize;
+    const polA_T = new Array(m).fill(PolF.F.zero);
+    const polB_T = new Array(m).fill(PolF.F.zero);
+    const polC_T = new Array(m).fill(PolF.F.zero);
+
+    for (let s=0; s<vk_proof.nVars; s++) {
+        for (let c in vk_proof.polsA[s]) {
+            polA_T[c] = F.add(polA_T[c], F.mul(witness[s], vk_proof.polsA[s][c]));
+        }
+        for (let c in vk_proof.polsB[s]) {
+            polB_T[c] = F.add(polB_T[c], F.mul(witness[s], vk_proof.polsB[s][c]));
+        }
+        for (let c in vk_proof.polsC[s]) {
+            polC_T[c] = F.add(polC_T[c], F.mul(witness[s], vk_proof.polsC[s][c]));
+        }
+    }
+
+    const polA_S = PolF.ifft(polA_T);
+    const polB_S = PolF.ifft(polB_T);
+
+    const polAB_S = PolF.mul(polA_S, polB_S);
+
+    const polC_S = PolF.ifft(polC_T);
+
+    const polABC_S = PolF.sub(polAB_S, polC_S);
+
+    const polZ_S = new Array(m+1).fill(F.zero);
+    polZ_S[m] = F.one;
+    polZ_S[0] = F.neg(F.one);
+
+    let H_S = PolF.div(polABC_S, polZ_S);
+/*
+    const H2S = PolF.mul(H_S, polZ_S);
+
+    if (PolF.equals(H2S, polABC_S)) {
+        console.log("Is Divisible!");
+    } else {
+        console.log("ERROR: Not divisible!");
+    }
+*/
+
+    /* add coefficients of the polynomial (d2*A + d1*B - d3) + d1*d2*Z */
+
+    H_S = PolF.extend(H_S, m+1);
+
+    for (let i=0; i<m; i++) {
+        const d2A = PolF.F.mul(d2, polA_S[i]);
+        const d1B = PolF.F.mul(d1, polB_S[i]);
+        H_S[i] = PolF.F.add(H_S[i], PolF.F.add(d2A, d1B));
+    }
+
+    H_S[0] = PolF.F.sub(H_S[0], d3);
+
+    // Z = x^m -1
+    const d1d2 = PolF.F.mul(d1, d2);
+    H_S[m] = PolF.F.add(H_S[m], d1d2);
+    H_S[0] = PolF.F.sub(H_S[0], d1d2);
+
+    H_S = PolF.reduce(PolF.affine(H_S));
+
+    return H_S;
+}

src/ratfield.js

@@ -0,0 +1,127 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const fUtils = require("./futils.js");
+
+class RatField {
+    constructor(F) {
+        this.F = F;
+        this.zero = [F.zero, F.one];
+        this.one = [F.one, F.one];
+        this.two = [F.two, F.one];
+        this.twoinv = [F.one, F.two];
+        this.q = F.q;
+    }
+
+    add(a,b) {
+        return [
+            this.F.add(
+                this.F.mul(a[0], b[1]),
+                this.F.mul(a[1], b[0])),
+            this.F.mul(a[1], b[1])];
+    }
+
+    double(a) {
+        return [this.F.add(a[0], a[0]), a[1]];
+    }
+
+    sub(a,b) {
+        return [
+            this.F.sub(
+                this.F.mul(a[0], b[1]),
+                this.F.mul(a[1], b[0])),
+            this.F.mul(a[1], b[1])];
+    }
+
+    neg(a) {
+        return [this.F.neg(a[0]), a[1]];
+    }
+
+    mul(a,b) {
+        return [
+            this.F.mul(a[0], b[0]),
+            this.F.mul(a[1], b[1]),
+        ];
+    }
+
+    copy(a) {
+        return [a[0], a[1]];
+    }
+
+    div(a, b) {
+        return [
+            this.F.mul(a[0], b[1]),
+            this.F.mul(a[1], b[0]),
+        ];
+    }
+
+    inverse(a) {
+        return [a[1], a[0]];
+    }
+
+    square(a) {
+        return [
+            this.F.square(a[0]),
+            this.F.square(a[1])
+        ];
+    }
+
+    mulScalar(base, e) {
+        return [this.F.mulScalar(base[0], e) , base[1]];
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
+    equals(a, b) {
+        return this.F.equals(
+            this.F.mul(a[0], b[1]),
+            this.F.mul(a[1], b[0])
+        );
+    }
+
+    isZero(a) {
+        return this.F.isZero(a[0]);
+    }
+
+    affine(a) {
+        return [this.F.div(a[0], a[1]), this.F.one];
+    }
+
+    toString(a) {
+        const ca = this.affine(a);
+        return `"0x${ca[0].toString(16)}"`;
+    }
+
+    random() {
+        return [this.F.random(), this.F.one];
+    }
+
+    fromF(a) {
+        return [a, this.F.one];
+    }
+
+    toF(a) {
+        return this.affine(a)[0];
+    }
+}
+
+
+module.exports = RatField;

src/setup_groth.js

@@ -0,0 +1,212 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+const bigInt = require("./bigint.js");
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+const PolF = new PolField(new ZqField(bn128.r));
+const F = new ZqField(bn128.r);
+
+module.exports = function setup(circuit) {
+    const setup = {
+        vk_proof : {
+            protocol: "groth",
+            nVars: circuit.nVars,
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        vk_verifier: {
+            protocol: "groth",
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        toxic: {}
+    };
+
+
+    setup.vk_proof.domainBits = PolF.log2(circuit.nConstraints + circuit.nPubInputs + circuit.nOutputs +1 -1) +1;
+    setup.vk_proof.domainSize = 1 << setup.vk_proof.domainBits;
+
+    calculatePolinomials(setup, circuit);
+    setup.toxic.t = F.random();
+    calculateEncriptedValuesAtT(setup, circuit);
+
+    return setup;
+};
+
+
+function calculatePolinomials(setup, circuit) {
+
+    setup.vk_proof.polsA = new Array(circuit.nVars);
+    setup.vk_proof.polsB = new Array(circuit.nVars);
+    setup.vk_proof.polsC = new Array(circuit.nVars);
+    for (let i=0; i<circuit.nVars; i++) {
+        setup.vk_proof.polsA[i] = {};
+        setup.vk_proof.polsB[i] = {};
+        setup.vk_proof.polsC[i] = {};
+    }
+    for (let c=0; c<circuit.nConstraints; c++) {
+
+        for (let s in circuit.constraints[c][0]) {
+            setup.vk_proof.polsA[s][c] = bigInt(circuit.constraints[c][0][s]);
+        }
+        for (let s in circuit.constraints[c][1]) {
+            setup.vk_proof.polsB[s][c] = bigInt(circuit.constraints[c][1][s]);
+        }
+        for (let s in circuit.constraints[c][2]) {
+            setup.vk_proof.polsC[s][c] = bigInt(circuit.constraints[c][2][s]);
+        }
+    }
+
+    /**
+     * add and process the constraints
+     *     input_i * 0 = 0
+     * to ensure soundness of input consistency
+     */
+    for (let i = 0; i < circuit.nPubInputs + circuit.nOutputs + 1; ++i)
+    {
+        setup.vk_proof.polsA[i][circuit.nConstraints + i] = F.one;
+    }
+}
+
+function calculateValuesAtT(setup, circuit) {
+    const z_t = PolF.computeVanishingPolinomial(setup.vk_proof.domainBits, setup.toxic.t);
+    const u = PolF.evaluateLagrangePolynomials(setup.vk_proof.domainBits, setup.toxic.t);
+
+    const a_t = new Array(circuit.nVars).fill(F.zero);
+    const b_t = new Array(circuit.nVars).fill(F.zero);
+    const c_t = new Array(circuit.nVars).fill(F.zero);
+
+    // TODO: substitute setup.polsA for coeficients
+    for (let s=0; s<circuit.nVars; s++) {
+        for (let c in setup.vk_proof.polsA[s]) {
+            a_t[s] = F.add(a_t[s], F.mul(u[c], setup.vk_proof.polsA[s][c]));
+        }
+        for (let c in setup.vk_proof.polsB[s]) {
+            b_t[s] = F.add(b_t[s], F.mul(u[c], setup.vk_proof.polsB[s][c]));
+        }
+        for (let c in setup.vk_proof.polsC[s]) {
+            c_t[s] = F.add(c_t[s], F.mul(u[c], setup.vk_proof.polsC[s][c]));
+        }
+    }
+
+    return {a_t, b_t, c_t, z_t};
+
+}
+
+
+
+
+function calculateEncriptedValuesAtT(setup, circuit) {
+
+    const v = calculateValuesAtT(setup, circuit);
+    setup.vk_proof.A = new Array(circuit.nVars);
+    setup.vk_proof.B1 = new Array(circuit.nVars);
+    setup.vk_proof.B2 = new Array(circuit.nVars);
+    setup.vk_proof.C = new Array(circuit.nVars);
+    setup.vk_verifier.IC = new Array(circuit.nPublic);
+
+    setup.toxic.kalfa = F.random();
+    setup.toxic.kbeta = F.random();
+    setup.toxic.kgamma = F.random();
+    setup.toxic.kdelta = F.random();
+
+    let invDelta = F.inverse(setup.toxic.kdelta);
+    let invGamma = F.inverse(setup.toxic.kgamma);
+
+    setup.vk_proof.vk_alfa_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kalfa));
+    setup.vk_proof.vk_beta_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kbeta));
+    setup.vk_proof.vk_delta_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kdelta));
+
+    setup.vk_proof.vk_beta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kbeta));
+    setup.vk_proof.vk_delta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kdelta));
+
+
+    setup.vk_verifier.vk_alfa_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kalfa));
+
+    setup.vk_verifier.vk_beta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kbeta));
+    setup.vk_verifier.vk_gamma_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kgamma));
+    setup.vk_verifier.vk_delta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kdelta));
+
+    setup.vk_verifier.vk_alfabeta_12 = bn128.F12.affine(bn128.pairing( setup.vk_verifier.vk_alfa_1 , setup.vk_verifier.vk_beta_2 ));
+
+    for (let s=0; s<circuit.nVars; s++) {
+
+        const A = G1.affine(G1.mulScalar(G1.g, v.a_t[s]));
+
+        setup.vk_proof.A[s] = A;
+
+        const B1 = G1.affine(G1.mulScalar(G1.g, v.b_t[s]));
+
+        setup.vk_proof.B1[s] = B1;
+
+        const B2 = G2.affine(G2.mulScalar(G2.g, v.b_t[s]));
+
+        setup.vk_proof.B2[s] = B2;
+    }
+
+    for (let s=0; s<=setup.vk_proof.nPublic; s++) {
+        let ps =
+            F.mul(
+                invGamma,
+                F.add(
+                    F.add(
+                        F.mul(v.a_t[s], setup.toxic.kbeta),
+                        F.mul(v.b_t[s], setup.toxic.kalfa)),
+                    v.c_t[s]));
+
+        const IC = G1.affine(G1.mulScalar(G1.g, ps));
+        setup.vk_verifier.IC[s]=IC;
+    }
+
+    for (let s=setup.vk_proof.nPublic+1; s<circuit.nVars; s++) {
+        let ps =
+            F.mul(
+                invDelta,
+                F.add(
+                    F.add(
+                        F.mul(v.a_t[s], setup.toxic.kbeta),
+                        F.mul(v.b_t[s], setup.toxic.kalfa)),
+                    v.c_t[s]));
+        const C = G1.affine(G1.mulScalar(G1.g, ps));
+        setup.vk_proof.C[s]=C;
+    }
+
+    // Calculate HExps
+
+    const maxH = setup.vk_proof.domainSize+1;
+
+    setup.vk_proof.hExps = new Array(maxH);
+
+    const zod = F.mul(invDelta, v.z_t);
+
+    setup.vk_proof.hExps[0] = G1.affine(G1.mulScalar(G1.g, zod));
+    let eT = setup.toxic.t;
+    for (let i=1; i<maxH; i++) {
+        setup.vk_proof.hExps[i] = G1.affine(G1.mulScalar(G1.g, F.mul(eT, zod)));
+        eT = F.mul(eT, setup.toxic.t);
+    }
+}
+

src/setup_kimleeoh.js

@@ -0,0 +1,233 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+const bigInt = require("./bigint.js");
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+const PolF = new PolField(new ZqField(bn128.r));
+const F = new ZqField(bn128.r);
+
+module.exports = function setup(circuit) {
+    const setup = {
+        vk_proof : {
+            protocol: "groth",
+            nVars: circuit.nVars,
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        vk_verifier: {
+            protocol: "groth",
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        toxic: {}
+    };
+
+
+    setup.vk_proof.domainBits = PolF.log2(circuit.nConstraints + circuit.nPubInputs + circuit.nOutputs +1 -1) +1;
+    setup.vk_proof.domainSize = 1 << setup.vk_proof.domainBits;
+
+    calculatePolinomials(setup, circuit);
+    setup.toxic.t = F.random();
+    calculateEncriptedValuesAtT(setup, circuit);
+
+    return setup;
+};
+
+
+function calculatePolinomials(setup, circuit) {
+
+    setup.vk_proof.polsA = new Array(circuit.nVars);
+    setup.vk_proof.polsB = new Array(circuit.nVars);
+    setup.vk_proof.polsC = new Array(circuit.nVars);
+    for (let i=0; i<circuit.nVars; i++) {
+        setup.vk_proof.polsA[i] = {};
+        setup.vk_proof.polsB[i] = {};
+        setup.vk_proof.polsC[i] = {};
+    }
+    for (let c=0; c<circuit.nConstraints; c++) {
+
+        for (let s in circuit.constraints[c][0]) {
+            setup.vk_proof.polsA[s][c] = bigInt(circuit.constraints[c][0][s]);
+        }
+        for (let s in circuit.constraints[c][1]) {
+            setup.vk_proof.polsB[s][c] = bigInt(circuit.constraints[c][1][s]);
+        }
+        for (let s in circuit.constraints[c][2]) {
+            setup.vk_proof.polsC[s][c] = bigInt(circuit.constraints[c][2][s]);
+        }
+    }
+
+    /**
+     * add and process the constraints
+     *     input_i * 0 = 0
+     * to ensure soundness of input consistency
+     */
+    for (let i = 0; i < circuit.nPubInputs + circuit.nOutputs + 1; ++i)
+    {
+        setup.vk_proof.polsA[i][circuit.nConstraints + i] = F.one;
+    }
+}
+
+function calculateValuesAtT(setup, circuit) {
+    const z_t = PolF.computeVanishingPolinomial(setup.vk_proof.domainBits, setup.toxic.t);
+    const u = PolF.evaluateLagrangePolynomials(setup.vk_proof.domainBits, setup.toxic.t);
+
+    const a_t = new Array(circuit.nVars).fill(F.zero);
+    const b_t = new Array(circuit.nVars).fill(F.zero);
+    const c_t = new Array(circuit.nVars).fill(F.zero);
+
+    // TODO: substitute setup.polsA for coeficients
+    for (let s=0; s<circuit.nVars; s++) {
+        for (let c in setup.vk_proof.polsA[s]) {
+            a_t[s] = F.add(a_t[s], F.mul(u[c], setup.vk_proof.polsA[s][c]));
+        }
+        for (let c in setup.vk_proof.polsB[s]) {
+            b_t[s] = F.add(b_t[s], F.mul(u[c], setup.vk_proof.polsB[s][c]));
+        }
+        for (let c in setup.vk_proof.polsC[s]) {
+            c_t[s] = F.add(c_t[s], F.mul(u[c], setup.vk_proof.polsC[s][c]));
+        }
+    }
+
+    return {a_t, b_t, c_t, z_t};
+
+}
+
+
+
+
+function calculateEncriptedValuesAtT(setup, circuit) {
+
+    const v = calculateValuesAtT(setup, circuit);
+    setup.vk_proof.A = new Array(circuit.nVars);
+    setup.vk_proof.Adelta = new Array(circuit.nVars);
+    setup.vk_proof.B1 = new Array(circuit.nVars);
+    setup.vk_proof.B2 = new Array(circuit.nVars);
+    setup.vk_proof.C = new Array(circuit.nVars);
+    setup.vk_verifier.IC = new Array(circuit.nPublic);
+
+    setup.toxic.kalfa = F.random();
+    setup.toxic.kbeta = F.random();
+    setup.toxic.kgamma = F.random();
+    setup.toxic.kdelta = F.random();
+
+    const gammaSquare = F.mul(setup.toxic.kgamma, setup.toxic.kgamma);
+
+    setup.vk_proof.vk_alfa_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kalfa));
+    setup.vk_proof.vk_beta_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kbeta));
+    setup.vk_proof.vk_delta_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kdelta));
+    setup.vk_proof.vk_alfadelta_1 = G1.affine(G1.mulScalar( G1.g, F.mul(setup.toxic.kalfa, setup.toxic.kdelta)));
+
+    setup.vk_proof.vk_beta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kbeta));
+
+
+    setup.vk_verifier.vk_alfa_1 = G1.affine(G1.mulScalar( G1.g, setup.toxic.kalfa));
+
+    setup.vk_verifier.vk_beta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kbeta));
+    setup.vk_verifier.vk_gamma_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kgamma));
+    setup.vk_verifier.vk_delta_2 = G2.affine(G2.mulScalar( G2.g, setup.toxic.kdelta));
+
+    setup.vk_verifier.vk_alfabeta_12 = bn128.F12.affine(bn128.pairing( setup.vk_verifier.vk_alfa_1 , setup.vk_verifier.vk_beta_2 ));
+
+    for (let s=0; s<circuit.nVars; s++) {
+
+        const A = G1.affine(G1.mulScalar(G1.g, F.mul(setup.toxic.kgamma, v.a_t[s])));
+
+        setup.vk_proof.A[s] = A;
+        setup.vk_proof.Adelta[s] = G1.affine(G1.mulScalar(A, setup.toxic.kdelta));
+
+        const B1 = G1.affine(G1.mulScalar(G1.g, F.mul(setup.toxic.kgamma, v.b_t[s])));
+
+        setup.vk_proof.B1[s] = B1;
+
+        const B2 = G2.affine(G2.mulScalar(G2.g, F.mul(setup.toxic.kgamma, v.b_t[s])));
+
+        setup.vk_proof.B2[s] = B2;
+    }
+
+    for (let s=0; s<=setup.vk_proof.nPublic; s++) {
+
+        let ps =
+            F.add(
+                F.mul(
+                    setup.toxic.kgamma,
+                    v.c_t[s]
+                ),
+                F.add(
+                    F.mul(
+                        setup.toxic.kbeta,
+                        v.a_t[s]
+                    ),
+                    F.mul(
+                        setup.toxic.kalfa,
+                        v.b_t[s]
+                    )
+                )
+            );
+
+        const IC = G1.affine(G1.mulScalar(G1.g, ps));
+        setup.vk_verifier.IC[s]=IC;
+    }
+
+    for (let s=setup.vk_proof.nPublic+1; s<circuit.nVars; s++) {
+        let ps =
+            F.add(
+                F.mul(
+                    gammaSquare,
+                    v.c_t[s]
+                ),
+                F.add(
+                    F.mul(
+                        F.mul(setup.toxic.kbeta, setup.toxic.kgamma),
+                        v.a_t[s]
+                    ),
+                    F.mul(
+                        F.mul(setup.toxic.kalfa, setup.toxic.kgamma),
+                        v.b_t[s]
+                    )
+                )
+            );
+
+        const C = G1.affine(G1.mulScalar(G1.g, ps));
+        setup.vk_proof.C[s]=C;
+    }
+
+    // Calculate HExps
+
+    const maxH = setup.vk_proof.domainSize+1;
+
+    setup.vk_proof.hExps = new Array(maxH);
+
+    const zod = F.mul(gammaSquare, v.z_t);
+
+    setup.vk_proof.hExps[0] = G1.affine(G1.mulScalar(G1.g, zod));
+    let eT = setup.toxic.t;
+    for (let i=1; i<maxH; i++) {
+        setup.vk_proof.hExps[i] = G1.affine(G1.mulScalar(G1.g, F.mul(eT, zod)));
+        eT = F.mul(eT, setup.toxic.t);
+    }
+}
+

src/setup_original.js

@@ -0,0 +1,238 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint.js");
+
+const BN128 = require("./bn128.js");
+const PolField = require("./polfield.js");
+const ZqField = require("./zqfield.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+const PolF = new PolField(new ZqField(bn128.r));
+const F = new ZqField(bn128.r);
+
+module.exports = function setup(circuit) {
+    const setup = {
+        vk_proof : {
+            protocol: "original",
+            nVars: circuit.nVars,
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        vk_verifier: {
+            protocol: "original",
+            nPublic: circuit.nPubInputs + circuit.nOutputs
+        },
+        toxic: {}
+    };
+
+
+    setup.vk_proof.domainBits = PolF.log2(circuit.nConstraints + circuit.nPubInputs + circuit.nOutputs +1 -1) +1;
+    setup.vk_proof.domainSize = 1 << setup.vk_proof.domainBits;
+
+    calculatePolinomials(setup, circuit);
+    setup.toxic.t = F.random();
+    calculateEncriptedValuesAtT(setup, circuit);
+    calculateHexps(setup, circuit);
+
+    return setup;
+};
+
+
+function calculatePolinomials(setup, circuit) {
+
+    setup.vk_proof.polsA = new Array(circuit.nVars);
+    setup.vk_proof.polsB = new Array(circuit.nVars);
+    setup.vk_proof.polsC = new Array(circuit.nVars);
+    for (let i=0; i<circuit.nVars; i++) {
+        setup.vk_proof.polsA[i] = {};
+        setup.vk_proof.polsB[i] = {};
+        setup.vk_proof.polsC[i] = {};
+    }
+    for (let c=0; c<circuit.nConstraints; c++) {
+
+        for (let s in circuit.constraints[c][0]) {
+            setup.vk_proof.polsA[s][c] = bigInt(circuit.constraints[c][0][s]);
+        }
+        for (let s in circuit.constraints[c][1]) {
+            setup.vk_proof.polsB[s][c] = bigInt(circuit.constraints[c][1][s]);
+        }
+        for (let s in circuit.constraints[c][2]) {
+            setup.vk_proof.polsC[s][c] = bigInt(circuit.constraints[c][2][s]);
+        }
+    }
+
+    /**
+     * add and process the constraints
+     *     input_i * 0 = 0
+     * to ensure soundness of input consistency
+     */
+    for (let i = 0; i < circuit.nPubInputs + circuit.nOutputs + 1; ++i)
+    {
+        setup.vk_proof.polsA[i][circuit.nConstraints + i] = F.one;
+    }
+}
+
+function calculateValuesAtT(setup, circuit) {
+    const z_t = PolF.computeVanishingPolinomial(setup.vk_proof.domainBits, setup.toxic.t);
+    const u = PolF.evaluateLagrangePolynomials(setup.vk_proof.domainBits, setup.toxic.t);
+
+    const a_t = new Array(circuit.nVars).fill(F.zero);
+    const b_t = new Array(circuit.nVars).fill(F.zero);
+    const c_t = new Array(circuit.nVars).fill(F.zero);
+
+    // TODO: substitute setup.polsA for coeficients
+    for (let s=0; s<circuit.nVars; s++) {
+        for (let c in setup.vk_proof.polsA[s]) {
+            a_t[s] = F.add(a_t[s], F.mul(u[c], setup.vk_proof.polsA[s][c]));
+        }
+        for (let c in setup.vk_proof.polsB[s]) {
+            b_t[s] = F.add(b_t[s], F.mul(u[c], setup.vk_proof.polsB[s][c]));
+        }
+        for (let c in setup.vk_proof.polsC[s]) {
+            c_t[s] = F.add(c_t[s], F.mul(u[c], setup.vk_proof.polsC[s][c]));
+        }
+    }
+
+    return {a_t, b_t, c_t, z_t};
+
+}
+
+
+
+
+function calculateEncriptedValuesAtT(setup, circuit) {
+
+    const v = calculateValuesAtT(setup, circuit);
+    setup.vk_proof.A = new Array(circuit.nVars+1);
+    setup.vk_proof.B = new Array(circuit.nVars+1);
+    setup.vk_proof.C = new Array(circuit.nVars+1);
+    setup.vk_proof.Ap = new Array(circuit.nVars+1);
+    setup.vk_proof.Bp = new Array(circuit.nVars+1);
+    setup.vk_proof.Cp = new Array(circuit.nVars+1);
+    setup.vk_proof.Kp = new Array(circuit.nVars+3);
+    setup.vk_verifier.IC = new Array(circuit.nPublic);
+
+    setup.toxic.ka = F.random();
+    setup.toxic.kb = F.random();
+    setup.toxic.kc = F.random();
+    setup.toxic.ra = F.random();
+    setup.toxic.rb = F.random();
+    setup.toxic.rc = F.mul(setup.toxic.ra, setup.toxic.rb);
+    setup.toxic.kbeta = F.random();
+    setup.toxic.kgamma = F.random();
+
+    const gb = F.mul(setup.toxic.kbeta, setup.toxic.kgamma);
+
+    setup.vk_verifier.vk_a = G2.affine(G2.mulScalar( G2.g, setup.toxic.ka));
+    setup.vk_verifier.vk_b = G1.affine(G1.mulScalar( G1.g, setup.toxic.kb));
+    setup.vk_verifier.vk_c = G2.affine(G2.mulScalar( G2.g, setup.toxic.kc));
+    setup.vk_verifier.vk_gb_1 = G1.affine(G1.mulScalar( G1.g, gb));
+    setup.vk_verifier.vk_gb_2 = G2.affine(G2.mulScalar( G2.g, gb));
+    setup.vk_verifier.vk_g = G2.affine(G2.mulScalar( G2.g, setup.toxic.kgamma));
+
+    for (let s=0; s<circuit.nVars; s++) {
+
+        // A[i] = G1 * polA(t)
+        const raat = F.mul(setup.toxic.ra, v.a_t[s]);
+        const A = G1.affine(G1.mulScalar(G1.g, raat));
+
+        setup.vk_proof.A[s] = A;
+
+        if (s <= setup.vk_proof.nPublic) {
+            setup.vk_verifier.IC[s]=A;
+        }
+
+
+        // B1[i] = G1 * polB(t)
+        const rbbt = F.mul(setup.toxic.rb, v.b_t[s]);
+        const B1 = G1.affine(G1.mulScalar(G1.g, rbbt));
+
+        // B2[i] = G2 * polB(t)
+        const B2 = G2.affine(G2.mulScalar(G2.g, rbbt));
+
+        setup.vk_proof.B[s]=B2;
+
+        // C[i] = G1 * polC(t)
+        const rcct = F.mul(setup.toxic.rc, v.c_t[s]);
+        const C = G1.affine(G1.mulScalar( G1.g, rcct));
+        setup.vk_proof.C[s] =C;
+
+        // K = G1 * (A+B+C)
+
+        const kt = F.affine(F.add(F.add(raat, rbbt), rcct));
+        const K = G1.affine(G1.mulScalar( G1.g, kt));
+
+        /*
+        // Comment this lines to improve the process
+                const Ktest = G1.affine(G1.add(G1.add(A, B1), C));
+
+                if (!G1.equals(K, Ktest)) {
+                    console.log ("=====FAIL======");
+                }
+        */
+
+        if (s > setup.vk_proof.nPublic) {
+            setup.vk_proof.Ap[s] = G1.affine(G1.mulScalar(A, setup.toxic.ka));
+        }
+        setup.vk_proof.Bp[s] = G1.affine(G1.mulScalar(B1, setup.toxic.kb));
+        setup.vk_proof.Cp[s] = G1.affine(G1.mulScalar(C, setup.toxic.kc));
+        setup.vk_proof.Kp[s] = G1.affine(G1.mulScalar(K, setup.toxic.kbeta));
+    }
+
+    // Extra coeficients
+    const A = G1.mulScalar( G1.g, F.mul(setup.toxic.ra, v.z_t));
+    setup.vk_proof.A[circuit.nVars] = G1.affine(A);
+    setup.vk_proof.Ap[circuit.nVars] = G1.affine(G1.mulScalar(A, setup.toxic.ka));
+
+    const B1 = G1.mulScalar( G1.g, F.mul(setup.toxic.rb, v.z_t));
+    const B2 = G2.mulScalar( G2.g, F.mul(setup.toxic.rb, v.z_t));
+    setup.vk_proof.B[circuit.nVars] = G2.affine(B2);
+    setup.vk_proof.Bp[circuit.nVars] = G1.affine(G1.mulScalar(B1, setup.toxic.kb));
+
+    const C = G1.mulScalar( G1.g, F.mul(setup.toxic.rc, v.z_t));
+    setup.vk_proof.C[circuit.nVars] = G1.affine(C);
+    setup.vk_proof.Cp[circuit.nVars] = G1.affine(G1.mulScalar(C, setup.toxic.kc));
+
+    setup.vk_proof.Kp[circuit.nVars  ] = G1.affine(G1.mulScalar(A, setup.toxic.kbeta));
+    setup.vk_proof.Kp[circuit.nVars+1] = G1.affine(G1.mulScalar(B1, setup.toxic.kbeta));
+    setup.vk_proof.Kp[circuit.nVars+2] = G1.affine(G1.mulScalar(C, setup.toxic.kbeta));
+
+//    setup.vk_verifier.A[0] = G1.affine(G1.add(setup.vk_verifier.A[0], setup.vk_proof.A[circuit.nVars]));
+
+    // vk_z
+    setup.vk_verifier.vk_z = G2.affine(G2.mulScalar(
+        G2.g,
+        F.mul(setup.toxic.rc, v.z_t)));
+}
+
+function calculateHexps(setup) {
+
+    const maxH = setup.vk_proof.domainSize+1;
+
+    setup.vk_proof.hExps = new Array(maxH);
+    setup.vk_proof.hExps[0] = G1.g;
+    let eT = setup.toxic.t;
+    for (let i=1; i<maxH; i++) {
+        setup.vk_proof.hExps[i] = G1.affine(G1.mulScalar(G1.g, eT));
+        eT = F.mul(eT, setup.toxic.t);
+    }
+}
+

src/stringifybigint.js

@@ -0,0 +1,55 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint.js");
+
+module.exports.stringifyBigInts = stringifyBigInts;
+module.exports.unstringifyBigInts = unstringifyBigInts;
+
+function stringifyBigInts(o) {
+    if ((typeof(o) == "bigint") || o.isZero !== undefined)  {
+        return o.toString(10);
+    } else if (Array.isArray(o)) {
+        return o.map(stringifyBigInts);
+    } else if (typeof o == "object") {
+        const res = {};
+        for (let k in o) {
+            res[k] = stringifyBigInts(o[k]);
+        }
+        return res;
+    } else {
+        return o;
+    }
+}
+
+function unstringifyBigInts(o) {
+    if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) ))  {
+        return bigInt(o);
+    } else if (Array.isArray(o)) {
+        return o.map(unstringifyBigInts);
+    } else if (typeof o == "object") {
+        const res = {};
+        for (let k in o) {
+            res[k] = unstringifyBigInts(o[k]);
+        }
+        return res;
+    } else {
+        return o;
+    }
+}

src/verifier.js

@@ -0,0 +1,67 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const BN128 = require("./bn128.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function isValid(vk_verifier, proof, publicSignals) {
+
+    let full_pi_a = vk_verifier.A[0];
+    for (let s= 0; s< vk_verifier.nPublic; s++) {
+        full_pi_a  = G1.add( full_pi_a, G1.mulScalar( vk_verifier.A[s+1], publicSignals[s]));
+    }
+
+    full_pi_a  = G1.add( full_pi_a, proof.pi_a);
+
+    if (! bn128.F12.equals(
+        bn128.pairing( proof.pi_a , vk_verifier.vk_a ),
+        bn128.pairing( proof.pi_ap , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( vk_verifier.vk_b,  proof.pi_b ),
+        bn128.pairing( proof.pi_bp , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( proof.pi_c , vk_verifier.vk_c ),
+        bn128.pairing( proof.pi_cp , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.F12.mul(
+            bn128.pairing( G1.add(full_pi_a, proof.pi_c) , vk_verifier.vk_gb_2 ),
+            bn128.pairing( vk_verifier.vk_gb_1 , proof.pi_b ),
+        ),
+        bn128.pairing( proof.pi_kp , vk_verifier.vk_g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( full_pi_a , proof.pi_b  ),
+        bn128.F12.mul(
+            bn128.pairing( proof.pi_h , vk_verifier.vk_z ),
+            bn128.pairing( proof.pi_c , G2.g  ),
+        )))
+        return false;
+
+    return true;
+};

src/verifier_groth.js

@@ -0,0 +1,46 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+
+const BN128 = require("./bn128.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+
+module.exports = function isValid(vk_verifier, proof, publicSignals) {
+
+    let cpub = vk_verifier.IC[0];
+    for (let s= 0; s< vk_verifier.nPublic; s++) {
+        cpub  = G1.add( cpub, G1.mulScalar( vk_verifier.IC[s+1], publicSignals[s]));
+    }
+
+    if (! bn128.F12.equals(
+        bn128.pairing( proof.pi_a , proof.pi_b ),
+        bn128.F12.mul(
+            vk_verifier.vk_alfabeta_12,
+            bn128.F12.mul(
+                bn128.pairing( cpub , vk_verifier.vk_gamma_2 ),
+                bn128.pairing( proof.pi_c , vk_verifier.vk_delta_2 )
+            ))))
+        return false;
+
+    return true;
+};

src/verifier_kimleeoh.js

@@ -0,0 +1,75 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+/* Implementation of this paper: https://eprint.iacr.org/2016/260.pdf */
+
+
+const BN128 = require("./bn128.js");
+const createKeccakHash = require("keccak");
+const bigInt = require("./bigint");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function isValid(vk_verifier, proof, publicSignals) {
+
+    let cpub = vk_verifier.IC[0];
+    for (let s= 0; s< vk_verifier.nPublic; s++) {
+        cpub  = G1.add( cpub, G1.mulScalar( vk_verifier.IC[s+1], publicSignals[s]));
+    }
+
+    const buff = Buffer.concat([
+        proof.pi_a[0].beInt2Buff(32),
+        proof.pi_a[1].beInt2Buff(32),
+        proof.pi_b[0][0].beInt2Buff(32),
+        proof.pi_b[0][1].beInt2Buff(32),
+        proof.pi_b[1][0].beInt2Buff(32),
+        proof.pi_b[1][1].beInt2Buff(32)
+    ]);
+
+    const h1buff = createKeccakHash("keccak256").update(buff).digest();
+    const h2buff = createKeccakHash("keccak256").update(h1buff).digest();
+
+    const h1 = bigInt.beBuff2int(h1buff);
+    const h2 = bigInt.beBuff2int(h2buff);
+
+
+//    const h1 = bigInt.zero;
+//    const h2 = bigInt.zero;
+
+    console.log(h1.toString());
+    console.log(h2.toString());
+
+
+    if (! bn128.F12.equals(
+        bn128.pairing(
+            G1.add(proof.pi_a, G1.mulScalar(G1.g, h1)),
+            G2.add(proof.pi_b, G2.mulScalar(vk_verifier.vk_delta_2, h2))
+        ),
+        bn128.F12.mul(
+            vk_verifier.vk_alfabeta_12,
+            bn128.F12.mul(
+                bn128.pairing( cpub , vk_verifier.vk_gamma_2 ),
+                bn128.pairing( proof.pi_c , G2.g )
+            ))))
+        return false;
+
+    return true;
+};

src/verifier_original.js

@@ -0,0 +1,67 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const BN128 = require("./bn128.js");
+
+const bn128 = new BN128();
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+module.exports = function isValid(vk_verifier, proof, publicSignals) {
+
+    let full_pi_a = vk_verifier.IC[0];
+    for (let s= 0; s< vk_verifier.nPublic; s++) {
+        full_pi_a  = G1.add( full_pi_a, G1.mulScalar( vk_verifier.IC[s+1], publicSignals[s]));
+    }
+
+    full_pi_a  = G1.add( full_pi_a, proof.pi_a);
+
+    if (! bn128.F12.equals(
+        bn128.pairing( proof.pi_a , vk_verifier.vk_a ),
+        bn128.pairing( proof.pi_ap , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( vk_verifier.vk_b,  proof.pi_b ),
+        bn128.pairing( proof.pi_bp , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( proof.pi_c , vk_verifier.vk_c ),
+        bn128.pairing( proof.pi_cp , G2.g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.F12.mul(
+            bn128.pairing( G1.add(full_pi_a, proof.pi_c) , vk_verifier.vk_gb_2 ),
+            bn128.pairing( vk_verifier.vk_gb_1 , proof.pi_b )
+        ),
+        bn128.pairing( proof.pi_kp , vk_verifier.vk_g )))
+        return false;
+
+    if (! bn128.F12.equals(
+        bn128.pairing( full_pi_a , proof.pi_b  ),
+        bn128.F12.mul(
+            bn128.pairing( proof.pi_h , vk_verifier.vk_z ),
+            bn128.pairing( proof.pi_c , G2.g  )
+        )))
+        return false;
+
+    return true;
+};

src/zqfield.js

@@ -0,0 +1,151 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of snarkjs.
+
+    snarkjs is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    snarkjs is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    snarkjs. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const bigInt = require("./bigint");
+const fUtils = require("./futils.js");
+
+function getRandomByte() {
+    if (typeof window !== "undefined") { // Browser
+        if (typeof window.crypto !== "undefined") { // Supported
+            let array = new Uint8Array(1);
+            window.crypto.getRandomValues(array);
+            return array[0];
+        }
+        else { // fallback
+            return Math.floor(Math.random() * 256);
+        }
+    }
+    else { // NodeJS
+        return module.require("crypto").randomBytes(1)[0];
+    }
+}
+
+class ZqField {
+    constructor(q) {
+        this.q = bigInt(q);
+        this.zero = bigInt.zero;
+        this.one = bigInt.one;
+        this.minusone = this.q.sub(this.one);
+        this.add = bigInt.genAdd();
+        this.double = bigInt.genDouble();
+        this.sub = bigInt.genSub();
+        this.neg = bigInt.genNeg();
+        this.mul = bigInt.genMul(q);
+        this.inverse = bigInt.genInverse(q);
+        this.square = bigInt.genSquare(q);
+        this.equals = bigInt.genEquals(q);
+        this.affine = bigInt.genAffine(q);
+        this.isZero = bigInt.genIsZero(q);
+        this.two = this.add(this.one, this.one);
+        this.twoinv = this.inverse(this.two);
+
+        const e = this.minusone.shr(this.one);
+        this.nqr = this.two;
+        let r = this.exp(this.nqr, e);
+        while (!r.equals(this.minusone)) {
+            this.nqr = this.nqr.add(this.one);
+            r = this.exp(this.nqr, e);
+        }
+
+        this.s = this.zero;
+        this.t = this.minusone;
+
+        while (!this.t.isOdd()) {
+            this.s = this.s.add(this.one);
+            this.t = this.t.shr(this.one);
+        }
+
+        this.nqr_to_t = this.exp(this.nqr, this.t);
+    }
+
+    copy(a) {
+        return bigInt(a);
+    }
+
+    div(a, b) {
+        return this.mul(a, this.inverse(b));
+    }
+
+    mulScalar(base, e) {
+        return this.mul(base, bigInt(e));
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
+    toString(a) {
+        const ca = this.affine(a);
+        return `"0x${ca.toString(16)}"`;
+    }
+
+    random() {
+        let res = bigInt(0);
+        let n = bigInt(this.q);
+        while (!n.isZero()) {
+            res = res.shl(8).add(bigInt(getRandomByte()));
+            n = n.shr(8);
+        }
+        return res;
+    }
+
+    sqrt(n) {
+
+        n = this.affine(n);
+
+        if (n.equals(this.zero)) return this.zero;
+
+        // Test that have solution
+        const res = this.exp(n, this.minusone.shr(this.one));
+        if (!res.equals(this.one)) return null;
+
+        let m = parseInt(this.s);
+        let c = this.nqr_to_t;
+        let t = this.exp(n, this.t);
+        let r = this.exp(n, this.add(this.t, this.one).shr(this.one) );
+
+        while (!t.equals(this.one)) {
+            let sq = this.square(t);
+            let i = 1;
+            while (!sq.equals(this.one)) {
+                i++;
+                sq = this.square(sq);
+            }
+
+            // b = c ^ m-i-1
+            let b = c;
+            for (let j=0; j< m-i-1; j ++) b = this.square(b);
+
+            m = i;
+            c = this.square(b);
+            t = this.mul(t, c);
+            r = this.mul(r, b);
+        }
+
+        if (r.greater(this.q.shr(this.one))) {
+            r = this.neg(r);
+        }
+
+        return r;
+    }
+
+}
+
+
+module.exports = ZqField;

templates/verifier_groth.sol

@@ -0,0 +1,228 @@
+//
+// 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.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+//
+// 2019 OKIMS
+//      ported to solidity 0.5
+//      fixed linter warnings
+//      added requiere error messages
+//
+pragma solidity ^0.5.0;
+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 pure returns (G1Point memory) {
+        return G1Point(1, 2);
+    }
+    /// @return the generator of G2
+    function P2() internal pure returns (G2Point memory) {
+        // Original code point
+        return G2Point(
+            [11559732032986387107991004021392285783925812861821192530917403151452391805634,
+             10857046999023057135944570762232829481370756359578518086990519993285655852781],
+            [4082367875863433681332203403145435568316851327593401208105741076214120093531,
+             8495653923123431417604973247489272438418190587263600148770280649306958101930]
+        );
+
+/*
+        // Changed by Jordi point
+        return G2Point(
+            [10857046999023057135944570762232829481370756359578518086990519993285655852781,
+             11559732032986387107991004021392285783925812861821192530917403151452391805634],
+            [8495653923123431417604973247489272438418190587263600148770280649306958101930,
+             4082367875863433681332203403145435568316851327593401208105741076214120093531]
+        );
+*/
+    }
+    /// @return the negation of p, i.e. p.addition(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
+        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 addition(G1Point memory p1, G1Point memory p2) internal view 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;
+        // 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() }
+        }
+        require(success,"pairing-add-failed");
+    }
+    /// @return the product of a point on G1 and a scalar, i.e.
+    /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p.
+    function scalar_mul(G1Point memory p, uint s) internal view returns (G1Point memory r) {
+        uint[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() }
+        }
+        require (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 p1, G2Point[] memory p2) internal view returns (bool) {
+        require(p1.length == p2.length,"pairing-lengths-failed");
+        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;
+        // 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() }
+        }
+        require(success,"pairing-opcode-failed");
+        return out[0] != 0;
+    }
+    /// Convenience method for a pairing check for two pairs.
+    function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2) internal view 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 memory a1, G2Point memory a2,
+            G1Point memory b1, G2Point memory b2,
+            G1Point memory c1, G2Point memory c2
+    ) internal view 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 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[] 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 Verifier {
+    using Pairing for *;
+    struct VerifyingKey {
+        Pairing.G1Point alfa1;
+        Pairing.G2Point beta2;
+        Pairing.G2Point gamma2;
+        Pairing.G2Point delta2;
+        Pairing.G1Point[] IC;
+    }
+    struct Proof {
+        Pairing.G1Point A;
+        Pairing.G2Point B;
+        Pairing.G1Point C;
+    }
+    function verifyingKey() internal pure returns (VerifyingKey memory vk) {
+        vk.alfa1 = Pairing.G1Point(<%vk_alfa1%>);
+        vk.beta2 = Pairing.G2Point(<%vk_beta2%>);
+        vk.gamma2 = Pairing.G2Point(<%vk_gamma2%>);
+        vk.delta2 = Pairing.G2Point(<%vk_delta2%>);
+        vk.IC = new Pairing.G1Point[](<%vk_ic_length%>);
+        <%vk_ic_pts%>
+    }
+    function verify(uint[] memory input, Proof memory proof) internal view returns (uint) {
+        uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
+        VerifyingKey memory vk = verifyingKey();
+        require(input.length + 1 == vk.IC.length,"verifier-bad-input");
+        // Compute the linear combination vk_x
+        Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0);
+        for (uint i = 0; i < input.length; i++) {
+            require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field");
+            vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i]));
+        }
+        vk_x = Pairing.addition(vk_x, vk.IC[0]);
+        if (!Pairing.pairingProd4(
+            Pairing.negate(proof.A), proof.B,
+            vk.alfa1, vk.beta2,
+            vk_x, vk.gamma2,
+            proof.C, vk.delta2
+        )) return 1;
+        return 0;
+    }
+    function verifyProof(
+            uint[2] memory a,
+            uint[2][2] memory b,
+            uint[2] memory c,
+            uint[<%vk_input_length%>] memory input
+        ) public view returns (bool r) {
+        Proof memory proof;
+        proof.A = Pairing.G1Point(a[0], a[1]);
+        proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]);
+        proof.C = Pairing.G1Point(c[0], c[1]);
+        uint[] memory inputValues = new uint[](input.length);
+        for(uint i = 0; i < input.length; i++){
+            inputValues[i] = input[i];
+        }
+        if (verify(inputValues, proof) == 0) {
+            return true;
+        } else {
+            return false;
+        }
+    }
+    function verifyProof(bytes calldata proof, uint[<%vk_input_length%>] calldata inputs) external view returns (bool r) {
+        // solidity does not support decoding uint[2][2] yet
+        (uint[2] memory a, uint[2] memory b1, uint[2] memory b2, uint[2] memory c) = abi.decode(proof, (uint[2], uint[2], uint[2], uint[2]));
+        return verifyProof(a, [b1, b2], c, inputs);
+    }
+}

templates/verifier_kimleeoh.sol

@@ -0,0 +1,219 @@
+//
+// 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.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+pragma solidity ^0.4.17;
+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() pure internal returns (G1Point) {
+        return G1Point(1, 2);
+    }
+    /// @return the generator of G2
+    function P2() pure internal returns (G2Point) {
+        // Original code point
+        return G2Point(
+            [11559732032986387107991004021392285783925812861821192530917403151452391805634,
+             10857046999023057135944570762232829481370756359578518086990519993285655852781],
+            [4082367875863433681332203403145435568316851327593401208105741076214120093531,
+             8495653923123431417604973247489272438418190587263600148770280649306958101930]
+        );
+
+/*
+        // Changed by Jordi point
+        return G2Point(
+            [10857046999023057135944570762232829481370756359578518086990519993285655852781,
+             11559732032986387107991004021392285783925812861821192530917403151452391805634],
+            [8495653923123431417604973247489272438418190587263600148770280649306958101930,
+             4082367875863433681332203403145435568316851327593401208105741076214120093531]
+        );
+*/
+    }
+    /// @return the negation of p, i.e. p.addition(p.negate()) should be zero.
+    function negate(G1Point p) pure 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 addition(G1Point p1, G1Point p2) view 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 := staticcall(sub(gas, 2000), 6, 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.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p.
+    function scalar_mul(G1Point p, uint s) view internal returns (G1Point r) {
+        uint[3] memory input;
+        input[0] = p.X;
+        input[1] = p.Y;
+        input[2] = s;
+        bool success;
+        assembly {
+            success := staticcall(sub(gas, 2000), 7, 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) view 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 := 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() }
+        }
+        require(success);
+        return out[0] != 0;
+    }
+    /// Convenience method for a pairing check for two pairs.
+    function pairingProd2(G1Point a1, G2Point a2, G1Point b1, G2Point b2) view 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
+    ) view 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
+    ) view 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 Verifier {
+    using Pairing for *;
+    struct VerifyingKey {
+        Pairing.G1Point alfa1;
+        Pairing.G2Point beta2;
+        Pairing.G2Point gamma2;
+        Pairing.G2Point delta2;
+        Pairing.G1Point[] IC;
+    }
+    struct Proof {
+        Pairing.G1Point A;
+        Pairing.G2Point B;
+        Pairing.G1Point C;
+    }
+    function verifyingKey() pure internal returns (VerifyingKey vk) {
+        vk.alfa1 = Pairing.G1Point(<%vk_alfa1%>);
+        vk.beta2 = Pairing.G2Point(<%vk_beta2%>);
+        vk.gamma2 = Pairing.G2Point(<%vk_gamma2%>);
+        vk.delta2 = Pairing.G2Point(<%vk_delta2%>);
+        vk.IC = new Pairing.G1Point[](<%vk_ic_length%>);
+        <%vk_ic_pts%>
+    }
+    function verify(uint[] input, Proof proof) view internal returns (uint) {
+        uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
+        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++) {
+            require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field");
+            vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i]));
+        }
+        vk_x = Pairing.addition(vk_x, vk.IC[0]);
+        if (!Pairing.pairingProd4(
+            Pairing.negate(proof.A), proof.B,
+            vk.alfa1, vk.beta2,
+            vk_x, vk.gamma2,
+            proof.C, vk.delta2
+        )) return 1;
+        return 0;
+    }
+    function verifyProof(
+            uint[2] a,
+            uint[2][2] b,
+            uint[2] c,
+            uint[<%vk_input_length%>] input
+        ) view public returns (bool r) {
+        Proof memory proof;
+        proof.A = Pairing.G1Point(a[0], a[1]);
+        proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]);
+        proof.C = Pairing.G1Point(c[0], c[1]);
+        uint[] memory inputValues = new uint[](input.length);
+        for(uint i = 0; i < input.length; i++){
+            inputValues[i] = input[i];
+        }
+        if (verify(inputValues, proof) == 0) {
+            return true;
+        } else {
+            return false;
+        }
+    }
+    function verifyProof(bytes calldata proof, uint[<%vk_input_length%>] calldata inputs) external view returns (bool r) {
+        // solidity does not support decoding uint[2][2] yet
+        (uint[2] memory a, uint[2] memory b1, uint[2] memory b2, uint[2] memory c) = abi.decode(proof, (uint[2], uint[2], uint[2], uint[2]));
+        return verifyProof(a, [b1, b2], c, inputs);
+    }
+}

templates/verifier_original.sol

@@ -0,0 +1,260 @@
+//
+// 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.
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+//
+// 2019 OKIMS
+//      ported to solidity 0.5
+//      fixed linter warnings
+//      added requiere error messages
+//
+pragma solidity ^0.5.0;
+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 pure returns (G1Point memory) {
+        return G1Point(1, 2);
+    }
+    /// @return the generator of G2
+    function P2() internal pure returns (G2Point memory) {
+        // Original code point
+        return G2Point(
+            [11559732032986387107991004021392285783925812861821192530917403151452391805634,
+             10857046999023057135944570762232829481370756359578518086990519993285655852781],
+            [4082367875863433681332203403145435568316851327593401208105741076214120093531,
+             8495653923123431417604973247489272438418190587263600148770280649306958101930]
+        );
+    }
+    /// @return the negation of p, i.e. p.addition(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
+        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 addition(G1Point memory p1, G1Point memory p2)  internal view 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;
+        // 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() }
+        }
+        require(success,"pairing-add-failed");
+    }
+    /// @return the product of a point on G1 and a scalar, i.e.
+    /// p == p.scalar_mul(1) and p.addition(p) == p.scalar_mul(2) for all points p.
+    function scalar_mul(G1Point memory p, uint s) internal view returns (G1Point memory r) {
+        uint[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() }
+        }
+        require (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 p1, G2Point[] memory p2) internal view returns (bool) {
+        require(p1.length == p2.length,"pairing-lengths-failed");
+        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;
+        // 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() }
+        }
+        require(success,"pairing-opcode-failed");
+        return out[0] != 0;
+    }
+    /// Convenience method for a pairing check for two pairs.
+    function pairingProd2(G1Point memory a1, G2Point memory a2, G1Point memory b1, G2Point memory b2) internal view 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 memory a1, G2Point memory a2,
+            G1Point memory b1, G2Point memory b2,
+            G1Point memory c1, G2Point memory c2
+    ) internal view 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 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[] 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 Verifier {
+    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 verifyingKey() internal pure returns (VerifyingKey memory vk) {
+        vk.A = Pairing.G2Point(<%vk_a%>);
+        vk.B = Pairing.G1Point(<%vk_b%>);
+        vk.C = Pairing.G2Point(<%vk_c%>);
+        vk.gamma = Pairing.G2Point(<%vk_g%>);
+        vk.gammaBeta1 = Pairing.G1Point(<%vk_gb1%>);
+        vk.gammaBeta2 = Pairing.G2Point(<%vk_gb2%>);
+        vk.Z = Pairing.G2Point(<%vk_z%>);
+        vk.IC = new Pairing.G1Point[](<%vk_ic_length%>);
+        <%vk_ic_pts%>
+    }
+    function verify(uint[] memory input, Proof memory proof) internal view returns (uint) {
+        uint256 snark_scalar_field = 21888242871839275222246405745257275088548364400416034343698204186575808495617;
+        VerifyingKey memory vk = verifyingKey();
+        require(input.length + 1 == vk.IC.length,"verifier-bad-input");
+        // Compute the linear combination vk_x
+        Pairing.G1Point memory vk_x = Pairing.G1Point(0, 0);
+        for (uint i = 0; i < input.length; i++) {
+            require(input[i] < snark_scalar_field,"verifier-gte-snark-scalar-field");
+            vk_x = Pairing.addition(vk_x, Pairing.scalar_mul(vk.IC[i + 1], input[i]));
+        }
+        vk_x = Pairing.addition(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.addition(vk_x, Pairing.addition(proof.A, proof.C))), vk.gammaBeta2,
+            Pairing.negate(vk.gammaBeta1), proof.B
+        )) return 4;
+        if (!Pairing.pairingProd3(
+                Pairing.addition(vk_x, proof.A), proof.B,
+                Pairing.negate(proof.H), vk.Z,
+                Pairing.negate(proof.C), Pairing.P2()
+        )) return 5;
+        return 0;
+    }
+    function verifyProof(
+            uint[2] memory a,
+            uint[2] memory a_p,
+            uint[2][2] memory b,
+            uint[2] memory b_p,
+            uint[2] memory c,
+            uint[2] memory c_p,
+            uint[2] memory h,
+            uint[2] memory k,
+            uint[<%vk_input_length%>] memory input
+        ) view public returns (bool r) {
+        Proof memory proof;
+        proof.A = Pairing.G1Point(a[0], a[1]);
+        proof.A_p = Pairing.G1Point(a_p[0], a_p[1]);
+        proof.B = Pairing.G2Point([b[0][0], b[0][1]], [b[1][0], b[1][1]]);
+        proof.B_p = Pairing.G1Point(b_p[0], b_p[1]);
+        proof.C = Pairing.G1Point(c[0], c[1]);
+        proof.C_p = Pairing.G1Point(c_p[0], c_p[1]);
+        proof.H = Pairing.G1Point(h[0], h[1]);
+        proof.K = Pairing.G1Point(k[0], k[1]);
+        uint[] memory inputValues = new uint[](input.length);
+        for(uint i = 0; i < input.length; i++){
+            inputValues[i] = input[i];
+        }
+        if (verify(inputValues, proof) == 0) {
+            return true;
+        } else {
+            return false;
+        }
+    }
+    function verifyProof(bytes calldata proof, uint[<%vk_input_length%>] calldata inputs) external view returns (bool r) {
+        // solidity does not support decoding uint[2][2] yet
+        (
+            uint[2] memory a,
+            uint[2] memory a_p,
+            uint[2] memory b1,
+            uint[2] memory b2,
+            uint[2] memory b_p,
+            uint[2] memory c,
+            uint[2] memory c_p,
+            uint[2] memory h,
+            uint[2] memory k
+        ) = abi.decode(proof, (uint[2], uint[2], uint[2], uint[2], uint[2], uint[2], uint[2], uint[2], uint[2]));
+        return verifyProof(a, a_p, [b1, b2], b_p, c, c_p, h, k, inputs);
+    }
+}
+
+
+
+

test/algebra.js

@@ -0,0 +1,254 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+
+const bigInt = require("../src/bigint.js");
+const BN128 = require("../src/bn128.js");
+const F1Field = require("../src/zqfield.js");
+
+const assert = chai.assert;
+
+
+describe("F1 testing", () => {
+    it("Should compute euclidean", () => {
+        const F = new F1Field(bigInt(7));
+        const res = F.inverse(bigInt(4));
+
+        assert(F.equals(res, bigInt(2)));
+    });
+
+    it("Should multiply and divide in F1", () => {
+        const bn128 = new BN128();
+        const a = bigInt("1");
+        const b = bn128.F1.affine(bigInt("-3"));
+        const c = bn128.F1.mul(a,b);
+        const d = bn128.F1.div(c,b);
+
+        assert(bn128.F1.equals(a, d));
+    });
+
+    it("Should compute sqrts", () => {
+        const bn128 = new BN128();
+        const F = new F1Field(bn128.r);
+        const a = bigInt("4");
+        let b = F.sqrt(a);
+        assert(F.equals(bigInt(0), F.sqrt(bigInt("0"))));
+        assert(F.equals(b, bigInt("2")));
+        assert(F.sqrt(F.nqr) === null);
+    });
+
+    it("Should compute sqrt of 100 random numbers", () => {
+        const bn128 = new BN128();
+        const F = new F1Field(bn128.r);
+        for (let j=0;j<100; j++) {
+            let a = F.random();
+            let s = F.sqrt(a);
+            if (s != null) {
+                assert(F.equals(F.square(s), a));
+            }
+        }
+    });
+});
+
+describe("Curve G1 Test", () => {
+    it("r*one == 0", () => {
+        const bn128 = new BN128();
+
+        const res = bn128.G1.mulScalar(bn128.G1.g, bn128.r);
+
+        assert(bn128.G1.equals(res, bn128.G1.zero), "G1 does not have range r");
+    });
+
+    it("Should add match in various in G1", () => {
+
+        const bn128 = new BN128();
+
+        const r1 = bigInt(33);
+        const r2 = bigInt(44);
+
+        const gr1 = bn128.G1.mulScalar(bn128.G1.g, r1);
+        const gr2 = bn128.G1.mulScalar(bn128.G1.g, r2);
+
+        const grsum1 = bn128.G1.add(gr1, gr2);
+
+        const grsum2 = bn128.G1.mulScalar(bn128.G1.g, r1.add(r2));
+
+        assert(bn128.G1.equals(grsum1, grsum2));
+    });
+});
+
+describe("Curve G2 Test", () => {
+    it ("r*one == 0", () => {
+        const bn128 = new BN128();
+
+        const res = bn128.G2.mulScalar(bn128.G2.g, bn128.r);
+
+        assert(bn128.G2.equals(res, bn128.G2.zero), "G2 does not have range r");
+    });
+
+    it("Should add match in various in G2", () => {
+        const bn128 = new BN128();
+
+        const r1 = bigInt(33);
+        const r2 = bigInt(44);
+
+        const gr1 = bn128.G2.mulScalar(bn128.G2.g, r1);
+        const gr2 = bn128.G2.mulScalar(bn128.G2.g, r2);
+
+        const grsum1 = bn128.G2.add(gr1, gr2);
+
+        const grsum2 = bn128.G2.mulScalar(bn128.G2.g, r1.add(r2));
+
+        /*
+        console.log(G2.toString(grsum1));
+        console.log(G2.toString(grsum2));
+        */
+
+        assert(bn128.G2.equals(grsum1, grsum2));
+    });
+});
+
+describe("F6 testing", () => {
+    it("Should multiply and divide in F6", () => {
+        const bn128 = new BN128();
+        const a =
+            [
+                [bigInt("1"), bigInt("2")],
+                [bigInt("3"), bigInt("4")],
+                [bigInt("5"), bigInt("6")]
+            ];
+        const b =
+            [
+                [bigInt("12"), bigInt("11")],
+                [bigInt("10"), bigInt("9")],
+                [bigInt("8"), bigInt("7")]
+            ];
+        const c = bn128.F6.mul(a,b);
+        const d = bn128.F6.div(c,b);
+
+        assert(bn128.F6.equals(a, d));
+    });
+});
+
+describe("F12 testing", () => {
+    it("Should multiply and divide in F12", () => {
+        const bn128 = new BN128();
+        const a =
+        [
+            [
+                [bigInt("1"), bigInt("2")],
+                [bigInt("3"), bigInt("4")],
+                [bigInt("5"), bigInt("6")]
+            ],
+            [
+                [bigInt("7"), bigInt("8")],
+                [bigInt("9"), bigInt("10")],
+                [bigInt("11"), bigInt("12")]
+            ]
+        ];
+        const b =
+        [
+            [
+                [bigInt("12"), bigInt("11")],
+                [bigInt("10"), bigInt("9")],
+                [bigInt("8"), bigInt("7")]
+            ],
+            [
+                [bigInt("6"), bigInt("5")],
+                [bigInt("4"), bigInt("3")],
+                [bigInt("2"), bigInt("1")]
+            ]
+        ];
+        const c = bn128.F12.mul(a,b);
+        const d = bn128.F12.div(c,b);
+
+        assert(bn128.F12.equals(a, d));
+    });
+});
+
+describe("Pairing", () => {
+/*
+    it("Should match pairing", () => {
+        for (let i=0; i<1; i++) {
+            const bn128 = new BN128();
+
+            const g1a = bn128.G1.mulScalar(bn128.G1.g, 25);
+            const g2a = bn128.G2.mulScalar(bn128.G2.g, 30);
+
+            const g1b = bn128.G1.mulScalar(bn128.G1.g, 30);
+            const g2b = bn128.G2.mulScalar(bn128.G2.g, 25);
+
+            const pre1a = bn128.precomputeG1(g1a);
+            const pre2a = bn128.precomputeG2(g2a);
+            const pre1b = bn128.precomputeG1(g1b);
+            const pre2b = bn128.precomputeG2(g2b);
+
+            const r1 = bn128.millerLoop(pre1a, pre2a);
+            const r2 = bn128.millerLoop(pre1b, pre2b);
+
+            const rbe = bn128.F12.mul(r1, bn128.F12.inverse(r2));
+
+            const res = bn128.finalExponentiation(rbe);
+
+            assert(bn128.F12.equals(res, bn128.F12.one));
+        }
+    }).timeout(10000);
+*/
+    it("Should generate another pairing pairing", () => {
+        for (let i=0; i<1; i++) {
+            const bn128 = new BN128();
+
+            const g1a = bn128.G1.mulScalar(bn128.G1.g, 10);
+            const g2a = bn128.G2.mulScalar(bn128.G2.g, 1);
+
+            const g1b = bn128.G1.mulScalar(bn128.G1.g, 1);
+            const g2b = bn128.G2.mulScalar(bn128.G2.g, 10);
+
+            const pre1a = bn128.precomputeG1(g1a);
+            const pre2a = bn128.precomputeG2(g2a);
+            const pre1b = bn128.precomputeG1(g1b);
+            const pre2b = bn128.precomputeG2(g2b);
+
+            const r1 = bn128.millerLoop(pre1a, pre2a);
+            const r2 = bn128.finalExponentiation(r1);
+
+            const r3 = bn128.millerLoop(pre1b, pre2b);
+
+            const r4 = bn128.finalExponentiation(r3);
+
+
+            console.log("ML1: " ,r1[0][0][0].affine(bn128.q).toString(16));
+            console.log("FE1: " ,r2[0][0][0].affine(bn128.q).toString(16));
+            console.log("ML2: " ,r3[0][0][0].affine(bn128.q).toString(16));
+            console.log("FE2: " ,r4[0][0][0].affine(bn128.q).toString(16));
+
+            assert(bn128.F12.equals(r2, r4));
+
+
+/*            const r2 = bn128.millerLoop(pre1b, pre2b);
+
+            const rbe = bn128.F12.mul(r1, bn128.F12.inverse(r2));
+
+            const res = bn128.finalExponentiation(rbe);
+
+            assert(bn128.F12.equals(res, bn128.F12.one)); */
+        }
+    }).timeout(10000);
+});

test/calculatewitness.js

@@ -0,0 +1,40 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or 
+    modify it under the terms of the GNU General Public License as published by the 
+    Free Software Foundation, either version 3 of the License, or (at your option) 
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for 
+    more details.
+
+    You should have received a copy of the GNU General Public License along with 
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+const fs = require("fs");
+const path = require("path");
+
+const Circuit = require("../src/circuit.js");
+const BN128 = require("../src/bn128.js");
+const F1Field = require("../src/zqfield.js");
+
+const assert = chai.assert;
+
+
+describe("Calculate witness", () => {
+    it("Should calculate the witness of a sum circuit", () => {
+
+        const cirDef = JSON.parse(fs.readFileSync(path.join(__dirname, "circuit", "sum.json"), "utf8"));
+        const cir = new Circuit(cirDef);
+        const witness = cir.calculateWitness({"a": "33", "b": "34"});
+
+        assert.equal(witness[cir.getSignalIdx("main.out")].toString(), "67");
+    });
+});

test/pols.js

@@ -0,0 +1,217 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+
+const bigInt = require("../src/bigint.js");
+const PolField = require("../src/polfield.js");
+const ZqField = require("../src/zqfield");
+
+const assert = chai.assert;
+
+const r  = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+
+describe("Polynomial field", () => {
+    it("Should compute a multiplication", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(1), bigInt(2), bigInt(3)];
+        const b = [bigInt(1), bigInt(2), bigInt(3)];
+        const res = PF.mul(a,b);
+
+        assert(PF.equals(res, [bigInt(1), bigInt(4), bigInt(10), bigInt(12), bigInt(9)]));
+    });
+    it("Should compute a multiplication 2", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(5), bigInt(1)];
+        const b = [bigInt(-5), bigInt(1)];
+        const res = PF.mul(a,b);
+
+        assert(PF.equals(res, [bigInt(-25), bigInt(0), bigInt(1)]));
+    });
+    it("Should compute an addition", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(5), bigInt(1)];
+        const b = [bigInt(-5), bigInt(1)];
+        const res = PF.add(a,b);
+
+        assert(PF.equals(res, [bigInt(0), bigInt(2)]));
+    });
+    it("Should compute a substraction", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(5), bigInt(3), bigInt(4)];
+        const b = [bigInt(5), bigInt(1)];
+        const res = PF.sub(a,b);
+
+        assert(PF.equals(res, [bigInt(0), bigInt(2), bigInt(4)]));
+    });
+    it("Should compute reciprocal", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(4), bigInt(1), bigInt(-3), bigInt(-1), bigInt(2),bigInt(1), bigInt(-1), bigInt(1)];
+        const res = PF._reciprocal(a, 3, 0);
+
+        assert(PF.equals(res, [bigInt(12), bigInt(15), bigInt(3), bigInt(-4), bigInt(-3), bigInt(0), bigInt(1), bigInt(1)]));
+    });
+    it("Should div2", () => {
+        const PF = new PolField(new ZqField(r));
+
+        // x^6
+        const a = [bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(0),bigInt(0), bigInt(1)];
+        // x^5
+        const b = [bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(0), bigInt(1)];
+
+        const res = PF._div2(6, b);
+        assert(PF.equals(res, [bigInt(0), bigInt(1)]));
+
+        const res2 = PF.div(a,b);
+        assert(PF.equals(res2, [bigInt(0), bigInt(1)]));
+    });
+    it("Should div", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
+        const b = [bigInt(8), bigInt(9), bigInt(10), bigInt(11), bigInt(12), bigInt(13)];
+
+        const c = PF.mul(a,b);
+        const d = PF.div(c,b);
+
+        assert(PF.equals(a, d));
+    });
+    it("Should div big/small", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
+        const b = [bigInt(8), bigInt(9)];
+
+        const c = PF.mul(a,b);
+        const d = PF.div(c,b);
+
+        assert(PF.equals(a, d));
+    });
+    it("Should div random big", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const a = [];
+        const b = [];
+        for (let i=0; i<1000; i++) a.push(bigInt(Math.floor(Math.random()*100000) -500000));
+        for (let i=0; i<900; i++) b.push(bigInt(Math.floor(Math.random()*100000) -500000));
+
+        const c = PF.mul(a,b);
+
+        const d = PF.div(c,b);
+
+        assert(PF.equals(a, d));
+    }).timeout(10000);
+    it("Should evaluate and zero", () => {
+        const PF = new PolField(new ZqField(r));
+        const p = [PF.F.neg(bigInt(2)), bigInt(1)];
+        const v = PF.eval(p, bigInt(2));
+        assert(PF.F.equals(v, bigInt(0)));
+    });
+    it("Should evaluate bigger number", () => {
+        const PF = new PolField(new ZqField(r));
+        const p = [bigInt(1), bigInt(2), bigInt(3)];
+        const v = PF.eval(p, bigInt(2));
+        assert(PF.F.equals(v, bigInt(17)));
+    });
+    it("Should create lagrange polynomial minmal", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const points=[];
+        points.push([bigInt(1), bigInt(1)]);
+        points.push([bigInt(2), bigInt(2)]);
+        points.push([bigInt(3), bigInt(5)]);
+
+        const p=PF.lagrange(points);
+
+        for (let i=0; i<points.length; i++) {
+            const v = PF.eval(p, points[i][0]);
+            assert(PF.F.equals(v, points[i][1]));
+        }
+    });
+    it("Should create lagrange polynomial", () => {
+        const PF = new PolField(new ZqField(r));
+
+        const points=[];
+        points.push([bigInt(1), bigInt(2)]);
+        points.push([bigInt(2), bigInt(-2)]);
+        points.push([bigInt(3), bigInt(0)]);
+        points.push([bigInt(4), bigInt(453345)]);
+
+        const p=PF.lagrange(points);
+
+        for (let i=0; i<points.length; i++) {
+            const v = PF.eval(p, points[i][0]);
+            assert(PF.F.equals(v, points[i][1]));
+        }
+    });
+    it("Should test ruffini", () => {
+        const PF = new PolField(new ZqField(r));
+        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
+
+        const b = PF.mul(a, [bigInt(-7), bigInt(1)]);
+        const c = PF.ruffini(b, bigInt(7));
+
+        assert(PF.equals(a, c));
+    });
+    it("Should test roots", () => {
+        const PF = new PolField(new ZqField(r));
+        let rt;
+
+
+        rt = PF.oneRoot(256, 16);
+        for (let i=0; i<8; i++) {
+            rt = PF.F.mul(rt, rt);
+        }
+        assert(rt.equals(PF.F.one));
+
+        rt = PF.oneRoot(256, 15);
+        for (let i=0; i<8; i++) {
+            rt = PF.F.mul(rt, rt);
+        }
+        assert(rt.equals(PF.F.one));
+
+        rt = PF.oneRoot(8, 3);
+        for (let i=0; i<3; i++) {
+            rt = PF.F.mul(rt, rt);
+        }
+        assert(rt.equals(PF.F.one));
+
+        rt = PF.oneRoot(8, 0);
+        assert(rt.equals(PF.F.one));
+
+    });
+    it("Should create a polynomial with values at roots with fft", () => {
+        const PF = new PolField(new ZqField(r));
+        const a = [bigInt(1), bigInt(2), bigInt(3), bigInt(4), bigInt(5),bigInt(6), bigInt(7)];
+
+        const p = PF.ifft(a);
+
+        for (let i=0; i<a.length; i++) {
+            const s = PF.F.affine(PF.eval(p, PF.oneRoot(8,i)));
+            assert(s.equals(a[i]));
+        }
+
+    });
+
+});

test/ratzqfield.js

@@ -0,0 +1,89 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or 
+    modify it under the terms of the GNU General Public License as published by the 
+    Free Software Foundation, either version 3 of the License, or (at your option) 
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for 
+    more details.
+
+    You should have received a copy of the GNU General Public License along with 
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+
+const bigInt = require("../src/bigint.js");
+const ZqField = require("../src/zqfield.js");
+const RatField = require("../src/ratfield.js");
+
+const q  = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+const Z = new ZqField(q);
+const R = new RatField(Z);
+
+const assert = chai.assert;
+
+function r(a,b) {
+    return [bigInt(a), bigInt(b)];
+}
+
+
+describe("Rational zq Field", () => {
+    it("Should compare correctly", () => {
+        assert( R.equals(r(3,5), r(6,10)));
+        assert(!R.equals(r(3,5), r(6,11)));
+    });
+    it("Should add correctly", () => {
+        const a = r(7,4);
+        const b = r(5,12);
+
+        assert(R.equals( R.add(a,b), r(13, 6)));
+    });
+    it("Should substract", () => {
+        const a = r(7,4);
+        const b = r(5,12);
+
+        assert(R.equals( R.sub(a,b), r(4, 3)));
+    });
+    it("Should multiply", () => {
+        const a = r(7,4);
+        const b = r(5,12);
+
+        assert(R.equals( R.mul(a,b), r(35, 48)));
+    });
+    it("Should div", () => {
+        const a = r(7,4);
+        const b = r(5,12);
+
+        assert(R.equals( R.div(a,b), r(7*12, 5*4)));
+    });
+    it("Should square", () => {
+        const a = r(7,4);
+
+        assert(R.equals( R.square(a), r(49, 16)));
+    });
+    it("Should affine", () => {
+        const a = r(12,4);
+        const aa = R.affine(a);
+        assert(Z.equals( aa[0], bigInt(3)));
+        assert(Z.equals( aa[1], Z.one));
+    });
+    it("Should convert from Z to R", () => {
+        const vz = bigInt(34);
+        const vr = R.fromF(vz);
+
+        assert(R.equals( vr, r(34,1)));
+    });
+    it("Should convert from R to Z", () => {
+        const vr = r(32, 2);
+        const vz = R.toF(vr);
+
+        assert(Z.equals( vz, bigInt(16)));
+    });
+});

test/zksnark.js

@@ -0,0 +1,196 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+const fs = require("fs");
+const path = require("path");
+const bigInt = require("../src/bigint.js");
+
+const Circuit = require("../src/circuit.js");
+const zkSnark = require("../index.js").original;
+const BN128 = require("../src/bn128.js");
+const PolField = require("../src/polfield.js");
+const ZqField = require("../src/zqfield.js");
+
+const {stringifyBigInts, unstringifyBigInts} = require("../src/stringifybigint.js");
+
+const bn128 = new BN128();
+const PolF = new PolField(new ZqField(bn128.r));
+const G1 = bn128.G1;
+const G2 = bn128.G2;
+
+const assert = chai.assert;
+
+
+describe("zkSnark original", () => {
+    it("Load a circuit, create trusted setup, create a proof and validate it", () => {
+
+
+        const cirDef = JSON.parse(fs.readFileSync(path.join(__dirname, "circuit", "sum.json"), "utf8"));
+        const cir = new Circuit(cirDef);
+
+        const setup = zkSnark.setup(cir);
+        const strSetup = stringifyBigInts(setup);
+        fs.writeFileSync("vk_proof.json", JSON.stringify(strSetup.vk_proof), "utf-8");
+        fs.writeFileSync("vk_verifier.json", JSON.stringify(strSetup.vk_verifier), "utf-8");
+
+
+        function polT2S(p) {
+            const p_T = new Array(setup.vk_proof.domainSize).fill(bigInt(0));
+
+            for (let c in p) {
+                p_T[c] = p[c];
+            }
+
+            return PolF.ifft(p_T);
+        }
+
+/*
+        const setup = {};
+        setup.vk_proof = unstringifyBigInts(JSON.parse(fs.readFileSync("vk_proof.json", "utf8")));
+        setup.vk_verifier = unstringifyBigInts(JSON.parse(fs.readFileSync("vk_verifier.json", "utf8")));
+*/
+        const witness = cir.calculateWitness({"a": "33", "b": "34"});
+
+        const {proof, publicSignals} = zkSnark.genProof(setup.vk_proof, witness);
+
+/*
+        const polA = new Array(cir.nVars);
+        const polB = new Array(cir.nVars);
+        const polC = new Array(cir.nVars);
+        for (let i=0; i<cir.nVars; i++) {
+            polA[i] = polT2S(setup.vk_proof.polsA[i]);
+            polB[i] = polT2S(setup.vk_proof.polsB[i]);
+            polC[i] = polT2S(setup.vk_proof.polsC[i]);
+        }
+
+        PolF._setRoots(setup.vk_proof.domainBits);
+        for (let c=0; c<setup.vk_proof.domainSize; c++) {
+            let A = bigInt(0);
+            let B = bigInt(0);
+            let C = bigInt(0);
+            for (let s=0; s<cir.nVars; s++) {
+                A = PolF.F.add(A, PolF.F.mul(PolF.eval(polA[s], PolF.roots[setup.vk_proof.domainBits][c]), witness[s]));
+                B = PolF.F.add(B, PolF.F.mul(PolF.eval(polB[s], PolF.roots[setup.vk_proof.domainBits][c]), witness[s]));
+                C = PolF.F.add(C, PolF.F.mul(PolF.eval(polC[s], PolF.roots[setup.vk_proof.domainBits][c]), witness[s]));
+            }
+            assert(PolF.F.equals(PolF.F.mul(A,B), C));
+        }
+
+        let A = bigInt(0);
+        let B = bigInt(0);
+        let C = bigInt(0);
+        for (let s=0; s<cir.nVars; s++) {
+            A = PolF.F.add(A, PolF.F.mul(PolF.eval(polA[s], setup.toxic.t), witness[s]));
+            B = PolF.F.add(B, PolF.F.mul(PolF.eval(polB[s], setup.toxic.t), witness[s]));
+            C = PolF.F.add(C, PolF.F.mul(PolF.eval(polC[s], setup.toxic.t), witness[s]));
+        }
+
+        let A2 = bigInt(0);
+        let B2 = bigInt(0);
+        let C2 = bigInt(0);
+        const u = PolF.evaluateLagrangePolynomials(setup.vk_proof.domainBits, setup.toxic.t);
+        for (let s=0; s<cir.nVars; s++) {
+            let at = PolF.F.zero;
+            for (let c in setup.vk_proof.polsA[s]) {
+                at = PolF.F.add(at, PolF.F.mul(u[c], setup.vk_proof.polsA[s][c]));
+            }
+            A2 = PolF.F.add(A2, PolF.F.mul(at, witness[s]));
+
+            let bt = PolF.F.zero;
+            for (let c in setup.vk_proof.polsB[s]) {
+                bt = PolF.F.add(bt, PolF.F.mul(u[c], setup.vk_proof.polsB[s][c]));
+            }
+            B2 = PolF.F.add(B2, PolF.F.mul(bt, witness[s]));
+
+            let ct = PolF.F.zero;
+            for (let c in setup.vk_proof.polsC[s]) {
+                ct = PolF.F.add(ct, PolF.F.mul(u[c], setup.vk_proof.polsC[s][c]));
+            }
+            C2 = PolF.F.add(C2, PolF.F.mul(ct, witness[s]));
+        }
+
+        A=PolF.F.affine(A);
+        B=PolF.F.affine(B);
+        C=PolF.F.affine(C);
+        A2=PolF.F.affine(A2);
+        B2=PolF.F.affine(B2);
+        C2=PolF.F.affine(C2);
+
+        assert(PolF.F.equals(C,C2));
+        assert(PolF.F.equals(B,B2));
+        assert(PolF.F.equals(A,A2));
+        const ABC = PolF.F.affine(PolF.F.sub(PolF.F.mul(A,B), C));
+
+
+
+        assert.equal(witness[cir.getSignalIdx("main.out")].toString(), "67");
+
+        const H = PolF.eval(proof.h, setup.toxic.t).affine();
+
+        const Z = PolF.F.sub(PolF.F.exp(setup.toxic.t, setup.vk_proof.domainSize), bigInt(1));
+
+        const HZ = PolF.F.affine(PolF.F.mul(H,Z));
+        assert(PolF.F.equals(ABC, HZ));
+
+
+        const gH = G1.affine(G1.mulScalar( G1.g, H));
+        const gZ = G2.affine(G2.mulScalar( G2.g, Z));
+        const gA = G1.affine(G1.mulScalar( G1.g, A));
+        const gB = G2.affine(G2.mulScalar( G2.g, B));
+        const gC = G1.affine(G1.mulScalar( G1.g, C));
+
+        assert(G1.equals(gH, proof.pi_h));
+        assert(G2.equals(gZ, setup.vk_verifier.vk_z));
+        assert(G2.equals(gB, proof.pi_b));
+        assert(G1.equals(gC, proof.pi_c));
+//        assert(G1.equals(gA, proof.pi_a));
+*/
+        assert( zkSnark.isValid(setup.vk_verifier, proof, publicSignals));
+    }).timeout(10000000);
+/*
+    it("validate sha256_2", () => {
+
+        const cirDef = JSON.parse(fs.readFileSync(path.join(__dirname, "circuit", "sha256_2.json"), "utf8"));
+        const cir = new Circuit(cirDef);
+
+        console.log("Start setup: "+Date().toString());
+        const setup = zkSnark.setup(cir);
+        const strSetup = stringifyBigInts(setup);
+        fs.writeFileSync("sha256_2_vk_proof.json", JSON.stringify(strSetup.vk_proof), "utf-8");
+        fs.writeFileSync("sha256_2_vk_verifier.json", JSON.stringify(strSetup.vk_verifier), "utf-8");
+
+
+//        const setup = {};
+//        setup.vk_proof = unstringifyBigInts(JSON.parse(fs.readFileSync("vk_proof.json", "utf8")));
+//        setup.vk_verifier = unstringifyBigInts(JSON.parse(fs.readFileSync("vk_verifier.json", "utf8")));
+
+        const witness = cir.calculateWitness({"a": "1", "b": "2"});
+
+//        assert.equal(witness[cir.getSignalIdx("main.out")].toString(), "67");
+
+        console.log("Start calculating the proof: "+Date().toString());
+        const {proof, publicSignals} = zkSnark.genProof(setup.vk_proof, witness);
+
+        console.log("Start verifiying: "+ Date().toString());
+        assert( zkSnark.isValid(setup.vk_verifier, proof, publicSignals));
+    }).timeout(10000000);
+*/
+
+});

test/zksnark_groth.js

@@ -0,0 +1,44 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+const fs = require("fs");
+const path = require("path");
+
+const Circuit = require("../src/circuit.js");
+const zkSnark = require("../index.js").groth;
+
+const assert = chai.assert;
+
+describe("zkSnark Groth", () => {
+    it("Load a circuit, create trusted setup, create a proof and validate it", () => {
+
+
+        const cirDef = JSON.parse(fs.readFileSync(path.join(__dirname, "circuit", "sum.json"), "utf8"));
+        const cir = new Circuit(cirDef);
+
+        const setup = zkSnark.setup(cir);
+
+        const witness = cir.calculateWitness({"a": "33", "b": "34"});
+
+        const {proof, publicSignals} = zkSnark.genProof(setup.vk_proof, witness);
+
+        assert( zkSnark.isValid(setup.vk_verifier, proof, publicSignals));
+    }).timeout(10000000);
+});

test/zksnark_kimleeoh.js

@@ -0,0 +1,44 @@
+/*
+    Copyright 2018 0kims association.
+
+    This file is part of zksnark JavaScript library.
+
+    zksnark JavaScript library is a free software: you can redistribute it and/or
+    modify it under the terms of the GNU General Public License as published by the
+    Free Software Foundation, either version 3 of the License, or (at your option)
+    any later version.
+
+    zksnark JavaScript library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
+    more details.
+
+    You should have received a copy of the GNU General Public License along with
+    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
+*/
+
+const chai = require("chai");
+const fs = require("fs");
+const path = require("path");
+
+const Circuit = require("../src/circuit.js");
+const zkSnark = require("../index.js").kimleeoh;
+
+const assert = chai.assert;
+
+describe("zkSnark KimLeeOh", () => {
+    it("Load a circuit, create trusted setup, create a proof and validate it", () => {
+
+
+        const cirDef = JSON.parse(fs.readFileSync(path.join(__dirname, "circuit", "sum.json"), "utf8"));
+        const cir = new Circuit(cirDef);
+
+        const setup = zkSnark.setup(cir);
+
+        const witness = cir.calculateWitness({"a": "33", "b": "34"});
+
+        const {proof, publicSignals} = zkSnark.genProof(setup.vk_proof, witness);
+
+        assert( zkSnark.isValid(setup.vk_verifier, proof, publicSignals));
+    }).timeout(10000000);
+});