snarks part done

README

@@ -0,0 +1,107 @@
+# javascript implementation of zkSnark
+
+This is a javascript implementation of zkSnarks.
+
+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.
+
+## Install
+
+```
+npm install zkSnark
+```
+
+## Usage
+
+### import
+
+```
+const zkSnark = require("zksnark");
+```
+
+### Load a circuit.
+
+```
+// "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.
+
+```
+    // `signalId` can always be a number or an alias string
+
+    circuit.m; // number of constrains
+    circuit.n; // number of signals
+    circuit.p; // number of public signals (nPublicInputs + nOutputs)
+
+    // The array of signals is always sorted in this order:
+    // [ outputs, publicInputs, privedInputs, internalSignals, constants]
+
+    // returns a,b and c coeficients of the `signalId` on a given `constrain`
+    circuit.a(constrain, signalId)
+    circuit.b(constrain, signalId)
+    circuit.c(constrain, signalId)
+
+    circuit.nOutputs           // number of public outputs
+    circuit.nPublicInputs      // number of public inputs
+    circuit.nPrivateInputs     // number of private inputs
+    circuit.nInputs            // number of inputs ( nPublicInputs + nPrivateInputs)
+
+    circuit.outputIdx(i)       // returns the index of the i'th output
+    circuit.inputIdx(i)        // returns the index of the i'th input
+    circuit.inputPublicIdx(i)  // returns the index of the i'th public input
+    circuit.inputPrivateIdx(i) // returns the index of the i'th private input
+
+    // returns signal Idx given a signalId
+    // if the idx >= n , it is a constant
+    // if the idx == -1, the signal does not exist
+    circuit.signalId2idx(signalId);
+
+    // returns an array aliases names for a given signalId
+    circuit.signalNames(signalId)
+
+    // input is a key value object where keys are the signal names
+    //   of all the inputs (public and private)
+    // returns an array of values that represent the witness
+    circuit.generateWitness(input)
+```
+
+### Trusted setup
+
+```
+const setup = zkSnark.setup(circuit);
+fs.writeFileSink("myCircuit.vk_proof", JSON.stringify(setup.vk_proof), "utf8");
+fs.writeFileSink("myCircuit.vk_verifier", JSON.stringify(setup.vk_verifier), "utf8");
+setup.toxic  // Must be discarded.
+```
+
+### Generate proof
+
+```
+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.generateWitness(input);
+const vk_proof = JSON.parse(fs.readFileSync("myCircuit.vk_proof", "utf8"));
+
+const {proof, publicSignals} = zkSnark.genProof(vk_proof, witness);
+```
+
+### Verifier
+
+```
+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");
+}
+```

README.md

@@ -34,9 +34,9 @@ const circuit = new zkSnark.Circuit(circuitDef);
 ```
     // `signalId` can always be a number or an alias string
 
-    circuit.m; // number of constrains
-    circuit.n; // number of signals
-    circuit.p; // number of public signals (nPublicInputs + nOutputs)
+    circuit.nConstrains; // number of constrains
+    circuit.nSignals; // number of signals
+    circuit.nPublic; // number of public signals (nOutputs + nPublicInputs)
 
     // The array of signals is always sorted in this order:
     // [ outputs, publicInputs, privedInputs, internalSignals, constants]

src/gt.js

@@ -0,0 +1,20 @@
+const bigInt = require("big-integer");
+const ZnField = require("./znfield.js");
+
+module.eports = class Gt {
+
+    constructor() {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+
+    mul(p1, p2) {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+
+    equal(p1, p2) {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+};

src/pairing.js

@@ -5,6 +5,8 @@ This module calculate the pairing of p1 and p2 where p1 in G1 and p2 in G2
 const bigInt = require("big-integer");
 
 module.exports = function pairing(p1, p2) {
+
+
     // TODO
     throw new Error("Not Implementted");
 };

src/polfield.js

@@ -37,6 +37,10 @@ class PolField {
         throw new Error("Not Implementted");
     }
 
+    eval(p, x) {
+        throw new Error("Not Implementted");
+    }
+
     lagrange(points) {
         throw new Error("Not Implementted");
     }

src/prover.js

@@ -1,5 +1,86 @@
+const bigInt = require("big-integer");
+
+const ZnField = require("./znfield.js");
+const G1Curve = require("./g1curve");
+const G2Curve = require("./g2curve");
+const PolField = require("./polfield.js");
+
+const F = new ZnField(bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617"));
+const G1 = new G1Curve();
+const G2 = new G2Curve();
+const PolF = new PolField(F);
 
 
 module.exports = function genProof(vk_proof, witness) {
 
-}
+    const proof = {};
+
+    proof.pi_a = G1.zero();
+    proof.pi_ap = G1.zero();
+    proof.pi_b = G2.zero();
+    proof.pi_bp = G2.zero();
+    proof.pi_c = G1.zero();
+    proof.pi_cp = G1.zero();
+    proof.pi_kp = G1.zero();
+    proof.pi_h = G1.zero();
+
+
+    for (let s= vk_proof.nPublic; s< vk_proof.nSignals; s++) {
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_a  = G1.add( proof.pi_a, G1.mulEscalar( vk_proof.A[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_ap = G1.add( proof.pi_ap, G1.mulEscalar( vk_proof.Ap[s], witness[s]));
+    }
+
+    for (let s= 0; s< vk_proof.nSignals; s++) {
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_b  = G2.add( proof.pi_b, G1.mulEscalar( vk_proof.B[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_bp = G1.add( proof.pi_bp, G1.mulEscalar( vk_proof.Bp[s], witness[s]));
+
+        // pi_a  = pi_a  + A[s]  * witness[s];
+        proof.pi_c  = G1.add( proof.pi_c, G1.mulEscalar( vk_proof.C[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_cp = G1.add( proof.pi_cp, G1.mulEscalar( vk_proof.Cp[s], witness[s]));
+
+        // pi_ap = pi_ap + Ap[s] * witness[s];
+        proof.pi_kp = G1.add( proof.pi_kp, G1.mulEscalar( vk_proof.Kp[s], witness[s]));
+    }
+
+    let polA = [];
+    let polB = [];
+    let polC = [];
+
+    for (let s= 0; s< vk_proof.nSignals; 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 );
+
+    for (let i = 0; i < h.length; i++) {
+        proof.pi_h = G1.add( proof.pi_h, G1.mulEscalar( vk_proof.hExps[i], h[i]));
+    }
+
+};

src/setup.js

@@ -1,5 +1,160 @@
+const bigInt = require("big-integer");
 
+const ZnField = require("./znfield.js");
+const PolField = require("./polfield.js");
+const G1Curve = require("./g1curve");
+const G2Curve = require("./g2curve");
+
+const F = new ZnField(bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617"));
+const PolF = new PolField(F);
+const G1 = new G1Curve();
+const G2 = new G2Curve();
 
 module.exports = function setup(circuit) {
+    const setup = {
+        vk_proof : {
+            nSignals: circuit.nSignals,
+            nPublic: circuit.nPublic
+        },
+        vk_verifier: {
+            nPublic: circuit.nPublic
+        },
+        toxic: {}
+    };
 
+    calculatePolinomials(setup, circuit);
+    setup.toxic.t = F.random();
+    calculateEncriptedValuesAtT(setup, circuit);
+    calculateHexps(setup, circuit);
+};
+
+function calculatePolinomials(setup, circuit) {
+    // Calculate the points that must cross each polinomial
+    const aPoints = [];
+    const bPoints = [];
+    const cPoints = [];
+    for (let s = 0; circuit.nSignals; s++) {
+        aPoints[s] = [];
+        bPoints[s] = [];
+        cPoints[s] = [];
+        for (let c=0; c<circuit.nConstrains; c++) {
+            aPoints[s].push([bigInt(c), circuit.a(c, s)]);
+            bPoints[s].push([bigInt(c), circuit.b(c, s)]);
+            cPoints[s].push([bigInt(c), circuit.c(c, s)]);
+        }
+    }
+
+    // Calculate the polinomials using Lagrange
+    setup.vk_proof.polsA = [];
+    setup.vk_proof.polsB = [];
+    setup.vk_proof.polsC = [];
+    for (let s=0; s<circuit.nSignals; s++) {
+        setup.vk_proof.polsA.push(PolF.lagrange( aPoints[s] ));
+        setup.vk_proof.polsB.push(PolF.lagrange( bPoints[s] ));
+        setup.vk_proof.polsC.push(PolF.lagrange( cPoints[s] ));
+    }
+
+    // Calculate Z polinomial
+    // Z = 1
+    setup.vk_proof.polZ = [bigInt(1)];
+    for (let c=0; c<circuit.nConstrains; c++) {
+        // Z = Z * (x - p_c)
+        setup.vk_proof.polZ = PolF.mul(
+            setup.vk_proof.polZ,
+            [F.neg(bigInt(c)), bigInt(1)] );
+    }
 }
+
+function calculateEncriptedValuesAtT(setup, circuit) {
+    setup.vk_proof.A = [];
+    setup.vk_proof.B = [];
+    setup.vk_proof.C = [];
+    setup.vk_proof.Ap = [];
+    setup.vk_proof.Bp = [];
+    setup.vk_proof.Cp = [];
+    setup.vk_proof.Kp = [];
+    setup.vk_verifier.A = [];
+
+    setup.toxic.ka = F.random();
+    setup.toxic.kb = F.random();
+    setup.toxic.kc = F.random();
+    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.mulEscalar( G2.g, setup.toxic.ka);
+    setup.vk_verifier.vk_b = G1.mulEscalar( G1.g, setup.toxic.kb);
+    setup.vk_verifier.vk_c = G2.mulEscalar( G2.g, setup.toxic.kc);
+    setup.vk_verifier.vk_gb_1 = G1.mulEscalar( G1.g, gb);
+    setup.vk_verifier.vk_gb_2 = G2.mulEscalar( G2.g, gb);
+    setup.vk_verifier.vk_g = G2.mulEscalar( G2.g, setup.toxic.kgamma);
+
+    for (let s=0; s<circuit.nSignals; s++) {
+
+        // A[i] = G1 * polA(t)
+        const A = G1.mulEscalar(
+            G1.g,
+            PolF.eval(setup.vk_proof.polsA[s], setup.vk_proof.t));
+        setup.vk_proof.A.push(A);
+
+        if (s < circuit.nPublicSignals) {
+            setup.vk_verifier.A.pusj(A);
+        }
+
+        // B1[i] = G1 * polB(t)
+        const B1 = G1.mulEscalar(
+            G1.g,
+            PolF.eval(setup.vk_proof.polsB[s], setup.vk_proof.t));
+
+        // B2[i] = G2 * polB(t)
+        const B2 = G2.mulEscalar(
+            G2.g,
+            PolF.eval(setup.vk_proof.polsB[s], setup.vk_proof.t));
+        setup.vk_proof.B.push(B2);
+
+        // C[i] = G1 * polC(t)
+        const C = G1.mulEscalar(
+            G1.g,
+            PolF.eval(setup.vk_proof.polsC[s], setup.vk_proof.t));
+        setup.vk_proof.C.push (C);
+
+        // K = G1 * (A+B+C)
+        const K = G1.mulEscalar(
+            G1.g,
+            G1.add(G1.add(A, B1), C));
+
+        setup.vk_proof.Ap.push(G1.mulEscalar(A, setup.toxic.ka));
+        setup.vk_proof.Bp.push(G1.mulEscalar(B1, setup.toxic.kb));
+        setup.vk_proof.Cp.push(G1.mulEscalar(C, setup.toxic.kc));
+        setup.vk_proof.Kp.push(G1.mulEscalar(K, setup.toxic.beta));
+    }
+
+    setup.vk_verifier.vk_z = G2.mulEscalar(
+        G2.g,
+        PolF.eval(setup.vk_proof.polZ, setup.vk_proof.t));
+}
+
+function calculateHexps(setup, circuit) {
+    let maxA = 0;
+    let maxB = 0;
+    let maxC = 0;
+    for (let s=0; s<circuit.nSignals; s++) {
+        maxA = Math.max(maxA, setup.vk_proof.polsA[s]);
+        maxB = Math.max(maxB, setup.vk_proof.polsB[s]);
+        maxC = Math.max(maxC, setup.vk_proof.polsC[s]);
+    }
+
+    let maxFull = Math.max(maxA * maxB - 1, maxC);
+
+    const maxH = maxFull - setup.vk_proof.polZ.length + 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.mulEscalar(G1.g, eT);
+        eT = F.mul(eT, setup.toxic.t);
+    }
+}
+

src/verifier.js

@@ -1,4 +1,52 @@
+const G1Curve = require("./g1curve");
+const G2Curve = require("./g2curve");
+const GT = require("./gt");
+
+const G1 = new G1Curve();
+const G2 = new G2Curve();
+const Gt = new GT();
+
+const pairing = require("./pairing");
 
 module.exports = function isValid(vk_verifier, proof, publicSignals) {
 
-}
+    let  full_pi_a = proof.pi_a;
+    for (let s= 0; s< vk_verifier.nPublic; s++) {
+
+        full_pi_a  = G1.add( full_pi_a, G1.mulEscalar( vk_verifier.A[s], publicSignals[s]));
+    }
+
+    if (! Gt.equal(
+        pairing( proof.pi_a , vk_verifier.vk_a ),
+        pairing( proof.pi_ap , G2.g )))
+        return false;
+
+    if (! Gt.equal(
+        pairing( vk_verifier.vk_b,  proof.pi_b ),
+        pairing( proof.pi_ap , G2.g )))
+        return false;
+
+    if (! Gt.equal(
+        pairing( proof.pi_c , vk_verifier.vk_c ),
+        pairing( proof.pi_cp , G2.g )))
+        return false;
+
+    if (! Gt.equal(
+        pairing( full_pi_a , proof.pi_b  ),
+        Gt.mul(
+            pairing( proof.pi_h , vk_verifier.vk_z ),
+            pairing( proof.pi_b , G2.g  ),
+        ),
+        pairing( proof.pi_kp , vk_verifier.vk_g )))
+        return false;
+
+    if (! Gt.equal(
+        Gt.mul(
+            pairing( G1.add(full_pi_a, proof.pi_c) , vk_verifier.vk_gb_2 ),
+            pairing( vk_verifier.vk_gb_1 , proof.pi_b ),
+        ),
+        pairing( proof.pi_kp , vk_verifier.vk_g )))
+        return false;
+
+    return true;
+};

src/znfield.js

@@ -19,6 +19,11 @@ class ZnField {
         throw new Error("Not Implementted");
     }
 
+    neg(a) {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+
     mul(a, b) {
         // TODO
         throw new Error("Not Implementted");
@@ -34,6 +39,16 @@ class ZnField {
         throw new Error("Not Implementted");
     }
 
+    isZero(a) {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+
+    random() {
+        // TODO
+        throw new Error("Not Implementted");
+    }
+
 }
 
 module.exports = ZnField;