Use ruffini for calculatig lagrange polinomials

file%3a/Users/jbaylina/git/personal/zksnark/src/polfield.js

@@ -1,260 +0,0 @@
-/*
-    This library do operations on polinomials where their coefficients are in field F
-
-    The polynomial P(x) = p0 + p1 * x + p2 * x^2 + p3 * x^3, ...
-    is represented by the array [ p0, p1, p2, p3, ...  ]
- */
-
-const bigInt = require("./bigInt");
-const ZqField = require("./zqfield");
-
-class PolFieldZq {
-    constructor (q) {
-        this.F = new ZqField(q);
-
-        let rem = q.sub(bigInt(1));
-        let s = 0;
-        while (!rem.isOdd()) {
-            s ++;
-            rem = rem.shiftRight(1);
-        }
-
-        this.w = new Array(s+1);
-        this.wi = new Array(s+1);
-        this.w[s] = this.F.exp(bigInt(5), 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--;
-        }
-
-    }
-
-    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(a, b) {
-        if (this.F.isZero(b)) return [];
-        const res = new Array(a.length);
-        for (let i=0; i<a.length; i++) {
-            res[i] = this.F.mul(a[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]);
-
-        const longestN = Math.max(a.length, b.length);
-        const bitsResult = log2(longestN-1)+2;
-        const m = 1 << bitsResult;
-        const ea = this.extend(a,m);
-        const eb = this.extend(b,m);
-
-        const ta = this._fft(ea, bitsResult, 0, 1, false);
-        const tb = this._fft(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 = this._fft(tres, bitsResult, 0, 1, true);
-
-        const twoinvm = this.F.inverse(bigInt(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 {
-            return p.slice(-n);
-        }
-    }
-
-    div(a, b) {
-        throw new Error("Not Implementted");
-    }
-
-    eval(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;
-    }
-
-    lagrange(points) {
-        throw new Error("Not Implementted");
-    }
-
-    _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= bigInt(1);
-        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;
-    }
-
-    _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 +(2k-2-scaleV) -(2k-2-scaleV)) /v =>
-        // res = rec * x^(m - (2k-2-scaleV)) =>
-        // res = rec * x^(m - 2k +2 + scaleV)
-
-        const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
-        const res = this.scaleX(rec, m - k*2 +2+scaleV);
-
-        return res;
-
-    }
-
-}
-
-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 ) );
-}
-
-module.exports = PolFieldZq;

src/bigint.js

@@ -17,8 +17,8 @@ if (typeof(BigInt) != "undefined") {
                 if (aux <= nq) {
                     aux = aux % q;
                 }
-                if (aux.isNegative()) {
-                    aux = aux.add(q);
+                if (aux < wBigInt.zero) {
+                    aux = aux + q;
                 }
             } else {
                 if (aux >= q) {

src/polfield.js

@@ -5,14 +5,14 @@
     is represented by the array [ p0, p1, p2, p3, ...  ]
  */
 
-const bigInt = require("./bigInt");
+const bigInt = require("./bigint.js");
 
-class PolFieldZq {
+class PolField {
     constructor (F) {
         this.F = F;
 
         const q = this.F.q;
-        let rem = q.sub(this.F.one);
+        let rem = q.sub(bigInt(1));
         let s = 0;
         while (!rem.isOdd()) {
             s ++;
@@ -79,7 +79,7 @@ class PolFieldZq {
             [b, a] = [a, b];
         }
 
-        if (b.length < log2(a.length)) {
+        if ((b.length <= 2) || (b.length < log2(a.length))) {
             return this.mulNormal(a,b);
         } else {
             return this.mulFFT(a,b);
@@ -151,14 +151,14 @@ class PolFieldZq {
     }
 
     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.F.one];
-            for (let j=0;j<points.length;j++) {
-                if (i!=j) {
-                    mpol = this.mul(mpol, [this.F.neg(points[j][0]), this.F.one]);
-                }
-            }
+            let mpol = this.ruffini(roots, points[i][0]);
             const factor =
                 this.F.mul(
                     this.F.inverse(this.eval(mpol, points[i][0])),
@@ -226,6 +226,15 @@ class PolFieldZq {
         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;
@@ -333,4 +342,4 @@ 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 ) );
 }
 
-module.exports = PolFieldZq;
+module.exports = PolField;

src/ratzqfield.js → src/ratfield.js

@@ -1,6 +1,6 @@
 const fUtils = require("./futils.js");
 
-class RatZqField {
+class RatField {
     constructor(F) {
         this.F = F;
         this.zero = [F.zero, F.one];
@@ -105,4 +105,4 @@ class RatZqField {
 }
 
 
-module.exports = RatZqField;
+module.exports = RatField;

src/setup.js

@@ -3,11 +3,13 @@ const bigInt = require("./bigint.js");
 const BN128 = require("./BN128.js");
 const PolField = require("./polfield.js");
 const ZqField = require("./zqfield.js");
+const RatField = require("./ratfield.js");
 
 const bn128 = new BN128();
 const G1 = bn128.G1;
 const G2 = bn128.G2;
 const PolF = new PolField(new ZqField(bn128.r));
+const RatPolF = new PolField(new RatField(new ZqField(bn128.r)));
 const F = new ZqField(bn128.r);
 
 module.exports = function setup(circuit) {
@@ -40,9 +42,9 @@ function calculatePolinomials(setup, circuit) {
         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)]);
+            aPoints[s].push([[bigInt(c), F.one], [circuit.a(c, s), F.one]]);
+            bPoints[s].push([[bigInt(c), F.one], [circuit.b(c, s), F.one]]);
+            cPoints[s].push([[bigInt(c), F.one], [circuit.c(c, s), F.one]]);
         }
     }
 
@@ -51,10 +53,15 @@ function calculatePolinomials(setup, circuit) {
     setup.vk_proof.polsB = [];
     setup.vk_proof.polsC = [];
     for (let s=0; s<circuit.nSignals; s++) {
-        console.log(`Caclcualte Pol ${s}/${circuit.nSignals}`);
-        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] ));
+//        console.log(`Caclcualte Pol ${s}/${circuit.nSignals}`);
+        const pA = RatPolF.lagrange( aPoints[s] );
+        const pB = RatPolF.lagrange( bPoints[s] );
+        const pC = RatPolF.lagrange( cPoints[s] );
+
+        setup.vk_proof.polsA.push( unrat(pA) );
+        setup.vk_proof.polsB.push( unrat(pB) );
+        setup.vk_proof.polsC.push( unrat(pC) );
+
     }
 
     // Calculate Z polinomial
@@ -96,7 +103,7 @@ function calculateEncriptedValuesAtT(setup, circuit) {
     for (let s=0; s<circuit.nSignals; s++) {
 
         // A[i] = G1 * polA(t)
-        const at = PolF.eval(setup.vk_proof.polsA[s], setup.toxic.t);
+        const at = F.affine(PolF.eval(setup.vk_proof.polsA[s], setup.toxic.t));
         const A = G1.affine(G1.mulScalar(G1.g, at));
 
         setup.vk_proof.A.push(A);
@@ -107,7 +114,7 @@ function calculateEncriptedValuesAtT(setup, circuit) {
 
 
         // B1[i] = G1 * polB(t)
-        const bt = PolF.eval(setup.vk_proof.polsB[s], setup.toxic.t);
+        const bt = F.affine(PolF.eval(setup.vk_proof.polsB[s], setup.toxic.t));
         const B1 = G1.affine(G1.mulScalar(G1.g, bt));
 
         // B2[i] = G2 * polB(t)
@@ -116,13 +123,13 @@ function calculateEncriptedValuesAtT(setup, circuit) {
         setup.vk_proof.B.push(B2);
 
         // C[i] = G1 * polC(t)
-        const ct = PolF.eval(setup.vk_proof.polsC[s], setup.toxic.t);
+        const ct = F.affine(PolF.eval(setup.vk_proof.polsC[s], setup.toxic.t));
         const C = G1.affine(G1.mulScalar( G1.g, ct));
         setup.vk_proof.C.push (C);
 
         // K = G1 * (A+B+C)
 
-        const kt = F.add(F.add(at, bt), ct);
+        const kt = F.affine(F.add(F.add(at, bt), ct));
         const K = G1.affine(G1.mulScalar( G1.g, kt));
 
 
@@ -169,3 +176,11 @@ function calculateHexps(setup, circuit) {
     }
 }
 
+function unrat(p) {
+    const res = new Array(p.length);
+    for (let i=0; i<p.length; i++) {
+        res[i] = RatPolF.F.toF(p[i]);
+    }
+    return res;
+}
+

test/pols.js

@@ -141,5 +141,14 @@ describe("Polinomial field", () => {
             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));
+    });
 
 });

test/ratzqfield.js

@@ -2,11 +2,11 @@ const chai = require("chai");
 
 const bigInt = require("../src/bigint.js");
 const ZqField = require("../src/zqfield.js");
-const RatZqField = require("../src/ratzqfield.js");
+const RatField = require("../src/ratfield.js");
 
 const q  = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
 const Z = new ZqField(q);
-const R = new RatZqField(Z);
+const R = new RatField(Z);
 
 const assert = chai.assert;
 

vk_verifier.json

@@ -1 +1 @@
-{"nPublic":2,"A":[["0","1","0"],["0","1","0"],["0","1","0"]],"vk_a":[["10910302893854256300335313159192947444388132687074523434871198422054676751347","7128911999163755080071576365381312078199150810378083348330952764137111826309"],["18631850238317279011886579705479432506796416675676074259923090354119752710032","11613125271011748641588689311610150724463404115865535933368983811438235418330"],["1","0"]],"vk_b":["14021005419725675778621050747090735283429719877068464218769467811976154477903","13400327218680122582347155709033494654797979408389561950304209881074672567956","1"],"vk_c":[["3096051994409557504719773510360462097114704303646108617318273214347944304327","21060178932557065464613441158524747948458716806166605021180362439829514495363"],["13711469505507426929293229841903695489923719718740047084134989818704335937579","16689306268247690470861364441748198782838298216373469479699367433528545900642"],["1","0"]],"vk_gb_1":["6323076061844787963801699179984388237278671131058334789970950232032140773376","1289442623160734848462556712373448525459100416297212719395950333399658173112","1"],"vk_gb_2":[["14738403669696391106523308033989669531459082697567002658683173458264070358472","7115351592298265627577071367133297887460251153742186717064165044604072075208"],["5684452168257595880393745672144928966665179424697978770339950828964351397925","16005652883870491274891326398599328665806046577140362628567012925774147115231"],["1","0"]],"vk_g":[["13057967944664071939530697379611124014113572609236714070685841838860689079766","4921285704318374954421284662839198492272478322335189504342768676294475453825"],["16821731243154385058674189668904278548308574642868092417486261078313511500423","14329710484989081757569399730710287771777297111484092478685760712065088557056"],["1","0"]],"vk_z":[["9830782349217318574531840014041507435528173882006141768847850813321843762209","908701408738093737682928637200323566556898851221230193697915803980061312337"],["18420854262130852746249857908832658786725598484918874058527841900342812415992","11905336095877065527602013373361492354917686666454749599264218906638347950295"],["1","0"]]}
+{"nPublic":2,"A":[["0","1","0"],["0","1","0"],["0","1","0"]],"vk_a":[["1114178395252120380395835212597801981089399905319368502910322038327297636405","5033894282647920143094588130989706038816118666385188297428164028250802121541"],["11204369287866566481790440577452570863155384959741708497053387501206022041196","5804122404011709706164213043421176877293761551268564612957682946191385948083"],["1","0"]],"vk_b":["21502216352809485080540484588657130416201550918596561744135679102208461442666","2868090884426856501439409534931120005724644305621622228858085860168686686429","1"],"vk_c":[["6132826916796173784201732531285327915041466217971374202416165094662772918168","21745292514182636990945632198433440675390812739972912576130340262689749324094"],["771505583294284223449947888751235336787816998120918568114562783124678603668","3393096609476927450002720393920165677184260635403434210470312068614019743097"],["1","0"]],"vk_gb_1":["12719499470261599561309259431682387098359700522807496275922119401706283527128","16621363578670067280062291944220200497396193306084620768371306905372731356597","1"],"vk_gb_2":[["10964959780919004944755595440619126945893196497479441585015855710878271674269","2128708169016642077859536709142486990439502854897055565299822951071887976085"],["2388598870284376494192851636260646163256895248220461084487594797988889825261","20110295053122713144819603341600445626597656441687959152080135372786154275292"],["1","0"]],"vk_g":[["12255811247188042732673820469397127953046292441028573933507149762907917860381","7279942967825808009089038706789890489125264289371774766033392871666671678200"],["7190249513755559992931891810866588807891969433945206422275821065594394539722","21314329220359655301619987728101583897798145529926111725521967279053488865751"],["1","0"]],"vk_z":[["17586236151988045592673833893440158242030817616966567700538296220528189715389","3551310632722212929105681060373481610723584194504089389345599320999381324165"],["9267522905249404702171212401947711344560303757795853174593820034048921438294","6158557086581678490843952132823078409925994557584598523494082907032631181314"],["1","0"]]}