From 2cf28030199f6f2b64950a6c621b11114b955225 Mon Sep 17 00:00:00 2001
From: Jordi Baylina <jordi@baylina.cat>
Date: Tue, 4 Sep 2018 07:13:24 +0200
Subject: [PATCH] Use ruffini for calculatig lagrange polinomials

---
 .../git/personal/zksnark/src/polfield.js      | 260 ------------------
 src/bigint.js                                 |   4 +-
 src/polfield.js                               |  31 ++-
 src/{ratzqfield.js => ratfield.js}            |   4 +-
 src/setup.js                                  |  37 ++-
 test/pols.js                                  |   9 +
 test/ratzqfield.js                            |   4 +-
 vk_proof.json                                 |   2 +-
 vk_verifier.json                              |   2 +-
 9 files changed, 63 insertions(+), 290 deletions(-)
 delete mode 100644 file%3a/Users/jbaylina/git/personal/zksnark/src/polfield.js
 rename src/{ratzqfield.js => ratfield.js} (97%)

diff --git a/file%3a/Users/jbaylina/git/personal/zksnark/src/polfield.js b/file%3a/Users/jbaylina/git/personal/zksnark/src/polfield.js
deleted file mode 100644
index 4a3dc3b..0000000
--- a/file%3a/Users/jbaylina/git/personal/zksnark/src/polfield.js
+++ /dev/null
@@ -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;
diff --git a/src/bigint.js b/src/bigint.js
index b578099..09da430 100644
--- a/src/bigint.js
+++ b/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) {
diff --git a/src/polfield.js b/src/polfield.js
index 9f571aa..afc81c3 100644
--- a/src/polfield.js
+++ b/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;
diff --git a/src/ratzqfield.js b/src/ratfield.js
similarity index 97%
rename from src/ratzqfield.js
rename to src/ratfield.js
index 5d68f68..df51404 100644
--- a/src/ratzqfield.js
+++ b/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;
diff --git a/src/setup.js b/src/setup.js
index 964832f..dfde407 100644
--- a/src/setup.js
+++ b/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;
+}
+
diff --git a/test/pols.js b/test/pols.js
index 9d83ee2..8c52c8f 100644
--- a/test/pols.js
+++ b/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));
+    });
 
 });
diff --git a/test/ratzqfield.js b/test/ratzqfield.js
index 61c311b..32e0b50 100644
--- a/test/ratzqfield.js
+++ b/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;
 
diff --git a/vk_proof.json b/vk_proof.json
index 16fe7d7..ed87ae6 100644
--- a/vk_proof.json
+++ b/vk_proof.json
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/vk_verifier.json b/vk_verifier.json
index ed9509e..0c6e72b 100644
--- a/vk_verifier.json
+++ b/vk_verifier.json
@@ -1 +1 @@
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