Use ruffini for calculatig lagrange polinomials
This commit is contained in:
Jordi Baylina
parent
2910b7cf7d
commit
2cf2803019
@ -1,260 +0,0 @@
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/*
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This library do operations on polinomials where their coefficients are in field F
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The polynomial P(x) = p0 + p1 * x + p2 * x^2 + p3 * x^3, ...
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is represented by the array [ p0, p1, p2, p3, ... ]
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*/
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const bigInt = require("./bigInt");
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const ZqField = require("./zqfield");
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class PolFieldZq {
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constructor (q) {
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this.F = new ZqField(q);
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let rem = q.sub(bigInt(1));
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let s = 0;
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while (!rem.isOdd()) {
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s ++;
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rem = rem.shiftRight(1);
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}
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this.w = new Array(s+1);
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this.wi = new Array(s+1);
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this.w[s] = this.F.exp(bigInt(5), rem);
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this.wi[s] = this.F.inverse(this.w[s]);
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let n=s-1;
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while (n>=0) {
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this.w[n] = this.F.square(this.w[n+1]);
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this.wi[n] = this.F.square(this.wi[n+1]);
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n--;
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}
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}
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add(a, b) {
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const m = Math.max(a.length, b.length);
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const res = new Array(m);
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for (let i=0; i<m; i++) {
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res[i] = this.F.add(a[i] || this.F.zero, b[i] || this.F.zero);
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}
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return this.reduce(res);
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}
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double(a) {
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return this.add(a,a);
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}
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sub(a, b) {
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const m = Math.max(a.length, b.length);
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const res = new Array(m);
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for (let i=0; i<m; i++) {
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res[i] = this.F.sub(a[i] || this.F.zero, b[i] || this.F.zero);
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}
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return this.reduce(res);
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}
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mulScalar(a, b) {
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if (this.F.isZero(b)) return [];
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const res = new Array(a.length);
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for (let i=0; i<a.length; i++) {
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res[i] = this.F.mul(a[i], b);
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}
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return res;
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}
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mul(a, b) {
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if (a.length == 0) return [];
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if (b.length == 0) return [];
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if (a.length == 1) return this.mulScalar(b, a[0]);
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if (b.length == 1) return this.mulScalar(a, b[0]);
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const longestN = Math.max(a.length, b.length);
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const bitsResult = log2(longestN-1)+2;
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const m = 1 << bitsResult;
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const ea = this.extend(a,m);
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const eb = this.extend(b,m);
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const ta = this._fft(ea, bitsResult, 0, 1, false);
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const tb = this._fft(eb, bitsResult, 0, 1, false);
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const tres = new Array(m);
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for (let i=0; i<m; i++) {
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tres[i] = this.F.mul(ta[i], tb[i]);
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}
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const res = this._fft(tres, bitsResult, 0, 1, true);
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const twoinvm = this.F.inverse(bigInt(m));
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const resn = new Array(m);
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for (let i=0; i<m; i++) {
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resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
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}
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return this.reduce(this.affine(resn));
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}
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square(a) {
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return this.mul(a,a);
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}
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scaleX(p, n) {
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if (n==0) {
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return p;
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} else if (n>0) {
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const z = new Array(n).fill(this.F.zero);
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return z.concat(p);
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} else {
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return p.slice(-n);
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}
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}
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div(a, b) {
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throw new Error("Not Implementted");
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}
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eval(p, x) {
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let v = this.F.zero;
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let ix = this.F.one;
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for (let i=0; i<p.length; i++) {
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v = this.F.add(v, this.F.mul(p[i], ix));
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ix = this.F.mul(ix, x);
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}
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return v;
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}
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lagrange(points) {
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throw new Error("Not Implementted");
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}
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_fft(pall, bits, offset, step) {
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const n = 1 << bits;
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if (n==1) {
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return [ pall[offset] ];
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}
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const ndiv2 = n >> 1;
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const p1 = this._fft(pall, bits-1, offset, step*2);
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const p2 = this._fft(pall, bits-1, offset+step, step*2);
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const out = new Array(n);
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let m= bigInt(1);
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for (let i=0; i<ndiv2; i++) {
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out[i] = this.F.add(p1[i], this.F.mul(m, p2[i]));
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out[i+ndiv2] = this.F.sub(p1[i], this.F.mul(m, p2[i]));
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m = this.F.mul(m, this.w[bits]);
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}
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return out;
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}
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extend(p, e) {
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if (e == p.length) return p;
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const z = new Array(e-p.length).fill(this.F.zero);
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return p.concat(z);
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}
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reduce(p) {
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if (p.length == 0) return p;
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if (! this.F.isZero(p[p.length-1]) ) return p;
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let i=p.length-1;
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while( i>0 && this.F.isZero(p[i]) ) i--;
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return p.slice(0, i+1);
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}
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affine(p) {
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for (let i=0; i<p.length; i++) {
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p[i] = this.F.affine(p[i]);
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}
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return p;
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}
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equals(a, b) {
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const pa = this.reduce(this.affine(a));
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const pb = this.reduce(this.affine(b));
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if (pa.length != pb.length) return false;
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for (let i=0; i<pb.length; i++) {
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if (!this.F.equals(pa[i], pb[i])) return false;
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}
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return true;
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}
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_next2Power(v) {
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v--;
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v |= v >> 1;
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v |= v >> 2;
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v |= v >> 4;
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v |= v >> 8;
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v |= v >> 16;
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v++;
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return v;
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}
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toString(p) {
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const ap = this.affine(p);
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let S = "";
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for (let i=ap.length-1; i>=0; i--) {
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if (!this.F.isZero(p[i])) {
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if (S!="") S += " + ";
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S = S + p[i].toString(10);
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if (i>0) {
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S = S + "x";
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if (i>1) {
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S = S + "^" +i;
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}
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}
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}
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}
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return S;
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}
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_reciprocal(p, bits) {
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const k = 1 << bits;
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if (k==1) {
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return [ this.F.inverse(p[0]) ];
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}
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const np = this.scaleX(p, -k/2);
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const q = this._reciprocal(np, bits-1);
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const a = this.scaleX(this.double(q), 3*k/2-2);
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const b = this.mul( this.square(q), p);
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return this.scaleX(this.sub(a,b), -(k-2));
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}
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// divides x^m / v
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_div2(m, v) {
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const kbits = log2(v.length-1)+1;
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const k = 1 << kbits;
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const scaleV = k - v.length;
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// rec = x^(k - 2) / v* x^scaleV =>
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// rec = x^(k-2-scaleV)/ v
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//
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// res = x^m/v = x^(m +(2k-2-scaleV) -(2k-2-scaleV)) /v =>
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// res = rec * x^(m - (2k-2-scaleV)) =>
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// res = rec * x^(m - 2k +2 + scaleV)
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const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
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const res = this.scaleX(rec, m - k*2 +2+scaleV);
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return res;
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}
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}
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function log2( V )
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{
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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 ) );
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}
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module.exports = PolFieldZq;
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@ -17,8 +17,8 @@ if (typeof(BigInt) != "undefined") {
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if (aux <= nq) {
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aux = aux % q;
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}
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if (aux.isNegative()) {
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aux = aux.add(q);
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if (aux < wBigInt.zero) {
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aux = aux + q;
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}
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} else {
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if (aux >= q) {
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@ -5,14 +5,14 @@
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is represented by the array [ p0, p1, p2, p3, ... ]
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*/
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const bigInt = require("./bigInt");
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const bigInt = require("./bigint.js");
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class PolFieldZq {
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class PolField {
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constructor (F) {
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this.F = F;
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const q = this.F.q;
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let rem = q.sub(this.F.one);
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let rem = q.sub(bigInt(1));
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let s = 0;
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while (!rem.isOdd()) {
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s ++;
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@ -79,7 +79,7 @@ class PolFieldZq {
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[b, a] = [a, b];
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}
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if (b.length < log2(a.length)) {
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if ((b.length <= 2) || (b.length < log2(a.length))) {
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return this.mulNormal(a,b);
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} else {
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return this.mulFFT(a,b);
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@ -151,14 +151,14 @@ class PolFieldZq {
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}
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lagrange(points) {
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let roots = [this.F.one];
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for (let i=0; i<points.length; i++) {
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roots = this.mul(roots, [this.F.neg(points[i][0]), this.F.one]);
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}
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let sum = [];
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for (let i=0; i<points.length; i++) {
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let mpol = [this.F.one];
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for (let j=0;j<points.length;j++) {
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if (i!=j) {
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mpol = this.mul(mpol, [this.F.neg(points[j][0]), this.F.one]);
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}
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}
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let mpol = this.ruffini(roots, points[i][0]);
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const factor =
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this.F.mul(
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this.F.inverse(this.eval(mpol, points[i][0])),
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@ -226,6 +226,15 @@ class PolFieldZq {
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return true;
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}
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ruffini(p, r) {
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const res = new Array(p.length-1);
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res[res.length-1] = p[p.length-1];
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for (let i = res.length-2; i>=0; i--) {
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res[i] = this.F.add(this.F.mul(res[i+1], r), p[i+1]);
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}
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return res;
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}
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_next2Power(v) {
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v--;
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v |= v >> 1;
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@ -333,4 +342,4 @@ function log2( V )
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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 ) );
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}
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module.exports = PolFieldZq;
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module.exports = PolField;
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@ -1,6 +1,6 @@
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const fUtils = require("./futils.js");
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class RatZqField {
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class RatField {
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constructor(F) {
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this.F = F;
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this.zero = [F.zero, F.one];
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@ -105,4 +105,4 @@ class RatZqField {
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}
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module.exports = RatZqField;
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module.exports = RatField;
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37
src/setup.js
37
src/setup.js
@ -3,11 +3,13 @@ const bigInt = require("./bigint.js");
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const BN128 = require("./BN128.js");
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const PolField = require("./polfield.js");
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const ZqField = require("./zqfield.js");
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const RatField = require("./ratfield.js");
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const bn128 = new BN128();
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const G1 = bn128.G1;
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const G2 = bn128.G2;
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const PolF = new PolField(new ZqField(bn128.r));
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const RatPolF = new PolField(new RatField(new ZqField(bn128.r)));
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const F = new ZqField(bn128.r);
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module.exports = function setup(circuit) {
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@ -40,9 +42,9 @@ function calculatePolinomials(setup, circuit) {
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bPoints[s] = [];
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cPoints[s] = [];
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for (let c=0; c<circuit.nConstrains; c++) {
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aPoints[s].push([bigInt(c), circuit.a(c, s)]);
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bPoints[s].push([bigInt(c), circuit.b(c, s)]);
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cPoints[s].push([bigInt(c), circuit.c(c, s)]);
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aPoints[s].push([[bigInt(c), F.one], [circuit.a(c, s), F.one]]);
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bPoints[s].push([[bigInt(c), F.one], [circuit.b(c, s), F.one]]);
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cPoints[s].push([[bigInt(c), F.one], [circuit.c(c, s), F.one]]);
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}
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}
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@ -51,10 +53,15 @@ function calculatePolinomials(setup, circuit) {
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setup.vk_proof.polsB = [];
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setup.vk_proof.polsC = [];
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for (let s=0; s<circuit.nSignals; s++) {
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console.log(`Caclcualte Pol ${s}/${circuit.nSignals}`);
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setup.vk_proof.polsA.push(PolF.lagrange( aPoints[s] ));
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setup.vk_proof.polsB.push(PolF.lagrange( bPoints[s] ));
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setup.vk_proof.polsC.push(PolF.lagrange( cPoints[s] ));
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// console.log(`Caclcualte Pol ${s}/${circuit.nSignals}`);
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const pA = RatPolF.lagrange( aPoints[s] );
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const pB = RatPolF.lagrange( bPoints[s] );
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const pC = RatPolF.lagrange( cPoints[s] );
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setup.vk_proof.polsA.push( unrat(pA) );
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setup.vk_proof.polsB.push( unrat(pB) );
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setup.vk_proof.polsC.push( unrat(pC) );
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}
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// Calculate Z polinomial
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@ -96,7 +103,7 @@ function calculateEncriptedValuesAtT(setup, circuit) {
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for (let s=0; s<circuit.nSignals; s++) {
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// A[i] = G1 * polA(t)
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const at = PolF.eval(setup.vk_proof.polsA[s], setup.toxic.t);
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const at = F.affine(PolF.eval(setup.vk_proof.polsA[s], setup.toxic.t));
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const A = G1.affine(G1.mulScalar(G1.g, at));
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setup.vk_proof.A.push(A);
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@ -107,7 +114,7 @@ function calculateEncriptedValuesAtT(setup, circuit) {
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// B1[i] = G1 * polB(t)
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const bt = PolF.eval(setup.vk_proof.polsB[s], setup.toxic.t);
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const bt = F.affine(PolF.eval(setup.vk_proof.polsB[s], setup.toxic.t));
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const B1 = G1.affine(G1.mulScalar(G1.g, bt));
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// B2[i] = G2 * polB(t)
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@ -116,13 +123,13 @@ function calculateEncriptedValuesAtT(setup, circuit) {
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setup.vk_proof.B.push(B2);
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// C[i] = G1 * polC(t)
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const ct = PolF.eval(setup.vk_proof.polsC[s], setup.toxic.t);
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const ct = F.affine(PolF.eval(setup.vk_proof.polsC[s], setup.toxic.t));
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const C = G1.affine(G1.mulScalar( G1.g, ct));
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setup.vk_proof.C.push (C);
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// K = G1 * (A+B+C)
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const kt = F.add(F.add(at, bt), ct);
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const kt = F.affine(F.add(F.add(at, bt), ct));
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const K = G1.affine(G1.mulScalar( G1.g, kt));
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@ -169,3 +176,11 @@ function calculateHexps(setup, circuit) {
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}
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}
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function unrat(p) {
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const res = new Array(p.length);
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for (let i=0; i<p.length; i++) {
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res[i] = RatPolF.F.toF(p[i]);
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
|
||||
@ -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));
|
||||
});
|
||||
|
||||
});
|
||||
|
||||
@ -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;
|
||||
|
||||
|
||||
File diff suppressed because one or more lines are too long
@ -1 +1 @@
|
||||
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|
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|
||||
Loading…
Reference in New Issue
Block a user