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jbaylinajbaylina
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Polynomial division done
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7 files changed

+699
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‎aux/calculate2roots.js

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const bigInt = require("../src/bigint.js");
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const ZqField = require("../src/zqfield.js");
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const r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
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const s = 28;
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const nqr_to_t = bigInt("19103219067921713944291392827692070036145651957329286315305642004821462161904");
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const t_minus_1_over_2 = bigInt("40770029410420498293352137776570907027550720424234931066070132305055");
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const root_unity = bigInt("19103219067921713944291392827692070036145651957329286315305642004821462161904");
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const t = bigInt("81540058820840996586704275553141814055101440848469862132140264610111");
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const F = new ZqField(r);
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function sqrt(a) {
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let v = s;
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let z = nqr_to_t;
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let w = F.exp(a, t_minus_1_over_2);
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let x = F.mul(a, w);
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let b = F.mul(x, w);
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// compute square root with Tonelli--Shanks
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// (does not terminate if not a square!)
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while (!F.equals(b, F.one))
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{
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let m = 0;
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let b2m = b;
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while (!F.equals(b2m, F.one))
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{
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/* invariant: b2m = b^(2^m) after entering this loop */
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b2m = F.square(b2m);
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m += 1;
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}
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let j = v-m-1;
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w = z;
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while (j > 0)
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{
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w = F.square(w);
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--j;
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} // w = z^2^(v-m-1)
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z = F.square(w);
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b = F.mul(b, z);
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x = F.mul(x, w);
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v = m;
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}
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return x;
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}
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const p_minus1= F.sub(r,bigInt(1));
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const gen = bigInt(bigInt(5));
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const twoto28= F.exp(bigInt(2), bigInt(28));
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const rem = F.div(p_minus1, twoto28);
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const w28 = F.exp(gen, rem);
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const one = F.exp(w28, twoto28);
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console.log(F.toString(w28));
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console.log(w28.toString(10));
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console.log(F.toString(one));

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

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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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mulEscalar(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.mulEscalar(b, a[0]);
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if (b.length == 1) return this.mulEscalar(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;

‎src/bigint.js

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let wBigInt;
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console.log("XXX");
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if (typeof(BigInt) != "undefined") {
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wBigInt = BigInt;
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wBigInt.one = wBigInt(1);

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