@kotevode/ffjavascript
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Finite Field Library in Javascript
2,081 lines (1,675 loc) • 170 kB
JavaScript
'use strict';
var crypto = require('crypto');
var wasmcurves = require('wasmcurves');
var os = require('os');
var Worker = require('@kotevode/web-worker');
var wasmbuilder = require('wasmbuilder');
/* global BigInt */
const hexLen = [ 0, 1, 2, 2, 3, 3, 3, 3, 4 ,4 ,4 ,4 ,4 ,4 ,4 ,4];
function fromString(s, radix) {
if ((!radix)||(radix==10)) {
return BigInt(s);
} else if (radix==16) {
if (s.slice(0,2) == "0x") {
return BigInt(s);
} else {
return BigInt("0x"+s);
}
}
}
const e = fromString;
function fromArray(a, radix) {
let acc =BigInt(0);
radix = BigInt(radix);
for (let i=0; i<a.length; i++) {
acc = acc*radix + BigInt(a[i]);
}
return acc;
}
function bitLength(a) {
const aS =a.toString(16);
return (aS.length-1)*4 +hexLen[parseInt(aS[0], 16)];
}
function isNegative(a) {
return BigInt(a) < BigInt(0);
}
function isZero(a) {
return !a;
}
function shiftLeft(a, n) {
return BigInt(a) << BigInt(n);
}
function shiftRight(a, n) {
return BigInt(a) >> BigInt(n);
}
const shl = shiftLeft;
const shr = shiftRight;
function isOdd(a) {
return (BigInt(a) & BigInt(1)) == BigInt(1);
}
function naf(n) {
let E = BigInt(n);
const res = [];
while (E) {
if (E & BigInt(1)) {
const z = 2 - Number(E % BigInt(4));
res.push( z );
E = E - BigInt(z);
} else {
res.push( 0 );
}
E = E >> BigInt(1);
}
return res;
}
function bits(n) {
let E = BigInt(n);
const res = [];
while (E) {
if (E & BigInt(1)) {
res.push(1);
} else {
res.push( 0 );
}
E = E >> BigInt(1);
}
return res;
}
function toNumber(s) {
if (s>BigInt(Number.MAX_SAFE_INTEGER )) {
throw new Error("Number too big");
}
return Number(s);
}
function toArray(s, radix) {
const res = [];
let rem = BigInt(s);
radix = BigInt(radix);
while (rem) {
res.unshift( Number(rem % radix));
rem = rem / radix;
}
return res;
}
function add(a, b) {
return BigInt(a) + BigInt(b);
}
function sub(a, b) {
return BigInt(a) - BigInt(b);
}
function neg(a) {
return -BigInt(a);
}
function mul(a, b) {
return BigInt(a) * BigInt(b);
}
function square(a) {
return BigInt(a) * BigInt(a);
}
function pow(a, b) {
return BigInt(a) ** BigInt(b);
}
function exp$1(a, b) {
return BigInt(a) ** BigInt(b);
}
function abs(a) {
return BigInt(a) >= 0 ? BigInt(a) : -BigInt(a);
}
function div(a, b) {
return BigInt(a) / BigInt(b);
}
function mod(a, b) {
return BigInt(a) % BigInt(b);
}
function eq(a, b) {
return BigInt(a) == BigInt(b);
}
function neq(a, b) {
return BigInt(a) != BigInt(b);
}
function lt(a, b) {
return BigInt(a) < BigInt(b);
}
function gt(a, b) {
return BigInt(a) > BigInt(b);
}
function leq(a, b) {
return BigInt(a) <= BigInt(b);
}
function geq(a, b) {
return BigInt(a) >= BigInt(b);
}
function band(a, b) {
return BigInt(a) & BigInt(b);
}
function bor(a, b) {
return BigInt(a) | BigInt(b);
}
function bxor(a, b) {
return BigInt(a) ^ BigInt(b);
}
function land(a, b) {
return BigInt(a) && BigInt(b);
}
function lor(a, b) {
return BigInt(a) || BigInt(b);
}
function lnot(a) {
return !BigInt(a);
}
// Returns a buffer with Little Endian Representation
function toRprLE(buff, o, e, n8) {
const s = "0000000" + e.toString(16);
const v = new Uint32Array(buff.buffer, buff.byteOffset + o, n8/4);
const l = (((s.length-7)*4 - 1) >> 5)+1; // Number of 32bit words;
for (let i=0; i<l; i++) v[i] = parseInt(s.substring(s.length-8*i-8, s.length-8*i), 16);
for (let i=l; i<v.length; i++) v[i] = 0;
for (let i=v.length*4; i<n8; i++) buff[i] = toNumber(band(shiftRight(e, i*8), 0xFF));
}
// Returns a buffer with Big Endian Representation
function toRprBE(buff, o, e, n8) {
const s = "0000000" + e.toString(16);
const v = new DataView(buff.buffer, buff.byteOffset + o, n8);
const l = (((s.length-7)*4 - 1) >> 5)+1; // Number of 32bit words;
for (let i=0; i<l; i++) v.setUint32(n8-i*4 -4, parseInt(s.substring(s.length-8*i-8, s.length-8*i), 16), false);
for (let i=0; i<n8/4-l; i++) v[i] = 0;
}
// Pases a buffer with Little Endian Representation
function fromRprLE(buff, o, n8) {
n8 = n8 || buff.byteLength;
o = o || 0;
const v = new Uint32Array(buff.buffer, buff.byteOffset + o, n8/4);
const a = new Array(n8/4);
v.forEach( (ch,i) => a[a.length-i-1] = ch.toString(16).padStart(8,"0") );
return fromString(a.join(""), 16);
}
// Pases a buffer with Big Endian Representation
function fromRprBE(buff, o, n8) {
n8 = n8 || buff.byteLength;
o = o || 0;
const v = new DataView(buff.buffer, buff.byteOffset + o, n8);
const a = new Array(n8/4);
for (let i=0; i<n8/4; i++) {
a[i] = v.getUint32(i*4, false).toString(16).padStart(8, "0");
}
return fromString(a.join(""), 16);
}
function toString(a, radix) {
return a.toString(radix);
}
function toLEBuff(a) {
const buff = new Uint8Array(Math.floor((bitLength(a) - 1) / 8) +1);
toRprLE(buff, 0, a, buff.byteLength);
return buff;
}
const zero = e(0);
const one = e(1);
var _Scalar = /*#__PURE__*/Object.freeze({
__proto__: null,
abs: abs,
add: add,
band: band,
bitLength: bitLength,
bits: bits,
bor: bor,
bxor: bxor,
div: div,
e: e,
eq: eq,
exp: exp$1,
fromArray: fromArray,
fromRprBE: fromRprBE,
fromRprLE: fromRprLE,
fromString: fromString,
geq: geq,
gt: gt,
isNegative: isNegative,
isOdd: isOdd,
isZero: isZero,
land: land,
leq: leq,
lnot: lnot,
lor: lor,
lt: lt,
mod: mod,
mul: mul,
naf: naf,
neg: neg,
neq: neq,
one: one,
pow: pow,
shiftLeft: shiftLeft,
shiftRight: shiftRight,
shl: shl,
shr: shr,
square: square,
sub: sub,
toArray: toArray,
toLEBuff: toLEBuff,
toNumber: toNumber,
toRprBE: toRprBE,
toRprLE: toRprLE,
toString: toString,
zero: zero
});
/*
Copyright 2018 0kims association.
This file is part of snarkjs.
snarkjs is a free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
snarkjs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/
/*
This library does operations on polynomials with coefficients in a field F.
A polynomial P(x) = p0 + p1 * x + p2 * x^2 + ... + pn * x^n is represented
by the array [ p0, p1, p2, ... , pn ].
*/
class PolField {
constructor (F) {
this.F = F;
let rem = F.sqrt_t;
let s = F.sqrt_s;
const five = this.F.add(this.F.add(this.F.two, this.F.two), this.F.one);
this.w = new Array(s+1);
this.wi = new Array(s+1);
this.w[s] = this.F.pow(five, rem);
this.wi[s] = this.F.inv(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--;
}
this.roots = [];
/* for (let i=0; i<16; i++) {
let r = this.F.one;
n = 1 << i;
const rootsi = new Array(n);
for (let j=0; j<n; j++) {
rootsi[j] = r;
r = this.F.mul(r, this.w[i]);
}
this.roots.push(rootsi);
}
*/
this._setRoots(15);
}
_setRoots(n) {
if (n > this.F.sqrt_s) n = this.s;
for (let i=n; (i>=0) && (!this.roots[i]); i--) {
let r = this.F.one;
const nroots = 1 << i;
const rootsi = new Array(nroots);
for (let j=0; j<nroots; j++) {
rootsi[j] = r;
r = this.F.mul(r, this.w[i]);
}
this.roots[i] = rootsi;
}
}
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(p, b) {
if (this.F.eq(b, this.F.zero)) return [];
if (this.F.eq(b, this.F.one)) return p;
const res = new Array(p.length);
for (let i=0; i<p.length; i++) {
res[i] = this.F.mul(p[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]);
if (b.length > a.length) {
[b, a] = [a, b];
}
if ((b.length <= 2) || (b.length < log2$2(a.length))) {
return this.mulNormal(a,b);
} else {
return this.mulFFT(a,b);
}
}
mulNormal(a, b) {
let res = [];
for (let i=0; i<b.length; i++) {
res = this.add(res, this.scaleX(this.mulScalar(a, b[i]), i) );
}
return res;
}
mulFFT(a,b) {
const longestN = Math.max(a.length, b.length);
const bitsResult = log2$2(longestN-1)+2;
this._setRoots(bitsResult);
const m = 1 << bitsResult;
const ea = this.extend(a,m);
const eb = this.extend(b,m);
const ta = __fft$1(this, ea, bitsResult, 0, 1);
const tb = __fft$1(this, eb, bitsResult, 0, 1);
const tres = new Array(m);
for (let i=0; i<m; i++) {
tres[i] = this.F.mul(ta[i], tb[i]);
}
const res = __fft$1(this, tres, bitsResult, 0, 1);
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, 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(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 {
if (-n >= p.length) return [];
return p.slice(-n);
}
}
eval2(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;
}
evaluate(p,x) {
const F = this.F;
if (p.length == 0) return F.zero;
const m = this._next2Power(p.length);
const ep = this.extend(p, m);
return _eval(ep, x, 0, 1, m);
function _eval(p, x, offset, step, n) {
if (n==1) return p[offset];
const newX = F.square(x);
const res= F.add(
_eval(p, newX, offset, step << 1, n >> 1),
F.mul(
x,
_eval(p, newX, offset+step , step << 1, n >> 1)));
return res;
}
}
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.ruffini(roots, points[i][0]);
const factor =
this.F.mul(
this.F.inv(this.evaluate(mpol, points[i][0])),
points[i][1]);
mpol = this.mulScalar(mpol, factor);
sum = this.add(sum, mpol);
}
return sum;
}
fft(p) {
if (p.length <= 1) return p;
const bits = log2$2(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
const ep = this.extend(p, m);
const res = __fft$1(this, ep, bits, 0, 1);
return res;
}
fft2(p) {
if (p.length <= 1) return p;
const bits = log2$2(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
const ep = this.extend(p, m);
__bitReverse(ep, bits);
const res = __fft2(this, ep, bits);
return res;
}
ifft(p) {
if (p.length <= 1) return p;
const bits = log2$2(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
const ep = this.extend(p, m);
const res = __fft$1(this, ep, bits, 0, 1);
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
const resn = new Array(m);
for (let i=0; i<m; i++) {
resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
}
return resn;
}
ifft2(p) {
if (p.length <= 1) return p;
const bits = log2$2(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
const ep = this.extend(p, m);
__bitReverse(ep, bits);
const res = __fft2(this, ep, bits);
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
const resn = new Array(m);
for (let i=0; i<m; i++) {
resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
}
return resn;
}
_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= this.F.one;
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.eq(p[p.length-1], this.F.zero) ) return p;
let i=p.length-1;
while( i>0 && this.F.eq(p[i], this.F.zero) ) i--;
return p.slice(0, i+1);
}
eq(a, b) {
const pa = this.reduce(a);
const pb = this.reduce(b);
if (pa.length != pb.length) return false;
for (let i=0; i<pb.length; i++) {
if (!this.F.eq(pa[i], pb[i])) return false;
}
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;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;
return v;
}
toString(p) {
const ap = this.normalize(p);
let S = "";
for (let i=ap.length-1; i>=0; i--) {
if (!this.F.eq(p[i], this.F.zero)) {
if (S!="") S += " + ";
S = S + p[i].toString(10);
if (i>0) {
S = S + "x";
if (i>1) {
S = S + "^" +i;
}
}
}
}
return S;
}
normalize(p) {
const res = new Array(p.length);
for (let i=0; i<p.length; i++) {
res[i] = this.F.normalize(p[i]);
}
return res;
}
_reciprocal(p, bits) {
const k = 1 << bits;
if (k==1) {
return [ this.F.inv(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$2(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 + (2*k-2 - scaleV) - (2*k-2 - scaleV)) /v =>
// res = rec * x^(m - (2*k-2 - scaleV)) =>
// res = rec * x^(m - 2*k + 2 + scaleV)
const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
const res = this.scaleX(rec, m - 2*k + 2 + scaleV);
return res;
}
div(_u, _v) {
if (_u.length < _v.length) return [];
const kbits = log2$2(_v.length-1)+1;
const k = 1 << kbits;
const u = this.scaleX(_u, k-_v.length);
const v = this.scaleX(_v, k-_v.length);
const n = v.length-1;
let m = u.length-1;
const s = this._reciprocal(v, kbits);
let t;
if (m>2*n) {
t = this.sub(this.scaleX([this.F.one], 2*n), this.mul(s, v));
}
let q = [];
let rem = u;
let us, ut;
let finish = false;
while (!finish) {
us = this.mul(rem, s);
q = this.add(q, this.scaleX(us, -2*n));
if ( m > 2*n ) {
ut = this.mul(rem, t);
rem = this.scaleX(ut, -2*n);
m = rem.length-1;
} else {
finish = true;
}
}
return q;
}
// returns the ith nth-root of one
oneRoot(n, i) {
let nbits = log2$2(n-1)+1;
let res = this.F.one;
let r = i;
if(i>=n) {
throw new Error("Given 'i' should be lower than 'n'");
}
else if (1<<nbits !== n) {
throw new Error(`Internal errlr: ${n} should equal ${1<<nbits}`);
}
while (r>0) {
if (r & 1 == 1) {
res = this.F.mul(res, this.w[nbits]);
}
r = r >> 1;
nbits --;
}
return res;
}
computeVanishingPolinomial(bits, t) {
const m = 1 << bits;
return this.F.sub(this.F.pow(t, m), this.F.one);
}
evaluateLagrangePolynomials(bits, t) {
const m= 1 << bits;
const tm = this.F.pow(t, m);
const u= new Array(m).fill(this.F.zero);
this._setRoots(bits);
const omega = this.w[bits];
if (this.F.eq(tm, this.F.one)) {
for (let i = 0; i < m; i++) {
if (this.F.eq(this.roots[bits][0],t)) { // i.e., t equals omega^i
u[i] = this.F.one;
return u;
}
}
}
const z = this.F.sub(tm, this.F.one);
// let l = this.F.mul(z, this.F.pow(this.F.twoinv, m));
let l = this.F.mul(z, this.F.inv(this.F.e(m)));
for (let i = 0; i < m; i++) {
u[i] = this.F.mul(l, this.F.inv(this.F.sub(t,this.roots[bits][i])));
l = this.F.mul(l, omega);
}
return u;
}
log2(V) {
return log2$2(V);
}
}
function log2$2( 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 ) );
}
function __fft$1(PF, pall, bits, offset, step) {
const n = 1 << bits;
if (n==1) {
return [ pall[offset] ];
} else if (n==2) {
return [
PF.F.add(pall[offset], pall[offset + step]),
PF.F.sub(pall[offset], pall[offset + step])];
}
const ndiv2 = n >> 1;
const p1 = __fft$1(PF, pall, bits-1, offset, step*2);
const p2 = __fft$1(PF, pall, bits-1, offset+step, step*2);
const out = new Array(n);
for (let i=0; i<ndiv2; i++) {
out[i] = PF.F.add(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
out[i+ndiv2] = PF.F.sub(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
}
return out;
}
function __fft2(PF, pall, bits) {
const n = 1 << bits;
if (n==1) {
return [ pall[0] ];
}
const ndiv2 = n >> 1;
const p1 = __fft2(PF, pall.slice(0, ndiv2), bits-1);
const p2 = __fft2(PF, pall.slice(ndiv2), bits-1);
const out = new Array(n);
for (let i=0; i<ndiv2; i++) {
out[i] = PF.F.add(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
out[i+ndiv2] = PF.F.sub(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
}
return out;
}
const _revTable$1 = [];
for (let i=0; i<256; i++) {
_revTable$1[i] = _revSlow$1(i, 8);
}
function _revSlow$1(idx, bits) {
let res =0;
let a = idx;
for (let i=0; i<bits; i++) {
res <<= 1;
res = res | (a &1);
a >>=1;
}
return res;
}
function rev(idx, bits) {
return (
_revTable$1[idx >>> 24] |
(_revTable$1[(idx >>> 16) & 0xFF] << 8) |
(_revTable$1[(idx >>> 8) & 0xFF] << 16) |
(_revTable$1[idx & 0xFF] << 24)
) >>> (32-bits);
}
function __bitReverse(p, bits) {
for (let k=0; k<p.length; k++) {
const r = rev(k, bits);
if (r>k) {
const tmp= p[k];
p[k] = p[r];
p[r] = tmp;
}
}
}
/*
Copyright 2018 0kims association.
This file is part of snarkjs.
snarkjs is a free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
snarkjs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/
function mulScalar(F, base, e) {
let res;
if (isZero(e)) return F.zero;
const n = naf(e);
if (n[n.length-1] == 1) {
res = base;
} else if (n[n.length-1] == -1) {
res = F.neg(base);
} else {
throw new Error("invlaud NAF");
}
for (let i=n.length-2; i>=0; i--) {
res = F.double(res);
if (n[i] == 1) {
res = F.add(res, base);
} else if (n[i] == -1) {
res = F.sub(res, base);
}
}
return res;
}
/*
exports.mulScalar = (F, base, e) =>{
let res = F.zero;
let rem = bigInt(e);
let exp = base;
while (! rem.eq(bigInt.zero)) {
if (rem.and(bigInt.one).eq(bigInt.one)) {
res = F.add(res, exp);
}
exp = F.double(exp);
rem = rem.shiftRight(1);
}
return res;
};
*/
function exp(F, base, e) {
if (isZero(e)) return F.one;
const n = bits(e);
if (n.length==0) return F.one;
let res = base;
for (let i=n.length-2; i>=0; i--) {
res = F.square(res);
if (n[i]) {
res = F.mul(res, base);
}
}
return res;
}
// Check here: https://eprint.iacr.org/2012/685.pdf
function buildSqrt (F) {
if ((F.m % 2) == 1) {
if (eq(mod(F.p, 4), 1 )) {
if (eq(mod(F.p, 8), 1 )) {
if (eq(mod(F.p, 16), 1 )) {
// alg7_muller(F);
alg5_tonelliShanks(F);
} else if (eq(mod(F.p, 16), 9 )) {
alg4_kong(F);
} else {
throw new Error("Field withot sqrt");
}
} else if (eq(mod(F.p, 8), 5 )) {
alg3_atkin(F);
} else {
throw new Error("Field withot sqrt");
}
} else if (eq(mod(F.p, 4), 3 )) {
alg2_shanks(F);
}
} else {
const pm2mod4 = mod(pow(F.p, F.m/2), 4);
if (pm2mod4 == 1) {
alg10_adj(F);
} else if (pm2mod4 == 3) {
alg9_adj(F);
} else {
alg8_complex(F);
}
}
}
function alg5_tonelliShanks(F) {
F.sqrt_q = pow(F.p, F.m);
F.sqrt_s = 0;
F.sqrt_t = sub(F.sqrt_q, 1);
while (!isOdd(F.sqrt_t)) {
F.sqrt_s = F.sqrt_s + 1;
F.sqrt_t = div(F.sqrt_t, 2);
}
let c0 = F.one;
while (F.eq(c0, F.one)) {
const c = F.random();
F.sqrt_z = F.pow(c, F.sqrt_t);
c0 = F.pow(F.sqrt_z, 2 ** (F.sqrt_s-1) );
}
F.sqrt_tm1d2 = div(sub(F.sqrt_t, 1),2);
F.sqrt = function(a) {
const F=this;
if (F.isZero(a)) return F.zero;
let w = F.pow(a, F.sqrt_tm1d2);
const a0 = F.pow( F.mul(F.square(w), a), 2 ** (F.sqrt_s-1) );
if (F.eq(a0, F.negone)) return null;
let v = F.sqrt_s;
let x = F.mul(a, w);
let b = F.mul(x, w);
let z = F.sqrt_z;
while (!F.eq(b, F.one)) {
let b2k = F.square(b);
let k=1;
while (!F.eq(b2k, F.one)) {
b2k = F.square(b2k);
k++;
}
w = z;
for (let i=0; i<v-k-1; i++) {
w = F.square(w);
}
z = F.square(w);
b = F.mul(b, z);
x = F.mul(x, w);
v = k;
}
return F.geq(x, F.zero) ? x : F.neg(x);
};
}
function alg4_kong(F) {
F.sqrt = function() {
throw new Error("Sqrt alg 4 not implemented");
};
}
function alg3_atkin(F) {
F.sqrt = function() {
throw new Error("Sqrt alg 3 not implemented");
};
}
function alg2_shanks(F) {
F.sqrt_q = pow(F.p, F.m);
F.sqrt_e1 = div( sub(F.sqrt_q, 3) , 4);
F.sqrt = function(a) {
if (this.isZero(a)) return this.zero;
// Test that have solution
const a1 = this.pow(a, this.sqrt_e1);
const a0 = this.mul(this.square(a1), a);
if ( this.eq(a0, this.negone) ) return null;
const x = this.mul(a1, a);
return F.geq(x, F.zero) ? x : F.neg(x);
};
}
function alg10_adj(F) {
F.sqrt = function() {
throw new Error("Sqrt alg 10 not implemented");
};
}
function alg9_adj(F) {
F.sqrt_q = pow(F.p, F.m/2);
F.sqrt_e34 = div( sub(F.sqrt_q, 3) , 4);
F.sqrt_e12 = div( sub(F.sqrt_q, 1) , 2);
F.frobenius = function(n, x) {
if ((n%2) == 1) {
return F.conjugate(x);
} else {
return x;
}
};
F.sqrt = function(a) {
const F = this;
const a1 = F.pow(a, F.sqrt_e34);
const alfa = F.mul(F.square(a1), a);
const a0 = F.mul(F.frobenius(1, alfa), alfa);
if (F.eq(a0, F.negone)) return null;
const x0 = F.mul(a1, a);
let x;
if (F.eq(alfa, F.negone)) {
x = F.mul(x0, [F.F.zero, F.F.one]);
} else {
const b = F.pow(F.add(F.one, alfa), F.sqrt_e12);
x = F.mul(b, x0);
}
return F.geq(x, F.zero) ? x : F.neg(x);
};
}
function alg8_complex(F) {
F.sqrt = function() {
throw new Error("Sqrt alg 8 not implemented");
};
}
function quarterRound(st, a, b, c, d) {
st[a] = (st[a] + st[b]) >>> 0;
st[d] = (st[d] ^ st[a]) >>> 0;
st[d] = ((st[d] << 16) | ((st[d]>>>16) & 0xFFFF)) >>> 0;
st[c] = (st[c] + st[d]) >>> 0;
st[b] = (st[b] ^ st[c]) >>> 0;
st[b] = ((st[b] << 12) | ((st[b]>>>20) & 0xFFF)) >>> 0;
st[a] = (st[a] + st[b]) >>> 0;
st[d] = (st[d] ^ st[a]) >>> 0;
st[d] = ((st[d] << 8) | ((st[d]>>>24) & 0xFF)) >>> 0;
st[c] = (st[c] + st[d]) >>> 0;
st[b] = (st[b] ^ st[c]) >>> 0;
st[b] = ((st[b] << 7) | ((st[b]>>>25) & 0x7F)) >>> 0;
}
function doubleRound(st) {
quarterRound(st, 0, 4, 8,12);
quarterRound(st, 1, 5, 9,13);
quarterRound(st, 2, 6,10,14);
quarterRound(st, 3, 7,11,15);
quarterRound(st, 0, 5,10,15);
quarterRound(st, 1, 6,11,12);
quarterRound(st, 2, 7, 8,13);
quarterRound(st, 3, 4, 9,14);
}
class ChaCha {
constructor(seed) {
seed = seed || [0,0,0,0,0,0,0,0];
this.state = [
0x61707865,
0x3320646E,
0x79622D32,
0x6B206574,
seed[0],
seed[1],
seed[2],
seed[3],
seed[4],
seed[5],
seed[6],
seed[7],
0,
0,
0,
0
];
this.idx = 16;
this.buff = new Array(16);
}
nextU32() {
if (this.idx == 16) this.update();
return this.buff[this.idx++];
}
nextU64() {
return add(mul(this.nextU32(), 0x100000000), this.nextU32());
}
nextBool() {
return (this.nextU32() & 1) == 1;
}
update() {
// Copy the state
for (let i=0; i<16; i++) this.buff[i] = this.state[i];
// Apply the rounds
for (let i=0; i<10; i++) doubleRound(this.buff);
// Add to the initial
for (let i=0; i<16; i++) this.buff[i] = (this.buff[i] + this.state[i]) >>> 0;
this.idx = 0;
this.state[12] = (this.state[12] + 1) >>> 0;
if (this.state[12] != 0) return;
this.state[13] = (this.state[13] + 1) >>> 0;
if (this.state[13] != 0) return;
this.state[14] = (this.state[14] + 1) >>> 0;
if (this.state[14] != 0) return;
this.state[15] = (this.state[15] + 1) >>> 0;
}
}
function getRandomBytes(n) {
let array = new Uint8Array(n);
if (process.browser) { // Browser
if (typeof globalThis.crypto !== "undefined") { // Supported
globalThis.crypto.getRandomValues(array);
} else { // fallback
for (let i=0; i<n; i++) {
array[i] = (Math.random()*4294967296)>>>0;
}
}
}
else { // NodeJS
crypto.randomFillSync(array);
}
return array;
}
function getRandomSeed() {
const arr = getRandomBytes(32);
const arrV = new Uint32Array(arr.buffer);
const seed = [];
for (let i=0; i<8; i++) {
seed.push(arrV[i]);
}
return seed;
}
let threadRng = null;
function getThreadRng() {
if (threadRng) return threadRng;
threadRng = new ChaCha(getRandomSeed());
return threadRng;
}
/*
Copyright 2018 0kims association.
This file is part of snarkjs.
snarkjs is a free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
snarkjs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/
/*
This library does operations on polynomials with coefficients in a field F.
A polynomial P(x) = p0 + p1 * x + p2 * x^2 + ... + pn * x^n is represented
by the array [ p0, p1, p2, ... , pn ].
*/
class FFT {
constructor (G, F, opMulGF) {
this.F = F;
this.G = G;
this.opMulGF = opMulGF;
let rem = F.sqrt_t || F.t;
let s = F.sqrt_s || F.s;
let nqr = F.one;
while (F.eq(F.pow(nqr, F.half), F.one)) nqr = F.add(nqr, F.one);
this.w = new Array(s+1);
this.wi = new Array(s+1);
this.w[s] = this.F.pow(nqr, rem);
this.wi[s] = this.F.inv(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--;
}
this.roots = [];
/*
for (let i=0; i<16; i++) {
let r = this.F.one;
n = 1 << i;
const rootsi = new Array(n);
for (let j=0; j<n; j++) {
rootsi[j] = r;
r = this.F.mul(r, this.w[i]);
}
this.roots.push(rootsi);
}
*/
this._setRoots(Math.min(s, 15));
}
_setRoots(n) {
for (let i=n; (i>=0) && (!this.roots[i]); i--) {
let r = this.F.one;
const nroots = 1 << i;
const rootsi = new Array(nroots);
for (let j=0; j<nroots; j++) {
rootsi[j] = r;
r = this.F.mul(r, this.w[i]);
}
this.roots[i] = rootsi;
}
}
fft(p) {
if (p.length <= 1) return p;
const bits = log2$1(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
if (p.length != m) {
throw new Error("Size must be multiple of 2");
}
const res = __fft(this, p, bits, 0, 1);
return res;
}
ifft(p) {
if (p.length <= 1) return p;
const bits = log2$1(p.length-1)+1;
this._setRoots(bits);
const m = 1 << bits;
if (p.length != m) {
throw new Error("Size must be multiple of 2");
}
const res = __fft(this, p, bits, 0, 1);
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
const resn = new Array(m);
for (let i=0; i<m; i++) {
resn[i] = this.opMulGF(res[(m-i)%m], twoinvm);
}
return resn;
}
}
function log2$1( 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 ) );
}
function __fft(PF, pall, bits, offset, step) {
const n = 1 << bits;
if (n==1) {
return [ pall[offset] ];
} else if (n==2) {
return [
PF.G.add(pall[offset], pall[offset + step]),
PF.G.sub(pall[offset], pall[offset + step])];
}
const ndiv2 = n >> 1;
const p1 = __fft(PF, pall, bits-1, offset, step*2);
const p2 = __fft(PF, pall, bits-1, offset+step, step*2);
const out = new Array(n);
for (let i=0; i<ndiv2; i++) {
out[i] = PF.G.add(p1[i], PF.opMulGF(p2[i], PF.roots[bits][i]));
out[i+ndiv2] = PF.G.sub(p1[i], PF.opMulGF(p2[i], PF.roots[bits][i]));
}
return out;
}
/* global BigInt */
class ZqField {
constructor(p) {
this.type="F1";
this.one = BigInt(1);
this.zero = BigInt(0);
this.p = BigInt(p);
this.m = 1;
this.negone = this.p-this.one;
this.two = BigInt(2);
this.half = this.p >> this.one;
this.bitLength = bitLength(this.p);
this.mask = (this.one << BigInt(this.bitLength)) - this.one;
this.n64 = Math.floor((this.bitLength - 1) / 64)+1;
this.n32 = this.n64*2;
this.n8 = this.n64*8;
this.R = this.e(this.one << BigInt(this.n64*64));
this.Ri = this.inv(this.R);
const e = this.negone >> this.one;
this.nqr = this.two;
let r = this.pow(this.nqr, e);
while (!this.eq(r, this.negone)) {
this.nqr = this.nqr + this.one;
r = this.pow(this.nqr, e);
}
this.s = 0;
this.t = this.negone;
while ((this.t & this.one) == this.zero) {
this.s = this.s + 1;
this.t = this.t >> this.one;
}
this.nqr_to_t = this.pow(this.nqr, this.t);
buildSqrt(this);
this.FFT = new FFT(this, this, this.mul.bind(this));
this.fft = this.FFT.fft.bind(this.FFT);
this.ifft = this.FFT.ifft.bind(this.FFT);
this.w = this.FFT.w;
this.wi = this.FFT.wi;
this.shift = this.square(this.nqr);
this.k = this.exp(this.nqr, 2**this.s);
}
e(a,b) {
let res;
if (!b) {
res = BigInt(a);
} else if (b==16) {
res = BigInt("0x"+a);
}
if (res < 0) {
let nres = -res;
if (nres >= this.p) nres = nres % this.p;
return this.p - nres;
} else {
return (res>= this.p) ? res%this.p : res;
}
}
add(a, b) {
const res = a + b;
return res >= this.p ? res-this.p : res;
}
sub(a, b) {
return (a >= b) ? a-b : this.p-b+a;
}
neg(a) {
return a ? this.p-a : a;
}
mul(a, b) {
return (a*b)%this.p;
}
mulScalar(base, s) {
return (base * this.e(s)) % this.p;
}
square(a) {
return (a*a) % this.p;
}
eq(a, b) {
return a==b;
}
neq(a, b) {
return a!=b;
}
lt(a, b) {
const aa = (a > this.half) ? a - this.p : a;
const bb = (b > this.half) ? b - this.p : b;
return aa < bb;
}
gt(a, b) {
const aa = (a > this.half) ? a - this.p : a;
const bb = (b > this.half) ? b - this.p : b;
return aa > bb;
}
leq(a, b) {
const aa = (a > this.half) ? a - this.p : a;
const bb = (b > this.half) ? b - this.p : b;
return aa <= bb;
}
geq(a, b) {
const aa = (a > this.half) ? a - this.p : a;
const bb = (b > this.half) ? b - this.p : b;
return aa >= bb;
}
div(a, b) {
return this.mul(a, this.inv(b));
}
idiv(a, b) {
if (!b) throw new Error("Division by zero");
return a / b;
}
inv(a) {
if (!a) throw new Error("Division by zero");
let t = this.zero;
let r = this.p;
let newt = this.one;
let newr = a % this.p;
while (newr) {
let q = r/newr;
[t, newt] = [newt, t-q*newt];
[r, newr] = [newr, r-q*newr];
}
if (t<this.zero) t += this.p;
return t;
}
mod(a, b) {
return a % b;
}
pow(b, e) {
return exp(this, b, e);
}
exp(b, e) {
return exp(this, b, e);
}
band(a, b) {
const res = ((a & b) & this.mask);
return res >= this.p ? res-this.p : res;
}
bor(a, b) {
const res = ((a | b) & this.mask);
return res >= this.p ? res-this.p : res;
}
bxor(a, b) {
const res = ((a ^ b) & this.mask);
return res >= this.p ? res-this.p : res;
}
bnot(a) {
const res = a ^ this.mask;
return res >= this.p ? res-this.p : res;
}
shl(a, b) {
if (Number(b) < this.bitLength) {
const res = (a << b) & this.mask;
return res >= this.p ? res-this.p : res;
} else {
const nb = this.p - b;
if (Number(nb) < this.bitLength) {
return a >> nb;
} else {
return this.zero;
}
}
}
shr(a, b) {
if (Number(b) < this.bitLength) {
return a >> b;
} else {
const nb = this.p - b;
if (Number(nb) < this.bitLength) {
const res = (a << nb) & this.mask;
return res >= this.p ? res-this.p : res;
} else {
return 0;
}
}
}
land(a, b) {
return (a && b) ? this.one : this.zero;
}
lor(a, b) {
return (a || b) ? this.one : this.zero;
}
lnot(a) {
return (a) ? this.zero : this.one;
}
sqrt_old(n) {
if (n == this.zero) return this.zero;
// Test that have solution
const res = this.pow(n, this.negone >> this.one);
if ( res != this.one ) return null;
let m = this.s;
let c = this.nqr_to_t;
let t = this.pow(n, this.t);
let r = this.pow(n, this.add(this.t, this.one) >> this.one );
while ( t != this.one ) {
let sq = this.square(t);
let i = 1;
while (sq != this.one ) {
i++;
sq = this.square(sq);
}
// b = c ^ m-i-1
let b = c;
for (let j=0; j< m-i-1; j ++) b = this.square(b);
m = i;
c = this.square(b);
t = this.mul(t, c);
r = this.mul(r, b);
}
if (r > (this.p >> this.one)) {
r = this.neg(r);
}
return r;
}
normalize(a, b) {
a = BigInt(a,b);
if (a < 0) {
let na = -a;
if (na >= this.p) na = na % this.p;
return this.p - na;
} else {
return (a>= this.p) ? a%this.p : a;
}
}
random() {
const nBytes = (this.bitLength*2 / 8);
let res =this.zero;
for (let i=0; i<nBytes; i++) {
res = (res << BigInt(8)) + BigInt(getRandomBytes(1)[0]);
}
return res % this.p;
}
toString(a, base) {
base = base || 10;
let vs;
if ((a > this.half)&&(base == 10)) {
const v = this.p-a;
vs = "-"+v.toString(base);
} else {
vs = a.toString(base);
}
return vs;
}
isZero(a) {
return a == this.zero;
}
fromRng(rng) {
let v;
do {
v=this.zero;
for (let i=0; i<this.n64; i++) {
v += rng.nextU64() << BigInt(64 *i);
}
v &= this.mask;
} while (v >= this.p);
v = (v * this.Ri) % this.p; // Convert from montgomery
return v;
}
fft(a) {
return this.FFT.fft(a);
}
ifft(a) {
return this.FFT.ifft(a);
}
// Returns a buffer with Little Endian Representation
toRprLE(buff, o, e) {
toRprLE(buff, o, e, this.n64*8);
}
// Returns a buffer with Big Endian Representation
toRprBE(buff, o, e) {
toRprBE(buff, o, e, this.n64*8);
}
// Returns a buffer with Big Endian Montgomery Representation
toRprBEM(buff, o, e) {
return this.toRprBE(buff, o, this.mul(this.R, e));
}
toRprLEM(buff, o, e) {
return this.toRprLE(buff, o, this.mul(this.R, e));
}
// Pases a buffer with Little Endian Representation
fromRprLE(buff, o) {
return fromRprLE(buff, o, this.n8);
}
// Pases a buffer with Big Endian Representation
fromRprBE(buff, o) {
return fromRprBE(buff, o, this.n8);
}
fromRprLEM(buff, o) {
return this.mul(this.fromRprLE(buff, o), this.Ri);
}
fromRprBEM(buff, o) {
return this.mul(this.fromRprBE(buff, o), this.Ri);
}
toObject(a) {
return a;
}
}
/*
Copyright 2018 0kims association.
This file is part of snarkjs.
snarkjs is a free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
snarkjs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/
class F2Field {
constructor(F, nonResidue) {
this.type="F2";
this.F = F;
this.zero = [this.F.zero, this.F.zero];
this.one = [this.F.one, this.F.zero];
this.negone = this.neg(this.one);
this.nonResidue = nonResidue;
this.m = F.m*2;
this.p = F.p;
this.n64 = F.n64*2;
this.n32 = this.n64*2;
this.n8 = this.n64*8;
buildSqrt(this);
}
_mulByNonResidue(a) {
return this.F.mul(this.nonResidue, a);
}
copy(a) {
return [this.F.copy(a[0]), this.F.copy(a[1])];
}
add(a, b) {
return [
this.F.add(a[0], b[0]),
this.F.add(a[1], b[1])
];
}
double(a) {
return this.add(a,a);
}
sub(a, b) {
return [
this.F.sub(a[0], b[0]),
this.F.sub(a[1], b[1])
];
}
neg(a) {
return this.sub(this.zero, a);
}
conjugate(a) {
return [
a[0],
this.F.neg(a[1])
];
}
mul(a, b) {
const aA = this.F.mul(a[0] , b[0]);
const bB = this.F.mul(a[1] , b[1]);
return [
this.F.add( aA , this._mulByNonResidue(bB)),
this.F.sub(
this.F.mul(
this.F.add(a[0], a[1]),
this.F.add(b[0], b[1])),
this.F.add(aA, bB))];
}
inv(a) {
const t0 = this.F.square(a[0]);
const t1 = this.F.square(a[1]);
const t2 = this.F.sub(t0, this._mulByNonResidue(t1));
const t3 = this.F.inv(t2);
return [
this.F.mul(a[0], t3),
this.F.neg(this.F.mul( a[1], t3)) ];
}
div(a, b) {
return this.mul(a, this.inv(b));
}
square(a) {
const ab = this.F.mul(a[0] , a[1]);
/*
[
(a + b) * (a + non_residue * b) - ab - non_residue * ab,
ab + ab
];
*/
return [
this.F.sub(
this.F.mul(
this.F.add(a[0], a[1]) ,
this.F.add(
a[0] ,
this._mulByNonResidue(a[1]))),
this.F.add(
ab,
this._mulByNonResidue(ab))),
this.F.add(ab, ab)
];
}
isZero(a) {
return this.F.isZero(a[0]) && this.F.isZero(a[1]);
}
eq(a, b) {
return this.F.eq(a[0], b[0]) && this.F.eq(a[1], b[1]);
}
mulScalar(base, e) {
return mulScalar(this, base, e);
}
pow(base, e) {
return exp(this, base, e);
}
exp(base, e) {
return exp(this, base, e);
}
toString(a) {
return `[ ${this.F.toString(a[0])} , ${this.F.toString(a[1])} ]`;
}
fromRng(rng) {
const c0 = this.F.fromRng(rng);
const c1 = this.F.fromRng(rng);
return [c0, c1];
}
gt(a, b) {
if (this.F.gt(a[0], b[0])) return true;
if (this.F.gt(b[0], a[0])) return false;
if (this.F.gt(a[1], b[1])) return true;
return false;
}
geq(a, b) {
return this.gt(a, b) || this.eq(a, b);
}
lt(a, b) {
return !this.geq(a,b);
}
leq(a, b) {
return !this.gt(a,b);
}
neq(a, b) {
return !this.eq(a,b);
}
random() {
return [this.F.random(), this.F.random()];
}
toRprLE(buff, o, e) {
this.F.toRprLE(buff, o, e[0]);
this.F.toRprLE(buff, o+this.F.n8, e[1]);
}
toRprBE(buff, o, e) {
this.F.toRprBE(buff, o, e[1]);
this.F.toRprBE(buff, o+this.F.n8, e[0]);
}
toRprLEM(buff, o, e) {
this.F.toRprLEM(buff, o, e[0]);
this.F.toRprLEM(buff, o+this.F.n8, e[1]);
}
toRprBEM(buff, o, e) {
this.F.toRprBEM(buff, o, e[1]);
this.F.toRprBEM(buff, o+this.F.n8, e[0]);
}
fromRprLE(buff, o) {
o = o || 0;
const c0 = this.F.fromRprLE(buff, o);
const c1 = this.F.fromRprLE(buff, o+this.F.n8);
return [c0, c1];
}
fromRprBE(buff, o) {
o = o || 0;
const c1 = this.F.fromRprBE(buff, o);
const c0 = this.F.fromRprBE(buff, o+this.F.n8);
return [c0, c1];
}
fromRprLEM(buff, o) {
o = o || 0;
const c0 = this.F.fromRprLEM(buff, o);
const c1 = this.F.fromRprLEM(buff, o+this.F.n8);
return [c0, c1];
}
fromRprBEM(buff, o) {
o = o || 0;
const c1 = this.F.fromRprBEM(buff, o);
const c0 = this.F.fromRprBEM(buff, o+this.F.n8);
return [c0, c1];
}
toObject(a) {
return a;
}
}
/*
Copyright 2018 0kims association.
This file is part of snarkjs.
snarkjs is a free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
snarkjs is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
more details.
You should have received a copy of the GNU General Public License along with
snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/
class F3Field {
constructor(F, nonResidue) {
this.type="F3";
this.F = F;
this.zero = [this.F.zero, this.F.zero, this.F.zero];
this.one = [this.F.one, this.F.zero, this.F.zero];