@kotevode/ffjavascript
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Finite Field Library in Javascript
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JavaScript
/*
Copyright 2018 0kims association.
This file is part of zksnark JavaScript library.
zksnark JavaScript library 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.
zksnark JavaScript library 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
zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
*/
import * as chai from "chai";
import * as Scalar from "../src/scalar.js";
import PolField from "../src/polfield.js";
import ZqField from "../src/f1field.js";
const assert = chai.assert;
const r = Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617");
describe("Polynomial field", () => {
it("Should compute a multiplication", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(1), PF.F.e(2), PF.F.e(3)];
const b = [PF.F.e(1), PF.F.e(2), PF.F.e(3)];
const res = PF.mul(a,b);
assert(PF.eq(res, [PF.F.e(1), PF.F.e(4), PF.F.e(10), PF.F.e(12), PF.F.e(9)]));
});
it("Should compute a multiplication 2", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(5), PF.F.e(1)];
const b = [PF.F.e(-5), PF.F.e(1)];
const res = PF.mul(a,b);
assert(PF.eq(res, [PF.F.e(-25), PF.F.e(0), PF.F.e(1)]));
});
it("Should compute an addition", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(5), PF.F.e(1)];
const b = [PF.F.e(-5), PF.F.e(1)];
const res = PF.add(a,b);
assert(PF.eq(res, [PF.F.e(0), PF.F.e(2)]));
});
it("Should compute a substraction", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(5), PF.F.e(3), PF.F.e(4)];
const b = [PF.F.e(5), PF.F.e(1)];
const res = PF.sub(a,b);
assert(PF.eq(res, [PF.F.e(0), PF.F.e(2), PF.F.e(4)]));
});
it("Should compute reciprocal", () => {
const PF = new PolField(new ZqField(r));
const a = PF.normalize([PF.F.e(4), PF.F.e(1), PF.F.e(-3), PF.F.e(-1), PF.F.e(2),PF.F.e(1), PF.F.e(-1), PF.F.e(1)]);
const res = PF._reciprocal(a, 3, 0);
assert(PF.eq(res, PF.normalize([PF.F.e(12), PF.F.e(15), PF.F.e(3), PF.F.e(-4), PF.F.e(-3), PF.F.e(0), PF.F.e(1), PF.F.e(1)])));
});
it("Should div2", () => {
const PF = new PolField(new ZqField(r));
// x^6
const a = [PF.F.e(0), PF.F.e(0), PF.F.e(0), PF.F.e(0), PF.F.e(0),PF.F.e(0), PF.F.e(1)];
// x^5
const b = [PF.F.e(0), PF.F.e(0), PF.F.e(0), PF.F.e(0), PF.F.e(0), PF.F.e(1)];
const res = PF._div2(6, b);
assert(PF.eq(res, [PF.F.e(0), PF.F.e(1)]));
const res2 = PF.div(a,b);
assert(PF.eq(res2, [PF.F.e(0), PF.F.e(1)]));
});
it("Should div", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(1), PF.F.e(2), PF.F.e(3), PF.F.e(4), PF.F.e(5),PF.F.e(6), PF.F.e(7)];
const b = [PF.F.e(8), PF.F.e(9), PF.F.e(10), PF.F.e(11), PF.F.e(12), PF.F.e(13)];
const c = PF.mul(a,b);
const d = PF.div(c,b);
assert(PF.eq(a, d));
});
it("Should div big/small", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(1), PF.F.e(2), PF.F.e(3), PF.F.e(4), PF.F.e(5),PF.F.e(6), PF.F.e(7)];
const b = [PF.F.e(8), PF.F.e(9)];
const c = PF.mul(a,b);
const d = PF.div(c,b);
assert(PF.eq(a, d));
});
it("Should div random big", () => {
const PF = new PolField(new ZqField(r));
let a = [];
let b = [];
for (let i=0; i<1000; i++) a.push(PF.F.e(Math.floor(Math.random()*100000) -500000));
for (let i=0; i<900; i++) b.push(PF.F.e(Math.floor(Math.random()*100000) -500000));
a = PF.normalize(a);
b = PF.normalize(a);
const c = PF.mul(a,b);
const d = PF.div(c,b);
assert(PF.eq(a, d));
}).timeout(10000);
it("Should evaluate and zero", () => {
const PF = new PolField(new ZqField(r));
const p = [PF.F.neg(PF.F.e(2)), PF.F.e(1)];
const v = PF.evaluate(p, PF.F.e(2));
assert(PF.F.eq(v, PF.F.e(0)));
});
it("Should evaluate bigger number", () => {
const PF = new PolField(new ZqField(r));
const p = [PF.F.e(1), PF.F.e(2), PF.F.e(3)];
const v = PF.evaluate(p, PF.F.e(2));
assert(PF.F.eq(v, PF.F.e(17)));
});
it("Should create lagrange polynomial minmal", () => {
const PF = new PolField(new ZqField(r));
const points=[];
points.push([PF.F.e(1), PF.F.e(1)]);
points.push([PF.F.e(2), PF.F.e(2)]);
points.push([PF.F.e(3), PF.F.e(5)]);
const p=PF.lagrange(points);
for (let i=0; i<points.length; i++) {
const v = PF.evaluate(p, points[i][0]);
assert(PF.F.eq(v, points[i][1]));
}
});
it("Should create lagrange polynomial", () => {
const PF = new PolField(new ZqField(r));
const points=[];
points.push([PF.F.e(1), PF.F.e(2)]);
points.push([PF.F.e(2), PF.F.e(-2)]);
points.push([PF.F.e(3), PF.F.e(0)]);
points.push([PF.F.e(4), PF.F.e(453345)]);
const p=PF.lagrange(points);
for (let i=0; i<points.length; i++) {
const v = PF.evaluate(p, points[i][0]);
assert(PF.F.eq(v, points[i][1]));
}
});
it("Should test ruffini", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(1), PF.F.e(2), PF.F.e(3), PF.F.e(4), PF.F.e(5),PF.F.e(6), PF.F.e(7)];
const b = PF.mul(a, [PF.F.e(-7), PF.F.e(1)]);
const c = PF.ruffini(b, PF.F.e(7));
assert(PF.eq(a, c));
});
it("Should test roots", () => {
const PF = new PolField(new ZqField(r));
let rt;
rt = PF.oneRoot(256, 16);
for (let i=0; i<8; i++) {
rt = PF.F.mul(rt, rt);
}
assert(PF.F.eq(rt, PF.F.one));
rt = PF.oneRoot(256, 15);
for (let i=0; i<8; i++) {
rt = PF.F.mul(rt, rt);
}
assert(PF.F.eq(rt, PF.F.one));
rt = PF.oneRoot(8, 3);
for (let i=0; i<3; i++) {
rt = PF.F.mul(rt, rt);
}
assert(PF.F.eq(rt, PF.F.one));
rt = PF.oneRoot(8, 0);
assert(PF.F.eq(rt, PF.F.one));
});
it("Should create a polynomial with values at roots with fft", () => {
const PF = new PolField(new ZqField(r));
const a = [PF.F.e(1), PF.F.e(2), PF.F.e(3), PF.F.e(4), PF.F.e(5),PF.F.e(6), PF.F.e(7)];
const p = PF.ifft(a);
for (let i=0; i<a.length; i++) {
const s = PF.evaluate(p, PF.oneRoot(8,i));
assert(PF.F.eq(s, a[i]));
}
});
});