140 lines
3.8 KiB
JavaScript
140 lines
3.8 KiB
JavaScript
import { getCurveFromName, Scalar } from "ffjavascript";
|
|
|
|
export default async function buildBabyJub() {
|
|
const bn128 = await getCurveFromName("bn128");
|
|
return new BabyJub(bn128.Fr);
|
|
}
|
|
|
|
class BabyJub {
|
|
constructor(F) {
|
|
this.F = F;
|
|
this.p = Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617");
|
|
this.pm1d2 = Scalar.div(Scalar.sub(this.p, Scalar.e(1)), Scalar.e(2));
|
|
|
|
this.Generator = [
|
|
F.e("995203441582195749578291179787384436505546430278305826713579947235728471134"),
|
|
F.e("5472060717959818805561601436314318772137091100104008585924551046643952123905")
|
|
];
|
|
this.Base8 = [
|
|
F.e("5299619240641551281634865583518297030282874472190772894086521144482721001553"),
|
|
F.e("16950150798460657717958625567821834550301663161624707787222815936182638968203")
|
|
];
|
|
this.order = Scalar.fromString("21888242871839275222246405745257275088614511777268538073601725287587578984328");
|
|
this.subOrder = Scalar.shiftRight(this.order, 3);
|
|
this.A = F.e("168700");
|
|
this.D = F.e("168696");
|
|
}
|
|
|
|
|
|
addPoint(a,b) {
|
|
const F = this.F;
|
|
|
|
const res = [];
|
|
|
|
/* does the equivalent of:
|
|
res[0] = bigInt((a[0]*b[1] + b[0]*a[1]) * bigInt(bigInt("1") + d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
|
|
res[1] = bigInt((a[1]*b[1] - cta*a[0]*b[0]) * bigInt(bigInt("1") - d*a[0]*b[0]*a[1]*b[1]).inverse(q)).affine(q);
|
|
*/
|
|
|
|
const beta = F.mul(a[0],b[1]);
|
|
const gamma = F.mul(a[1],b[0]);
|
|
const delta = F.mul(
|
|
F.sub(a[1], F.mul(this.A, a[0])),
|
|
F.add(b[0], b[1])
|
|
);
|
|
const tau = F.mul(beta, gamma);
|
|
const dtau = F.mul(this.D, tau);
|
|
|
|
res[0] = F.div(
|
|
F.add(beta, gamma),
|
|
F.add(F.one, dtau)
|
|
);
|
|
|
|
res[1] = F.div(
|
|
F.add(delta, F.sub(F.mul(this.A,beta), gamma)),
|
|
F.sub(F.one, dtau)
|
|
);
|
|
|
|
return res;
|
|
}
|
|
|
|
mulPointEscalar(base, e) {
|
|
const F = this.F;
|
|
let res = [F.e("0"),F.e("1")];
|
|
let rem = e;
|
|
let exp = base;
|
|
|
|
while (! Scalar.isZero(rem)) {
|
|
if (Scalar.isOdd(rem)) {
|
|
res = this.addPoint(res, exp);
|
|
}
|
|
exp = this.addPoint(exp, exp);
|
|
rem = Scalar.shiftRight(rem, 1);
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
inSubgroup(P) {
|
|
const F = this.F;
|
|
if (!this.inCurve(P)) return false;
|
|
const res= this.mulPointEscalar(P, this.subOrder);
|
|
return (F.isZero(res[0]) && F.eq(res[1], F.one));
|
|
}
|
|
|
|
inCurve(P) {
|
|
const F = this.F;
|
|
const x2 = F.square(P[0]);
|
|
const y2 = F.square(P[1]);
|
|
|
|
if (!F.eq(
|
|
F.add(F.mul(this.A, x2), y2),
|
|
F.add(F.one, F.mul(F.mul(x2, y2), this.D)))) return false;
|
|
|
|
return true;
|
|
}
|
|
|
|
packPoint(P) {
|
|
const F = this.F;
|
|
const buff = new Uint8Array(32);
|
|
F.toRprLE(buff, 0, P[1]);
|
|
const n = F.toObject(P[0]);
|
|
if (Scalar.gt(n, this.pm1d2)) {
|
|
buff[31] = buff[31] | 0x80;
|
|
}
|
|
return buff;
|
|
}
|
|
|
|
unpackPoint(buff) {
|
|
const F = this.F;
|
|
let sign = false;
|
|
const P = new Array(2);
|
|
if (buff[31] & 0x80) {
|
|
sign = true;
|
|
buff[31] = buff[31] & 0x7F;
|
|
}
|
|
P[1] = F.fromRprLE(buff, 0);
|
|
if (Scalar.gt(F.toObject(P[1]), this.p)) return null;
|
|
|
|
const y2 = F.square(P[1]);
|
|
|
|
const x2 = F.div(
|
|
F.sub(F.one, y2),
|
|
F.sub(this.A, F.mul(this.D, y2))
|
|
);
|
|
|
|
const x2h = F.exp(x2, F.half);
|
|
if (! F.eq(F.one, x2h)) return null;
|
|
|
|
let x = F.sqrt(x2);
|
|
|
|
if (x == null) return null;
|
|
|
|
if (sign) x = F.neg(x);
|
|
|
|
P[0] = x;
|
|
|
|
return P;
|
|
}
|
|
}
|