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128 lines
3.2 KiB
128 lines
3.2 KiB
const F1Field = require("ffjavascript").F1Field;
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const Scalar = require("ffjavascript").Scalar;
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const utils = require("ffjavascript").utils;
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exports.addPoint = addPoint;
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exports.mulPointEscalar = mulPointEscalar;
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exports.inCurve = inCurve;
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exports.inSubgroup = inSubgroup;
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exports.packPoint = packPoint;
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exports.unpackPoint = unpackPoint;
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exports.p = Scalar.fromString("21888242871839275222246405745257275088548364400416034343698204186575808495617");
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const F = new F1Field(exports.p);
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exports.F = F;
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exports.Generator = [
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F.e("995203441582195749578291179787384436505546430278305826713579947235728471134"),
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F.e("5472060717959818805561601436314318772137091100104008585924551046643952123905")
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];
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exports.Base8 = [
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F.e("5299619240641551281634865583518297030282874472190772894086521144482721001553"),
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F.e("16950150798460657717958625567821834550301663161624707787222815936182638968203")
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];
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exports.order = Scalar.fromString("21888242871839275222246405745257275088614511777268538073601725287587578984328");
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exports.subOrder = Scalar.shiftRight(exports.order, 3);
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exports.A = F.e("168700");
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exports.D = F.e("168696");
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function addPoint(a,b) {
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const res = [];
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/* does the equivalent of:
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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);
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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);
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*/
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const beta = F.mul(a[0],b[1]);
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const gamma = F.mul(a[1],b[0]);
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const delta = F.mul(
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F.sub(a[1], F.mul(exports.A, a[0])),
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F.add(b[0], b[1])
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);
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const tau = F.mul(beta, gamma);
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const dtau = F.mul(exports.D, tau);
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res[0] = F.div(
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F.add(beta, gamma),
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F.add(F.one, dtau)
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);
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res[1] = F.div(
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F.add(delta, F.sub(F.mul(exports.A,beta), gamma)),
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F.sub(F.one, dtau)
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);
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return res;
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}
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function mulPointEscalar(base, e) {
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let res = [F.e("0"),F.e("1")];
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let rem = e;
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let exp = base;
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while (! Scalar.isZero(rem)) {
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if (Scalar.isOdd(rem)) {
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res = addPoint(res, exp);
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}
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exp = addPoint(exp, exp);
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rem = Scalar.shiftRight(rem, 1);
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}
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return res;
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}
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function inSubgroup(P) {
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if (!inCurve(P)) return false;
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const res= mulPointEscalar(P, exports.subOrder);
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return (F.isZero(res[0]) && F.eq(res[1], F.one));
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}
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function inCurve(P) {
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const x2 = F.square(P[0]);
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const y2 = F.square(P[1]);
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if (!F.eq(
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F.add(F.mul(exports.A, x2), y2),
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F.add(F.one, F.mul(F.mul(x2, y2), exports.D)))) return false;
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return true;
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}
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function packPoint(P) {
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const buff = utils.leInt2Buff(P[1], 32);
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if (F.lt(P[0], F.zero)) {
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buff[31] = buff[31] | 0x80;
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}
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return buff;
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}
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function unpackPoint(_buff) {
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const buff = Buffer.from(_buff);
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let sign = false;
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const P = new Array(2);
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if (buff[31] & 0x80) {
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sign = true;
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buff[31] = buff[31] & 0x7F;
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}
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P[1] = utils.leBuff2int(buff);
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if (Scalar.gt(P[1], exports.p)) return null;
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const y2 = F.square(P[1]);
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let x = F.sqrt(F.div(
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F.sub(F.one, y2),
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F.sub(exports.A, F.mul(exports.D, y2))));
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if (x == null) return null;
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if (sign) x = F.neg(x);
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P[0] = x;
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return P;
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}
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