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147 lines
3.7 KiB
147 lines
3.7 KiB
const bigInt = require("big-integer");
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const q = new bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
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module.eports = class G1Curve {
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constructor() {
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this.g = [ bigInt(1), bigInt(2), bigInt(1) ];
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this.zero = [ bigInt(0), bigInt(1), bigInt(0) ];
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}
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isZero(p) {
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return p[2].isZero();
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}
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add(p1, p2) {
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if (this.isZero(p1)) return p2;
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if (this.isZero(p2)) return p1;
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const res = new Array(3);
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const Z1Z1 = p1[2].square().mod(q);
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const Z2Z2 = p2[2].square().mod(q);
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const U1 = p1[0].times(Z2Z2).mod(q);
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const U2 = p2[0].times(Z1Z1).mod(q);
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const Z1_cubed = p1[2].times(Z1Z1).mod(q);
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const Z2_cubed = p2[2].times(Z2Z2).mod(q);
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const S1 = p1[1].times(Z2_cubed).mod(q);
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const S2 = p2[1].times(Z1_cubed).mod(q);
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if (U1.equals(U2) && (S1.equals(S2))) {
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return this.double(p1);
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}
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let H = U2.minus(U1);
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if (H.isNegative()) H = H.add(q);
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let S2_minus_S1 = S2.minus(S1);
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if (S2_minus_S1.isNegative()) S2_minus_S1 = S2_minus_S1.add(q);
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const I = H.add(H).square().mod(q);
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const J = H.times(I).mod(q);
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const r = S2_minus_S1.add(S2_minus_S1);
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const V = U1.times(I).mod(q);
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res[0] = r.square().minus(J).minus(V).minus(V).mod(q);
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if (res[0].isNegative()) res[0] = res[0].add(q);
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const S1_J = S1.times(J).mod(q);
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res[1] = r.times(V.minus(res[0])).minus(S1_J).minus(S1_J).mod(q);
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if (res[1].isNegative()) res[1] = res[1].add(q);
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res[2] = p1[2].add(p2[2]).square().minus(Z1Z1).minus(Z2Z2).mod(q);
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res[2] = res[2].times(H).mod(q);
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if (res[2].isNegative()) res[2] = res[2].add(q);
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return res;
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}
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double(p) {
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const res = new Array(3);
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if (this.isZero(p)) return p;
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const A = p[0].square().mod(q);
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const B = p[1].square().mod(q);
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const C = B.square().mod(q);
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let D = p[0].add(B).square().minus(A).minus(C);
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D = D.add(D);
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const E = A.times(3);
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const F = E.square();
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res[0] = F.minus(D).minus(D).mod(q);
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if (res[0].isNegative()) res[0] = res[0].add(q);
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const eightC = C.times(8);
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res[1] = E.times(D.minus(res[0])).minus(eightC).mod(q);
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if (res[1].isNegative()) res[1] = res[1].add(q);
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const Y1Z1 = p[1].times(p[2]);
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res[2] = Y1Z1.add(Y1Z1).mod(q);
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return res;
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}
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toAffineCoordinates(p) {
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if (this.isZero(p)) {
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return this.zero;
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} else {
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const Z_inv = p[2].modInv(q);
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const Z2_inv = Z_inv.square().mod(q);
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const Z3_inv = Z2_inv.times(Z_inv).mod(q);
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const res = new Array(3);
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res[0] = p[0].times(Z2_inv).mod(q);
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res[1] = p[1].times(Z3_inv).mod(q);
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res[2] = bigInt(1);
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return res;
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}
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}
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mulEscalar(base, e) {
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let res = this.zero;
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let rem = e;
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let exp = base;
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while (! rem.isZero()) {
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if (rem.isOdd()) {
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res = this.add(res, exp);
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}
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exp = this.double(exp);
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rem = rem.shiftRight(1);
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}
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return res;
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}
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};
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const G1 = new module.eports();
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const r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
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// const np = G1.mulEscalar(G1.g, bigInt(2));
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const np = G1.mulEscalar(G1.g, r.add(1));
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const p = G1.toAffineCoordinates(np);
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/*
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const np2 = G1.add(G1.g, G1.g);
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const np3 = G1.add(G1.g, np2);
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const p = G1.toAffineCoordinates(np3);
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*/
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console.log(p[0].toString() + ", " + p[1].toString() + ", " + p[2].toString());
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