g1 curve done

This commit is contained in:
Jordi Baylina 2018-08-10 23:57:35 +02:00
parent 6a02f83d41
commit 91fbc8ea2d
No known key found for this signature in database
GPG Key ID: 7480C80C1BE43112
3 changed files with 138 additions and 14 deletions

5
package-lock.json generated

@ -111,6 +111,11 @@
"resolved": "https://registry.npmjs.org/balanced-match/-/balanced-match-1.0.0.tgz",
"integrity": "sha1-ibTRmasr7kneFk6gK4nORi1xt2c="
},
"big-integer": {
"version": "1.6.34",
"resolved": "https://registry.npmjs.org/big-integer/-/big-integer-1.6.34.tgz",
"integrity": "sha512-+w6B0Uo0ZvTSzDkXjoBCTNK0oe+aVL+yPi7kwGZm8hd8+Nj1AFPoxoq1Bl/mEu/G/ivOkUc1LRqVR0XeWFUzuA=="
},
"brace-expansion": {
"version": "1.1.11",
"resolved": "https://registry.npmjs.org/brace-expansion/-/brace-expansion-1.1.11.tgz",

@ -18,6 +18,7 @@
"author": "Jordi Baylina",
"license": "GPL-3.0",
"dependencies": {
"big-integer": "^1.6.34",
"eslint": "^5.3.0"
},
"devDependencies": {

@ -1,29 +1,147 @@
const bigInt = require("big-integer");
const ZnField = require("./znfield.js");
const q = new bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
module.eports = class G1Curve {
constructor() {
this.F = new ZnField(bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583"));
this.g = [
];
this.g = [ bigInt(1), bigInt(2), bigInt(1) ];
this.zero = [ bigInt(0), bigInt(1), bigInt(0) ];
}
isZero(p) {
return p[2].isZero();
}
add(p1, p2) {
// TODO
throw new Error("Not Implementted");
if (this.isZero(p1)) return p2;
if (this.isZero(p2)) return p1;
const res = new Array(3);
const Z1Z1 = p1[2].square().mod(q);
const Z2Z2 = p2[2].square().mod(q);
const U1 = p1[0].times(Z2Z2).mod(q);
const U2 = p2[0].times(Z1Z1).mod(q);
const Z1_cubed = p1[2].times(Z1Z1).mod(q);
const Z2_cubed = p2[2].times(Z2Z2).mod(q);
const S1 = p1[1].times(Z2_cubed).mod(q);
const S2 = p2[1].times(Z1_cubed).mod(q);
if (U1.equals(U2) && (S1.equals(S2))) {
return this.double(p1);
}
let H = U2.minus(U1);
if (H.isNegative()) H = H.add(q);
let S2_minus_S1 = S2.minus(S1);
if (S2_minus_S1.isNegative()) S2_minus_S1 = S2_minus_S1.add(q);
const I = H.add(H).square().mod(q);
const J = H.times(I).mod(q);
const r = S2_minus_S1.add(S2_minus_S1);
const V = U1.times(I).mod(q);
res[0] = r.square().minus(J).minus(V).minus(V).mod(q);
if (res[0].isNegative()) res[0] = res[0].add(q);
const S1_J = S1.times(J).mod(q);
res[1] = r.times(V.minus(res[0])).minus(S1_J).minus(S1_J).mod(q);
if (res[1].isNegative()) res[1] = res[1].add(q);
res[2] = p1[2].add(p2[2]).square().minus(Z1Z1).minus(Z2Z2).mod(q);
res[2] = res[2].times(H).mod(q);
if (res[2].isNegative()) res[2] = res[2].add(q);
return res;
}
double(p1) {
// TODO
throw new Error("Not Implementted");
double(p) {
const res = new Array(3);
if (this.isZero(p)) return p;
const A = p[0].square().mod(q);
const B = p[1].square().mod(q);
const C = B.square().mod(q);
let D = p[0].add(B).square().minus(A).minus(C);
D = D.add(D);
const E = A.times(3);
const F = E.square();
res[0] = F.minus(D).minus(D).mod(q);
if (res[0].isNegative()) res[0] = res[0].add(q);
const eightC = C.times(8);
res[1] = E.times(D.minus(res[0])).minus(eightC).mod(q);
if (res[1].isNegative()) res[1] = res[1].add(q);
const Y1Z1 = p[1].times(p[2]);
res[2] = Y1Z1.add(Y1Z1).mod(q);
return res;
}
mulEscalar(p1, e) {
// TODO
throw new Error("Not Implementted");
toAffineCoordinates(p) {
if (this.isZero(p)) {
return this.zero;
} else {
const Z_inv = p[2].modInv(q);
const Z2_inv = Z_inv.square().mod(q);
const Z3_inv = Z2_inv.times(Z_inv).mod(q);
const res = new Array(3);
res[0] = p[0].times(Z2_inv).mod(q);
res[1] = p[1].times(Z3_inv).mod(q);
res[2] = bigInt(1);
return res;
}
}
mulEscalar(base, e) {
let res = this.zero;
let rem = e;
let exp = base;
while (! rem.isZero()) {
if (rem.isOdd()) {
res = this.add(res, exp);
}
exp = this.double(exp);
rem = rem.shiftRight(1);
}
return res;
}
};
const G1 = new module.eports();
const r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
// const np = G1.mulEscalar(G1.g, bigInt(2));
const np = G1.mulEscalar(G1.g, r.add(1));
const p = G1.toAffineCoordinates(np);
/*
const np2 = G1.add(G1.g, G1.g);
const np3 = G1.add(G1.g, np2);
const p = G1.toAffineCoordinates(np3);
*/
console.log(p[0].toString() + ", " + p[1].toString() + ", " + p[2].toString());