js-ecutils
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JavaScript Library for Elliptic Curve Cryptography: key exchanges (Diffie-Hellman, Massey-Omura), ECDSA signatures, and Koblitz encoding. Suitable for crypto education and secure systems.
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JavaScript
"use strict";
var _globals = require("@jest/globals");
var _point = require("./core/point");
var _curve = require("./core/curve");
var _math = require("./utils/math");
function _slicedToArray(r, e) { return _arrayWithHoles(r) || _iterableToArrayLimit(r, e) || _unsupportedIterableToArray(r, e) || _nonIterableRest(); }
function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }
function _unsupportedIterableToArray(r, a) { if (r) { if ("string" == typeof r) return _arrayLikeToArray(r, a); var t = {}.toString.call(r).slice(8, -1); return "Object" === t && r.constructor && (t = r.constructor.name), "Map" === t || "Set" === t ? Array.from(r) : "Arguments" === t || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(t) ? _arrayLikeToArray(r, a) : void 0; } }
function _arrayLikeToArray(r, a) { (null == a || a > r.length) && (a = r.length); for (var e = 0, n = Array(a); e < a; e++) n[e] = r[e]; return n; }
function _iterableToArrayLimit(r, l) { var t = null == r ? null : "undefined" != typeof Symbol && r[Symbol.iterator] || r["@@iterator"]; if (null != t) { var e, n, i, u, a = [], f = !0, o = !1; try { if (i = (t = t.call(r)).next, 0 === l) { if (Object(t) !== t) return; f = !1; } else for (; !(f = (e = i.call(t)).done) && (a.push(e.value), a.length !== l); f = !0); } catch (r) { o = !0, n = r; } finally { try { if (!f && null != t["return"] && (u = t["return"](), Object(u) !== u)) return; } finally { if (o) throw n; } } return a; } }
function _arrayWithHoles(r) { if (Array.isArray(r)) return r; }
// ---------------------------------------------------------------------------
// Educational examples on small curves
//
// These tests use "toy" curves with small primes to illustrate elliptic
// curve concepts with values that can be verified by hand.
// ---------------------------------------------------------------------------
// ---------------------------------------------------------------------------
// E: y² = x³ + x + 1 over F₂₃ (n = 28, cofactor h = 1)
//
// Points used:
// P = (0, 1) — satisfies 1² ≡ 0³ + 0 + 1 ≡ 1 (mod 23) ✓
// Q = (6, 19) — satisfies 19² = 361 ≡ 16 ≡ 6³ + 6 + 1 = 223 ≡ 16 (mod 23) ✓
//
// Hand-calculated results:
// P + Q: λ = (19-1)·(6-0)⁻¹ = 18·4 = 72 ≡ 3 (mod 23)
// x₃ = 3² - 0 - 6 = 3 (mod 23)
// y₃ = 3·(0-3) - 1 = -10 ≡ 13 (mod 23)
// → (3, 13)
//
// 2·P: λ = (3·0²+1)·(2·1)⁻¹ = 1·12 = 12 (mod 23)
// x₃ = 12² - 0 = 144 ≡ 6 (mod 23)
// y₃ = 12·(0-6) - 1 = -73 ≡ 19 (mod 23)
// → (6, 19)
//
// -P: (0, -1 mod 23) = (0, 22)
// ---------------------------------------------------------------------------
(0, _globals.describe)('Educational: E/F₂₃ y² = x³ + x + 1', function () {
var curve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n,
coord: _curve.CoordinateSystem.AFFINE
});
var P = new _point.Point(0n, 1n, curve);
var Q = new _point.Point(6n, 19n, curve);
(0, _globals.test)('P(0,1) + Q(6,19) = (3, 13)', function () {
var R = P.add(Q);
(0, _globals.expect)(R.x).toBe(3n);
(0, _globals.expect)(R.y).toBe(13n);
});
(0, _globals.test)('2·P(0,1) = (6, 19)', function () {
var R = P.mul(2n);
(0, _globals.expect)(R.x).toBe(6n);
(0, _globals.expect)(R.y).toBe(19n);
});
(0, _globals.test)('3·P = 2·P + P (scalar multiplication consistency)', function () {
var R2 = P.mul(2n);
var R3manual = R2.add(P);
var R3 = P.mul(3n);
(0, _globals.expect)(R3.x).toBe(R3manual.x);
(0, _globals.expect)(R3.y).toBe(R3manual.y);
});
(0, _globals.test)('28·P = O (n·P is the identity)', function () {
(0, _globals.expect)(P.mul(28n).isIdentity).toBe(true);
});
(0, _globals.test)('P + (-P) = O (additive inverse)', function () {
(0, _globals.expect)(P.add(P.neg()).isIdentity).toBe(true);
});
(0, _globals.test)('-P(0,1) = (0, 22)', function () {
var neg = P.neg();
(0, _globals.expect)(neg.x).toBe(0n);
(0, _globals.expect)(neg.y).toBe(22n);
});
});
// ---------------------------------------------------------------------------
// E: y² = x³ + 2 over F₇ (n = 9, cofactor h = 1)
//
// Known points:
// (0, 3): 3² = 9 ≡ 2 ≡ 0³ + 2 (mod 7) ✓
// (0, 4): 4² = 16 ≡ 2 ≡ 0³ + 2 (mod 7) ✓
// (3, 1): 1² = 1 ≡ 3³ + 2 = 29 ≡ 1 (mod 7) ✓
// ---------------------------------------------------------------------------
(0, _globals.describe)('Educational: E/F₇ y² = x³ + 2', function () {
var curve = new _curve.CurveParams({
p: 7n,
a: 0n,
b: 2n,
n: 9n,
h: 1n,
coord: _curve.CoordinateSystem.AFFINE
});
(0, _globals.test)('(0,3) and (0,4) lie on the curve', function () {
(0, _globals.expect)(new _point.Point(0n, 3n, curve).isOnCurve()).toBe(true);
(0, _globals.expect)(new _point.Point(0n, 4n, curve).isOnCurve()).toBe(true);
});
(0, _globals.test)('point addition produces a valid curve point', function () {
var P = new _point.Point(0n, 3n, curve);
var Q = new _point.Point(3n, 1n, curve);
var R = P.add(Q);
(0, _globals.expect)(R.isOnCurve() || R.isIdentity).toBe(true);
});
});
// ---------------------------------------------------------------------------
// Quadratic residues and point compression (educational)
//
// Point compression stores (x, parity_of_y) instead of (x, y).
// Decompression recovers y by computing √(x³ + ax + b) mod p and
// selecting the root matching the parity bit.
// ---------------------------------------------------------------------------
(0, _globals.describe)('Educational: quadratic residues and point compression', function () {
// QR(F₂₃) = {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18}
(0, _globals.test)('QR set of F₂₃ matches expected values', function () {
var expectedQR = new Set([1n, 2n, 3n, 4n, 6n, 8n, 9n, 12n, 13n, 16n, 18n]);
for (var a = 1n; a < 23n; a++) {
(0, _globals.expect)((0, _math.isQuadraticResidue)(a, 23n)).toBe(expectedQR.has(a));
}
});
// √4 mod 23: r² ≡ 4 (mod 23) → r ∈ {2, 21}
(0, _globals.test)('√4 mod 23 equals 2 or 21', function () {
var r = (0, _math.modularSqrt)(4n, 23n);
(0, _globals.expect)([2n, 21n]).toContain(r);
(0, _globals.expect)(r * r % 23n).toBe(4n);
});
// compress → (x, parity), decompress → Point(x, y)
(0, _globals.test)('compress/decompress roundtrip on Z₂₃ curve', function () {
var curve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n
});
var P = new _point.Point(0n, 1n, curve);
var _P$compress = P.compress(),
_P$compress2 = _slicedToArray(_P$compress, 2),
x = _P$compress2[0],
parity = _P$compress2[1];
var recovered = _point.Point.decompress(x, parity, curve);
(0, _globals.expect)(recovered.x).toBe(P.x);
(0, _globals.expect)(recovered.y).toBe(P.y);
});
});
// ---------------------------------------------------------------------------
// Jacobian vs Affine arithmetic (educational)
//
// Jacobian coordinates (X, Y, Z) avoid modular inversions during
// intermediate operations, converting back only at the end:
// x = X / Z², y = Y / Z³
//
// Both coordinate systems must produce identical affine results.
// ---------------------------------------------------------------------------
(0, _globals.describe)('Educational: Jacobian vs Affine arithmetic', function () {
(0, _globals.test)('addition gives the same result in both coordinate systems', function () {
var affineCurve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n,
coord: _curve.CoordinateSystem.AFFINE
});
var jacobianCurve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n,
coord: _curve.CoordinateSystem.JACOBIAN
});
var Pa = new _point.Point(0n, 1n, affineCurve);
var Qa = new _point.Point(6n, 19n, affineCurve);
var Ra = Pa.add(Qa);
var Pj = new _point.Point(0n, 1n, jacobianCurve);
var Qj = new _point.Point(6n, 19n, jacobianCurve);
var Rj = Pj.add(Qj);
(0, _globals.expect)(Ra.x).toBe(Rj.x);
(0, _globals.expect)(Ra.y).toBe(Rj.y);
});
(0, _globals.test)('scalar multiplication gives the same result for k ∈ {2, 5, 13, 27}', function () {
var affineCurve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n,
coord: _curve.CoordinateSystem.AFFINE
});
var jacobianCurve = new _curve.CurveParams({
p: 23n,
a: 1n,
b: 1n,
n: 28n,
h: 1n,
coord: _curve.CoordinateSystem.JACOBIAN
});
var Pa = new _point.Point(0n, 1n, affineCurve);
var Pj = new _point.Point(0n, 1n, jacobianCurve);
for (var _i = 0, _arr = [2n, 5n, 13n, 27n]; _i < _arr.length; _i++) {
var k = _arr[_i];
var Ra = Pa.mul(k);
var Rj = Pj.mul(k);
(0, _globals.expect)(Ra.x).toBe(Rj.x);
(0, _globals.expect)(Ra.y).toBe(Rj.y);
}
});
});
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'@jest/globals'\nimport { Point } from './core/point'\nimport { CurveParams, CoordinateSystem } from './core/curve'\nimport { isQuadraticResidue, modularSqrt } from './utils/math'\n\n// ---------------------------------------------------------------------------\n// Educational examples on small curves\n//\n// These tests use \"toy\" curves with small primes to illustrate elliptic\n// curve concepts with values that can be verified by hand.\n// ---------------------------------------------------------------------------\n\n// ---------------------------------------------------------------------------\n// E: y² = x³ + x + 1  over F₂₃   (n = 28, cofactor h = 1)\n//\n// Points used:\n//   P = (0, 1)    — satisfies 1² ≡ 0³ + 0 + 1 ≡ 1 (mod 23) ✓\n//   Q = (6, 19)   — satisfies 19² = 361 ≡ 16 ≡ 6³ + 6 + 1 = 223 ≡ 16 (mod 23) ✓\n//\n// Hand-calculated results:\n//   P + Q:  λ = (19-1)·(6-0)⁻¹ = 18·4 = 72 ≡ 3 (mod 23)\n//           x₃ = 3² - 0 - 6 = 3 (mod 23)\n//           y₃ = 3·(0-3) - 1 = -10 ≡ 13 (mod 23)\n//           → (3, 13)\n//\n//   2·P:    λ = (3·0²+1)·(2·1)⁻¹ = 1·12 = 12 (mod 23)\n//           x₃ = 12² - 0 = 144 ≡ 6 (mod 23)\n//           y₃ = 12·(0-6) - 1 = -73 ≡ 19 (mod 23)\n//           → (6, 19)\n//\n//   -P:     (0, -1 mod 23) = (0, 22)\n// ---------------------------------------------------------------------------\n\ndescribe('Educational: E/F₂₃  y² = x³ + x + 1', () => {\n  const curve = new CurveParams({\n    p: 23n,\n    a: 1n,\n    b: 1n,\n    n: 28n,\n    h: 1n,\n    coord: CoordinateSystem.AFFINE,\n  })\n  const P = new Point(0n, 1n, curve)\n  const Q = new Point(6n, 19n, curve)\n\n  test('P(0,1) + Q(6,19) = (3, 13)', () => {\n    const R = P.add(Q)\n    expect(R.x).toBe(3n)\n    expect(R.y).toBe(13n)\n  })\n\n  test('2·P(0,1) = (6, 19)', () => {\n    const R = P.mul(2n)\n    expect(R.x).toBe(6n)\n    expect(R.y).toBe(19n)\n  })\n\n  test('3·P = 2·P + P  (scalar multiplication consistency)', () => {\n    const R2 = P.mul(2n)\n    const R3manual = R2.add(P)\n    const R3 = P.mul(3n)\n    expect(R3.x).toBe(R3manual.x)\n    expect(R3.y).toBe(R3manual.y)\n  })\n\n  test('28·P = O  (n·P is the identity)', () => {\n    expect(P.mul(28n).isIdentity).toBe(true)\n  })\n\n  test('P + (-P) = O  (additive inverse)', () => {\n    expect(P.add(P.neg()).isIdentity).toBe(true)\n  })\n\n  test('-P(0,1) = (0, 22)', () => {\n    const neg = P.neg()\n    expect(neg.x).toBe(0n)\n    expect(neg.y).toBe(22n)\n  })\n})\n\n// ---------------------------------------------------------------------------\n// E: y² = x³ + 2  over F₇   (n = 9, cofactor h = 1)\n//\n// Known points:\n//   (0, 3): 3² = 9 ≡ 2 ≡ 0³ + 2 (mod 7)  ✓\n//   (0, 4): 4² = 16 ≡ 2 ≡ 0³ + 2 (mod 7)  ✓\n//   (3, 1): 1² = 1 ≡ 3³ + 2 = 29 ≡ 1 (mod 7)  ✓\n// ---------------------------------------------------------------------------\n\ndescribe('Educational: E/F₇  y² = x³ + 2', () => {\n  const curve = new CurveParams({\n    p: 7n,\n    a: 0n,\n    b: 2n,\n    n: 9n,\n    h: 1n,\n    coord: CoordinateSystem.AFFINE,\n  })\n\n  test('(0,3) and (0,4) lie on the curve', () => {\n    expect(new Point(0n, 3n, curve).isOnCurve()).toBe(true)\n    expect(new Point(0n, 4n, curve).isOnCurve()).toBe(true)\n  })\n\n  test('point addition produces a valid curve point', () => {\n    const P = new Point(0n, 3n, curve)\n    const Q = new Point(3n, 1n, curve)\n    const R = P.add(Q)\n    expect(R.isOnCurve() || R.isIdentity).toBe(true)\n  })\n})\n\n// ---------------------------------------------------------------------------\n// Quadratic residues and point compression (educational)\n//\n// Point compression stores (x, parity_of_y) instead of (x, y).\n// Decompression recovers y by computing √(x³ + ax + b) mod p and\n// selecting the root matching the parity bit.\n// ---------------------------------------------------------------------------\n\ndescribe('Educational: quadratic residues and point compression', () => {\n  // QR(F₂₃) = {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18}\n  test('QR set of F₂₃ matches expected values', () => {\n    const expectedQR = new Set([1n, 2n, 3n, 4n, 6n, 8n, 9n, 12n, 13n, 16n, 18n])\n    for (let a = 1n; a < 23n; a++) {\n      expect(isQuadraticResidue(a, 23n)).toBe(expectedQR.has(a))\n    }\n  })\n\n  // √4 mod 23:  r² ≡ 4 (mod 23)  →  r ∈ {2, 21}\n  test('√4 mod 23 equals 2 or 21', () => {\n    const r = modularSqrt(4n, 23n)\n    expect([2n, 21n]).toContain(r)\n    expect((r * r) % 23n).toBe(4n)\n  })\n\n  // compress → (x, parity),  decompress → Point(x, y)\n  test('compress/decompress roundtrip on Z₂₃ curve', () => {\n    const curve = new CurveParams({\n      p: 23n,\n      a: 1n,\n      b: 1n,\n      n: 28n,\n      h: 1n,\n    })\n    const P = new Point(0n, 1n, curve)\n    const [x, parity] = P.compress()\n    const recovered = Point.decompress(x, parity, curve)\n    expect(recovered.x).toBe(P.x)\n    expect(recovered.y).toBe(P.y)\n  })\n})\n\n// ---------------------------------------------------------------------------\n// Jacobian vs Affine arithmetic (educational)\n//\n// Jacobian coordinates (X, Y, Z) avoid modular inversions during\n// intermediate operations, converting back only at the end:\n//   x = X / Z²,   y = Y / Z³\n//\n// Both coordinate systems must produce identical affine results.\n// ---------------------------------------------------------------------------\n\ndescribe('Educational: Jacobian vs Affine arithmetic', () => {\n  test('addition gives the same result in both coordinate systems', () => {\n    const affineCurve = new CurveParams({\n      p: 23n,\n      a: 1n,\n      b: 1n,\n      n: 28n,\n      h: 1n,\n      coord: CoordinateSystem.AFFINE,\n    })\n    const jacobianCurve = new CurveParams({\n      p: 23n,\n      a: 1n,\n      b: 1n,\n      n: 28n,\n      h: 1n,\n      coord: CoordinateSystem.JACOBIAN,\n    })\n    const Pa = new Point(0n, 1n, affineCurve)\n    const Qa = new Point(6n, 19n, affineCurve)\n    const Ra = Pa.add(Qa)\n\n    const Pj = new Point(0n, 1n, jacobianCurve)\n    const Qj = new Point(6n, 19n, jacobianCurve)\n    const Rj = Pj.add(Qj)\n\n    expect(Ra.x).toBe(Rj.x)\n    expect(Ra.y).toBe(Rj.y)\n  })\n\n  test('scalar multiplication gives the same result for k ∈ {2, 5, 13, 27}', () => {\n    const affineCurve = new CurveParams({\n      p: 23n,\n      a: 1n,\n      b: 1n,\n      n: 28n,\n      h: 1n,\n      coord: CoordinateSystem.AFFINE,\n    })\n    const jacobianCurve = new CurveParams({\n      p: 23n,\n      a: 1n,\n      b: 1n,\n      n: 28n,\n      h: 1n,\n      coord: CoordinateSystem.JACOBIAN,\n    })\n    const Pa = new Point(0n, 1n, affineCurve)\n    const Pj = new Point(0n, 1n, jacobianCurve)\n\n    for (const k of [2n, 5n, 13n, 27n]) {\n      const Ra = Pa.mul(k)\n      const Rj = Pj.mul(k)\n      expect(Ra.x).toBe(Rj.x)\n      expect(Ra.y).toBe(Rj.y)\n    }\n  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