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
;
var _globals = require("@jest/globals");
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; }
// ---------------------------------------------------------------------------
// Modular arithmetic basics
// ---------------------------------------------------------------------------
(0, _globals.describe)('Modular arithmetic utilities', function () {
(0, _globals.test)('modulus returns non-negative result for negative dividends', function () {
(0, _globals.expect)((0, _math.modulus)(-5n, 3n)).toBe(1n);
(0, _globals.expect)((0, _math.modulus)(-1n, 7n)).toBe(6n);
(0, _globals.expect)((0, _math.modulus)(5n, 3n)).toBe(2n);
});
(0, _globals.test)('modPow with m = 1 returns 0', function () {
(0, _globals.expect)((0, _math.modPow)(5n, 3n, 1n)).toBe(0n);
});
(0, _globals.test)('modPow computes base^exp mod m correctly', function () {
// 2^10 = 1024, 1024 mod 100 = 24
(0, _globals.expect)((0, _math.modPow)(2n, 10n, 100n)).toBe(24n);
// 3^0 = 1
(0, _globals.expect)((0, _math.modPow)(3n, 0n, 7n)).toBe(1n);
});
(0, _globals.test)('extendedGcd returns correct Bezout coefficients', function () {
var _extendedGcd = (0, _math.extendedGcd)(35n, 15n),
_extendedGcd2 = _slicedToArray(_extendedGcd, 3),
g = _extendedGcd2[0],
x = _extendedGcd2[1],
y = _extendedGcd2[2];
(0, _globals.expect)(g).toBe(5n);
(0, _globals.expect)(35n * x + 15n * y).toBe(g);
});
(0, _globals.test)('modInverse returns correct inverse', function () {
// 3 * 5 = 15 ≡ 1 (mod 7)
(0, _globals.expect)((0, _math.modInverse)(3n, 7n)).toBe(5n);
// Verify: a * a⁻¹ ≡ 1 (mod p)
var inv = (0, _math.modInverse)(17n, 23n);
(0, _globals.expect)(17n * inv % 23n).toBe(1n);
});
(0, _globals.test)('modInverse throws for non-coprime inputs', function () {
(0, _globals.expect)(function () {
return (0, _math.modInverse)(6n, 3n);
}).toThrow('Modular inverse does not exist');
});
});
// ---------------------------------------------------------------------------
// Quadratic residue testing — Euler's criterion
//
// A non-zero integer a is a quadratic residue mod p (odd prime) iff:
// a^((p-1)/2) ≡ 1 (mod p)
//
// If a ≡ 0 (mod p), then a is not considered a QR.
// ---------------------------------------------------------------------------
(0, _globals.describe)('Quadratic residue (Euler criterion)', function () {
(0, _globals.test)('1 is always a QR mod any prime', function () {
(0, _globals.expect)((0, _math.isQuadraticResidue)(1n, 7n)).toBe(true);
(0, _globals.expect)((0, _math.isQuadraticResidue)(1n, 23n)).toBe(true);
});
// 3^((7-1)/2) = 3³ = 27 ≡ 6 (mod 7) ≠ 1
(0, _globals.test)('3 is not a QR mod 7', function () {
(0, _globals.expect)((0, _math.isQuadraticResidue)(3n, 7n)).toBe(false);
});
(0, _globals.test)('0 ≡ 0 (mod p) returns false', function () {
(0, _globals.expect)((0, _math.isQuadraticResidue)(0n, 7n)).toBe(false);
(0, _globals.expect)((0, _math.isQuadraticResidue)(7n, 7n)).toBe(false);
});
// QR mod 23 = {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18}
(0, _globals.test)('complete QR set mod 23', function () {
var qrSet = 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(qrSet.has(a));
}
});
// 25 ≡ 2 (mod 23), and 2 ∈ QR(23)
(0, _globals.test)('values larger than p are reduced before testing', function () {
(0, _globals.expect)((0, _math.isQuadraticResidue)(25n, 23n)).toBe(true);
});
});
// ---------------------------------------------------------------------------
// Modular square root
//
// For p ≡ 3 (mod 4): √a = a^((p+1)/4) mod p (direct formula)
// For p ≡ 1 (mod 4): Tonelli-Shanks algorithm
//
// Returns null if a is not a quadratic residue mod p.
// ---------------------------------------------------------------------------
(0, _globals.describe)('Modular square root', function () {
// p = 23 ≡ 3 (mod 4) → direct formula: r = a^((p+1)/4) mod p
(0, _globals.test)('direct formula for p ≡ 3 (mod 4): √16 mod 23', function () {
var r = (0, _math.modularSqrt)(16n, 23n);
(0, _globals.expect)(r).not.toBe(null);
(0, _globals.expect)((0, _math.modPow)(r, 2n, 23n)).toBe(16n);
});
// p = 13 ≡ 1 (mod 4) → Tonelli-Shanks: 4² = 16 ≡ 3 (mod 13)
(0, _globals.test)('Tonelli-Shanks for p ≡ 1 (mod 4): √3 mod 13', function () {
var r = (0, _math.modularSqrt)(3n, 13n);
(0, _globals.expect)(r).not.toBe(null);
(0, _globals.expect)((0, _math.modPow)(r, 2n, 13n)).toBe(3n);
});
(0, _globals.test)('non-QR returns null: √5 mod 7', function () {
(0, _globals.expect)((0, _math.modularSqrt)(5n, 7n)).toBe(null);
});
(0, _globals.test)('√0 = 0', function () {
(0, _globals.expect)((0, _math.modularSqrt)(0n, 7n)).toBe(0n);
});
// Verify r² ≡ a (mod p) for every QR mod 23
(0, _globals.test)('roundtrip for all QR mod 23', function () {
for (var a = 1n; a < 23n; a++) {
var r = (0, _math.modularSqrt)(a, 23n);
if (r !== null) {
(0, _globals.expect)((0, _math.modPow)(r, 2n, 23n)).toBe(a);
}
}
});
// p = 17 ≡ 1 (mod 4): QR(17) = {1, 2, 4, 8, 9, 13, 15, 16}
(0, _globals.test)('Tonelli-Shanks for all QR mod 17', function () {
for (var _i = 0, _arr = [1n, 2n, 4n, 8n, 9n, 13n, 15n, 16n]; _i < _arr.length; _i++) {
var a = _arr[_i];
var r = (0, _math.modularSqrt)(a, 17n);
(0, _globals.expect)(r).not.toBe(null);
(0, _globals.expect)((0, _math.modPow)(r, 2n, 17n)).toBe(a);
}
});
(0, _globals.test)('non-QR mod 17 return null', function () {
for (var _i2 = 0, _arr2 = [3n, 5n, 6n, 7n, 10n, 11n, 12n, 14n]; _i2 < _arr2.length; _i2++) {
var a = _arr2[_i2];
(0, _globals.expect)((0, _math.modularSqrt)(a, 17n)).toBe(null);
}
});
// p = 41 ≡ 1 (mod 8): higher power of 2 in p-1 factorization
// 17² = 289 ≡ 2 (mod 41)
(0, _globals.test)('Tonelli-Shanks for p ≡ 1 (mod 8): √2 mod 41', function () {
var r = (0, _math.modularSqrt)(2n, 41n);
(0, _globals.expect)(r).not.toBe(null);
(0, _globals.expect)((0, _math.modPow)(r, 2n, 41n)).toBe(2n);
});
// √a where a > p (should reduce mod p first)
(0, _globals.test)('modularSqrt with a > p reduces correctly', function () {
// 27 ≡ 4 (mod 23), and √4 exists
var r = (0, _math.modularSqrt)(27n, 23n);
(0, _globals.expect)(r).not.toBe(null);
(0, _globals.expect)((0, _math.modPow)(r, 2n, 23n)).toBe(4n);
});
});
//# sourceMappingURL=data:application/json;charset=utf-8;base64,{"version":3,"names":["_globals","require","_math","_slicedToArray","r","e","_arrayWithHoles","_iterableToArrayLimit","_unsupportedIterableToArray","_nonIterableRest","TypeError","a","_arrayLikeToArray","t","toString","call","slice","constructor","name","Array","from","test","length","n","l","Symbol","iterator","i","u","f","o","next","Object","done","push","value","isArray","describe","expect","modulus","toBe","modPow","_extendedGcd","extendedGcd","_extendedGcd2","g","x","y","modInverse","inv","toThrow","isQuadraticResidue","qrSet","Set","has","modularSqrt","not","_i","_arr","_i2","_arr2"],"sources":["../../src/math.test.js"],"sourcesContent":["import { test, expect, describe } from '@jest/globals'\nimport {\n  isQuadraticResidue,\n  modularSqrt,\n  modPow,\n  modulus,\n  modInverse,\n  extendedGcd,\n} from './utils/math'\n\n// ---------------------------------------------------------------------------\n// Modular arithmetic basics\n// ---------------------------------------------------------------------------\n\ndescribe('Modular arithmetic utilities', () => {\n  test('modulus returns non-negative result for negative dividends', () => {\n    expect(modulus(-5n, 3n)).toBe(1n)\n    expect(modulus(-1n, 7n)).toBe(6n)\n    expect(modulus(5n, 3n)).toBe(2n)\n  })\n\n  test('modPow with m = 1 returns 0', () => {\n    expect(modPow(5n, 3n, 1n)).toBe(0n)\n  })\n\n  test('modPow computes base^exp mod m correctly', () => {\n    // 2^10 = 1024, 1024 mod 100 = 24\n    expect(modPow(2n, 10n, 100n)).toBe(24n)\n    // 3^0 = 1\n    expect(modPow(3n, 0n, 7n)).toBe(1n)\n  })\n\n  test('extendedGcd returns correct Bezout coefficients', () => {\n    const [g, x, y] = extendedGcd(35n, 15n)\n    expect(g).toBe(5n)\n    expect(35n * x + 15n * y).toBe(g)\n  })\n\n  test('modInverse returns correct inverse', () => {\n    // 3 * 5 = 15 ≡ 1 (mod 7)\n    expect(modInverse(3n, 7n)).toBe(5n)\n    // Verify: a * a⁻¹ ≡ 1 (mod p)\n    const inv = modInverse(17n, 23n)\n    expect((17n * inv) % 23n).toBe(1n)\n  })\n\n  test('modInverse throws for non-coprime inputs', () => {\n    expect(() => modInverse(6n, 3n)).toThrow('Modular inverse does not exist')\n  })\n})\n\n// ---------------------------------------------------------------------------\n// Quadratic residue testing — Euler's criterion\n//\n// A non-zero integer a is a quadratic residue mod p (odd prime) iff:\n//   a^((p-1)/2) ≡ 1  (mod p)\n//\n// If a ≡ 0 (mod p), then a is not considered a QR.\n// ---------------------------------------------------------------------------\n\ndescribe('Quadratic residue (Euler criterion)', () => {\n  test('1 is always a QR mod any prime', () => {\n    expect(isQuadraticResidue(1n, 7n)).toBe(true)\n    expect(isQuadraticResidue(1n, 23n)).toBe(true)\n  })\n\n  // 3^((7-1)/2) = 3³ = 27 ≡ 6 (mod 7) ≠ 1\n  test('3 is not a QR mod 7', () => {\n    expect(isQuadraticResidue(3n, 7n)).toBe(false)\n  })\n\n  test('0 ≡ 0 (mod p) returns false', () => {\n    expect(isQuadraticResidue(0n, 7n)).toBe(false)\n    expect(isQuadraticResidue(7n, 7n)).toBe(false)\n  })\n\n  // QR mod 23 = {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18}\n  test('complete QR set mod 23', () => {\n    const qrSet = 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(qrSet.has(a))\n    }\n  })\n\n  // 25 ≡ 2 (mod 23), and 2 ∈ QR(23)\n  test('values larger than p are reduced before testing', () => {\n    expect(isQuadraticResidue(25n, 23n)).toBe(true)\n  })\n})\n\n// ---------------------------------------------------------------------------\n// Modular square root\n//\n// For p ≡ 3 (mod 4):  √a = a^((p+1)/4) mod p   (direct formula)\n// For p ≡ 1 (mod 4):  Tonelli-Shanks algorithm\n//\n// Returns null if a is not a quadratic residue mod p.\n// ---------------------------------------------------------------------------\n\ndescribe('Modular square root', () => {\n  // p = 23 ≡ 3 (mod 4) → direct formula: r = a^((p+1)/4) mod p\n  test('direct formula for p ≡ 3 (mod 4): √16 mod 23', () => {\n    const r = modularSqrt(16n, 23n)\n    expect(r).not.toBe(null)\n    expect(modPow(r, 2n, 23n)).toBe(16n)\n  })\n\n  // p = 13 ≡ 1 (mod 4) → Tonelli-Shanks: 4² = 16 ≡ 3 (mod 13)\n  test('Tonelli-Shanks for p ≡ 1 (mod 4): √3 mod 13', () => {\n    const r = modularSqrt(3n, 13n)\n    expect(r).not.toBe(null)\n    expect(modPow(r, 2n, 13n)).toBe(3n)\n  })\n\n  test('non-QR returns null: √5 mod 7', () => {\n    expect(modularSqrt(5n, 7n)).toBe(null)\n  })\n\n  test('√0 = 0', () => {\n    expect(modularSqrt(0n, 7n)).toBe(0n)\n  })\n\n  // Verify r² ≡ a (mod p) for every QR mod 23\n  test('roundtrip for all QR mod 23', () => {\n    for (let a = 1n; a < 23n; a++) {\n      const r = modularSqrt(a, 23n)\n      if (r !== null) {\n        expect(modPow(r, 2n, 23n)).toBe(a)\n      }\n    }\n  })\n\n  // p = 17 ≡ 1 (mod 4): QR(17) = {1, 2, 4, 8, 9, 13, 15, 16}\n  test('Tonelli-Shanks for all QR mod 17', () => {\n    for (const a of [1n, 2n, 4n, 8n, 9n, 13n, 15n, 16n]) {\n      const r = modularSqrt(a, 17n)\n      expect(r).not.toBe(null)\n      expect(modPow(r, 2n, 17n)).toBe(a)\n    }\n  })\n\n  test('non-QR mod 17 return null', () => {\n    for (const a of [3n, 5n, 6n, 7n, 10n, 11n, 12n, 14n]) {\n      expect(modularSqrt(a, 17n)).toBe(null)\n    }\n  })\n\n  // p = 41 ≡ 1 (mod 8): higher power of 2 in p-1 factorization\n  // 17² = 289 ≡ 2 (mod 41)\n  test('Tonelli-Shanks for p ≡ 1 (mod 8): √2 mod 41', () => {\n    const r = modularSqrt(2n, 41n)\n    expect(r).not.toBe(null)\n    expect(modPow(r, 2n, 41n)).toBe(2n)\n  })\n\n  // √a where a > p (should reduce mod p first)\n  test('modularSqrt with a > p reduces correctly', () => {\n    // 27 ≡ 4 (mod 23), and √4 exists\n    const r = modularSqrt(27n, 23n)\n    expect(r).not.toBe(null)\n    expect(modPow(r, 2n, 23n)).toBe(4n)\n  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