js-ecutils
Version:
JavaScript Library for Elliptic Curve Cryptography: key exchanges (Diffie-Hellman, Massey-Omura), ECDSA signatures, and Koblitz encoding. Suitable for crypto education and secure systems.
213 lines (203 loc) • 18.2 kB
JavaScript
;
Object.defineProperty(exports, "__esModule", {
value: true
});
exports.extendedGcd = extendedGcd;
exports.isQuadraticResidue = isQuadraticResidue;
exports.modInverse = modInverse;
exports.modPow = modPow;
exports.modularSqrt = modularSqrt;
exports.modulus = modulus;
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 utilities for elliptic curve operations.
*
* Provides quadratic residue testing and modular square root computation,
* essential building blocks for point decompression and Koblitz encoding.
*/
/**
* Positive modulo helper.
*
* JavaScript's `%` operator can return negative results for negative
* dividends. This function ensures the result is always in [0, b).
*
* @param {BigInt} a - Dividend.
* @param {BigInt} b - Divisor (must be positive).
* @returns {BigInt} a mod b, always non-negative.
*/
function modulus(a, b) {
return (a % b + b) % b;
}
/**
* Extended Euclidean algorithm.
*
* Computes integers x, y such that:
*
* a·x + b·y = gcd(a, b)
*
* Used internally by {@link modInverse} to find multiplicative inverses.
*
* @param {BigInt} a
* @param {BigInt} b
* @returns {[BigInt, BigInt, BigInt]} [gcd(a,b), x, y]
*/
function extendedGcd(a, b) {
var old_r = a,
r = b;
var old_s = 1n,
s = 0n;
var old_t = 0n,
t = 1n;
while (r !== 0n) {
var q = old_r / r;
var _ref = [r, old_r - q * r];
old_r = _ref[0];
r = _ref[1];
var _ref2 = [s, old_s - q * s];
old_s = _ref2[0];
s = _ref2[1];
var _ref3 = [t, old_t - q * t];
old_t = _ref3[0];
t = _ref3[1];
}
return [old_r, old_s, old_t];
}
/**
* Modular multiplicative inverse of a modulo p.
*
* Returns x such that:
*
* a · x ≡ 1 (mod p)
*
* Computed via the extended Euclidean algorithm. Throws if gcd(a, p) ≠ 1
* (i.e., the inverse does not exist).
*
* @param {BigInt} a
* @param {BigInt} p
* @returns {BigInt} a⁻¹ mod p
*/
function modInverse(a, p) {
a = modulus(a, p);
var _extendedGcd = extendedGcd(a, p),
_extendedGcd2 = _slicedToArray(_extendedGcd, 2),
g = _extendedGcd2[0],
x = _extendedGcd2[1];
if (g !== 1n) {
throw new Error('Modular inverse does not exist.');
}
return modulus(x, p);
}
/**
* Modular exponentiation via binary method (square-and-multiply).
*
* Computes:
*
* base^exp mod m
*
* Runs in O(log exp) multiplications.
*
* @param {BigInt} base
* @param {BigInt} exp - Non-negative exponent.
* @param {BigInt} m - Modulus.
* @returns {BigInt}
*/
function modPow(base, exp, m) {
if (m === 1n) return 0n;
base = modulus(base, m);
var result = 1n;
while (exp > 0n) {
if (exp & 1n) {
result = result * base % m;
}
exp >>= 1n;
base = base * base % m;
}
return result;
}
/**
* Check whether a is a quadratic residue modulo p using Euler's criterion.
*
* A non-zero integer a is a quadratic residue mod p (an odd prime) iff:
*
* a^((p-1)/2) ≡ 1 (mod p)
*
* Returns false when a ≡ 0 (mod p).
*
* @param {BigInt} a - The integer to test (will be reduced mod p).
* @param {BigInt} p - An odd prime.
* @returns {boolean}
*/
function isQuadraticResidue(a, p) {
a = modulus(a, p);
if (a === 0n) return false;
return modPow(a, (p - 1n) / 2n, p) === 1n;
}
/**
* Compute a square root of a modulo p, or null if none exists.
*
* Uses the direct formula when p ≡ 3 (mod 4):
*
* r = a^((p+1)/4) mod p
*
* Falls back to the Tonelli-Shanks algorithm for the general case
* (p ≡ 1 mod 4):
*
* 1. Factor out powers of 2: p - 1 = Q · 2^S
* 2. Find a quadratic non-residue z
* 3. Initialize: M = S, c = z^Q, t = a^Q, r = a^((Q+1)/2)
* 4. Loop until t ≡ 1 (mod p):
* - Find least i such that t^(2^i) ≡ 1 (mod p)
* - b = c^(2^(M-i-1)), M = i, c = b², t = t·c, r = r·b
*
* @param {BigInt} a - The value whose square root is sought (reduced mod p).
* @param {BigInt} p - An odd prime.
* @returns {BigInt|null} r such that r² ≡ a (mod p), or null if a is not a QR.
*/
function modularSqrt(a, p) {
a = modulus(a, p);
if (a === 0n) return 0n;
if (!isQuadraticResidue(a, p)) return null;
// Shortcut for p ≡ 3 (mod 4)
if (p % 4n === 3n) {
return modPow(a, (p + 1n) / 4n, p);
}
// Tonelli-Shanks algorithm for the general case (p ≡ 1 mod 4)
// Factor out powers of 2: p - 1 = Q · 2^S
var s = 0n;
var q = p - 1n;
while (q % 2n === 0n) {
q /= 2n;
s += 1n;
}
// Find a quadratic non-residue
var z = 2n;
while (isQuadraticResidue(z, p)) {
z += 1n;
}
var m = s;
var c = modPow(z, q, p);
var t = modPow(a, q, p);
var r = modPow(a, (q + 1n) / 2n, p);
while (true) {
if (t === 1n) return r;
// Find the least i such that t^(2^i) ≡ 1 (mod p)
var i = 1n;
var temp = t * t % p;
while (temp !== 1n) {
temp = temp * temp % p;
i += 1n;
}
// Update
var b = modPow(c, 1n << m - i - 1n, p);
m = i;
c = b * b % p;
t = t * c % p;
r = r * b % p;
}
}
//# sourceMappingURL=data:application/json;charset=utf-8;base64,{"version":3,"names":["modulus","a","b","extendedGcd","old_r","r","old_s","s","old_t","t","q","_ref","_ref2","_ref3","modInverse","p","_extendedGcd","_extendedGcd2","_slicedToArray","g","x","Error","modPow","base","exp","m","result","isQuadraticResidue","modularSqrt","z","c","i","temp"],"sources":["../../../src/utils/math.js"],"sourcesContent":["/**\n * Modular arithmetic utilities for elliptic curve operations.\n *\n * Provides quadratic residue testing and modular square root computation,\n * essential building blocks for point decompression and Koblitz encoding.\n */\n\n/**\n * Positive modulo helper.\n *\n * JavaScript's `%` operator can return negative results for negative\n * dividends.  This function ensures the result is always in [0, b).\n *\n * @param {BigInt} a - Dividend.\n * @param {BigInt} b - Divisor (must be positive).\n * @returns {BigInt} a mod b, always non-negative.\n */\nexport function modulus(a, b) {\n  return ((a % b) + b) % b\n}\n\n/**\n * Extended Euclidean algorithm.\n *\n * Computes integers x, y such that:\n *\n *     a·x + b·y = gcd(a, b)\n *\n * Used internally by {@link modInverse} to find multiplicative inverses.\n *\n * @param {BigInt} a\n * @param {BigInt} b\n * @returns {[BigInt, BigInt, BigInt]} [gcd(a,b), x, y]\n */\nexport function extendedGcd(a, b) {\n  let old_r = a,\n    r = b\n  let old_s = 1n,\n    s = 0n\n  let old_t = 0n,\n    t = 1n\n  while (r !== 0n) {\n    const q = old_r / r\n    ;[old_r, r] = [r, old_r - q * r]\n    ;[old_s, s] = [s, old_s - q * s]\n    ;[old_t, t] = [t, old_t - q * t]\n  }\n  return [old_r, old_s, old_t]\n}\n\n/**\n * Modular multiplicative inverse of a modulo p.\n *\n * Returns x such that:\n *\n *     a · x ≡ 1  (mod p)\n *\n * Computed via the extended Euclidean algorithm.  Throws if gcd(a, p) ≠ 1\n * (i.e., the inverse does not exist).\n *\n * @param {BigInt} a\n * @param {BigInt} p\n * @returns {BigInt} a⁻¹ mod p\n */\nexport function modInverse(a, p) {\n  a = modulus(a, p)\n  const [g, x] = extendedGcd(a, p)\n  if (g !== 1n) {\n    throw new Error('Modular inverse does not exist.')\n  }\n  return modulus(x, p)\n}\n\n/**\n * Modular exponentiation via binary method (square-and-multiply).\n *\n * Computes:\n *\n *     base^exp  mod m\n *\n * Runs in O(log exp) multiplications.\n *\n * @param {BigInt} base\n * @param {BigInt} exp - Non-negative exponent.\n * @param {BigInt} m   - Modulus.\n * @returns {BigInt}\n */\nexport function modPow(base, exp, m) {\n  if (m === 1n) return 0n\n  base = modulus(base, m)\n  let result = 1n\n  while (exp > 0n) {\n    if (exp & 1n) {\n      result = (result * base) % m\n    }\n    exp >>= 1n\n    base = (base * base) % m\n  }\n  return result\n}\n\n/**\n * Check whether a is a quadratic residue modulo p using Euler's criterion.\n *\n * A non-zero integer a is a quadratic residue mod p (an odd prime) iff:\n *\n *     a^((p-1)/2) ≡ 1  (mod p)\n *\n * Returns false when a ≡ 0 (mod p).\n *\n * @param {BigInt} a - The integer to test (will be reduced mod p).\n * @param {BigInt} p - An odd prime.\n * @returns {boolean}\n */\nexport function isQuadraticResidue(a, p) {\n  a = modulus(a, p)\n  if (a === 0n) return false\n  return modPow(a, (p - 1n) / 2n, p) === 1n\n}\n\n/**\n * Compute a square root of a modulo p, or null if none exists.\n *\n * Uses the direct formula when p ≡ 3 (mod 4):\n *\n *     r = a^((p+1)/4)  mod p\n *\n * Falls back to the Tonelli-Shanks algorithm for the general case\n * (p ≡ 1 mod 4):\n *\n *   1. Factor out powers of 2:  p - 1 = Q · 2^S\n *   2. Find a quadratic non-residue z\n *   3. Initialize:  M = S,  c = z^Q,  t = a^Q,  r = a^((Q+1)/2)\n *   4. Loop until t ≡ 1 (mod p):\n *        - Find least i such that t^(2^i) ≡ 1 (mod p)\n *        - b = c^(2^(M-i-1)),  M = i,  c = b²,  t = t·c,  r = r·b\n *\n * @param {BigInt} a - The value whose square root is sought (reduced mod p).\n * @param {BigInt} p - An odd prime.\n * @returns {BigInt|null} r such that r² ≡ a (mod p), or null if a is not a QR.\n */\nexport function modularSqrt(a, p) {\n  a = modulus(a, p)\n  if (a === 0n) return 0n\n\n  if (!isQuadraticResidue(a, p)) return null\n\n  // Shortcut for p ≡ 3 (mod 4)\n  if (p % 4n === 3n) {\n    return modPow(a, (p + 1n) / 4n, p)\n  }\n\n  // Tonelli-Shanks algorithm for the general case (p ≡ 1 mod 4)\n  // Factor out powers of 2:  p - 1 = Q · 2^S\n  let s = 0n\n  let q = p - 1n\n  while (q % 2n === 0n) {\n    q /= 2n\n    s += 1n\n  }\n\n  // Find a quadratic non-residue\n  let z = 2n\n  while (isQuadraticResidue(z, p)) {\n    z += 1n\n  }\n\n  let m = s\n  let c = modPow(z, q, p)\n  let t = modPow(a, q, p)\n  let r = modPow(a, (q + 1n) / 2n, p)\n\n  while (true) {\n    if (t === 1n) return r\n    // Find the least i such that t^(2^i) ≡ 1 (mod p)\n    let i = 1n\n    let temp = (t * t) % p\n    while (temp !== 1n) {\n      temp = (temp * temp) % p\n      i += 1n\n    }\n    // Update\n    const b = modPow(c, 1n << (m - i - 1n), p)\n    m = i\n    c = (b * b) % p\n    t = (t * c) % p\n    r = (r * b) % p\n  }\n}\n"],"mappings":";;;;;;;;;;;;;;;;;AAAA;AACA;AACA;AACA;AACA;AACA;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASA,OAAOA,CAACC,CAAC,EAAEC,CAAC,EAAE;EAC5B,OAAO,CAAED,CAAC,GAAGC,CAAC,GAAIA,CAAC,IAAIA,CAAC;AAC1B;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASC,WAAWA,CAACF,CAAC,EAAEC,CAAC,EAAE;EAChC,IAAIE,KAAK,GAAGH,CAAC;IACXI,CAAC,GAAGH,CAAC;EACP,IAAII,KAAK,GAAG,EAAE;IACZC,CAAC,GAAG,EAAE;EACR,IAAIC,KAAK,GAAG,EAAE;IACZC,CAAC,GAAG,EAAE;EACR,OAAOJ,CAAC,KAAK,EAAE,EAAE;IACf,IAAMK,CAAC,GAAGN,KAAK,GAAGC,CAAC;IAClB,IAAAM,IAAA,GAAa,CAACN,CAAC,EAAED,KAAK,GAAGM,CAAC,GAAGL,CAAC,CAAC;IAA9BD,KAAK,GAAAO,IAAA;IAAEN,CAAC,GAAAM,IAAA;IAAA,IAAAC,KAAA,GACI,CAACL,CAAC,EAAED,KAAK,GAAGI,CAAC,GAAGH,CAAC,CAAC;IAA9BD,KAAK,GAAAM,KAAA;IAAEL,CAAC,GAAAK,KAAA;IAAA,IAAAC,KAAA,GACI,CAACJ,CAAC,EAAED,KAAK,GAAGE,CAAC,GAAGD,CAAC,CAAC;IAA9BD,KAAK,GAAAK,KAAA;IAAEJ,CAAC,GAAAI,KAAA;EACZ;EACA,OAAO,CAACT,KAAK,EAAEE,KAAK,EAAEE,KAAK,CAAC;AAC9B;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASM,UAAUA,CAACb,CAAC,EAAEc,CAAC,EAAE;EAC/Bd,CAAC,GAAGD,OAAO,CAACC,CAAC,EAAEc,CAAC,CAAC;EACjB,IAAAC,YAAA,GAAeb,WAAW,CAACF,CAAC,EAAEc,CAAC,CAAC;IAAAE,aAAA,GAAAC,cAAA,CAAAF,YAAA;IAAzBG,CAAC,GAAAF,aAAA;IAAEG,CAAC,GAAAH,aAAA;EACX,IAAIE,CAAC,KAAK,EAAE,EAAE;IACZ,MAAM,IAAIE,KAAK,CAAC,iCAAiC,CAAC;EACpD;EACA,OAAOrB,OAAO,CAACoB,CAAC,EAAEL,CAAC,CAAC;AACtB;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASO,MAAMA,CAACC,IAAI,EAAEC,GAAG,EAAEC,CAAC,EAAE;EACnC,IAAIA,CAAC,KAAK,EAAE,EAAE,OAAO,EAAE;EACvBF,IAAI,GAAGvB,OAAO,CAACuB,IAAI,EAAEE,CAAC,CAAC;EACvB,IAAIC,MAAM,GAAG,EAAE;EACf,OAAOF,GAAG,GAAG,EAAE,EAAE;IACf,IAAIA,GAAG,GAAG,EAAE,EAAE;MACZE,MAAM,GAAIA,MAAM,GAAGH,IAAI,GAAIE,CAAC;IAC9B;IACAD,GAAG,KAAK,EAAE;IACVD,IAAI,GAAIA,IAAI,GAAGA,IAAI,GAAIE,CAAC;EAC1B;EACA,OAAOC,MAAM;AACf;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASC,kBAAkBA,CAAC1B,CAAC,EAAEc,CAAC,EAAE;EACvCd,CAAC,GAAGD,OAAO,CAACC,CAAC,EAAEc,CAAC,CAAC;EACjB,IAAId,CAAC,KAAK,EAAE,EAAE,OAAO,KAAK;EAC1B,OAAOqB,MAAM,CAACrB,CAAC,EAAE,CAACc,CAAC,GAAG,EAAE,IAAI,EAAE,EAAEA,CAAC,CAAC,KAAK,EAAE;AAC3C;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASa,WAAWA,CAAC3B,CAAC,EAAEc,CAAC,EAAE;EAChCd,CAAC,GAAGD,OAAO,CAACC,CAAC,EAAEc,CAAC,CAAC;EACjB,IAAId,CAAC,KAAK,EAAE,EAAE,OAAO,EAAE;EAEvB,IAAI,CAAC0B,kBAAkB,CAAC1B,CAAC,EAAEc,CAAC,CAAC,EAAE,OAAO,IAAI;;EAE1C;EACA,IAAIA,CAAC,GAAG,EAAE,KAAK,EAAE,EAAE;IACjB,OAAOO,MAAM,CAACrB,CAAC,EAAE,CAACc,CAAC,GAAG,EAAE,IAAI,EAAE,EAAEA,CAAC,CAAC;EACpC;;EAEA;EACA;EACA,IAAIR,CAAC,GAAG,EAAE;EACV,IAAIG,CAAC,GAAGK,CAAC,GAAG,EAAE;EACd,OAAOL,CAAC,GAAG,EAAE,KAAK,EAAE,EAAE;IACpBA,CAAC,IAAI,EAAE;IACPH,CAAC,IAAI,EAAE;EACT;;EAEA;EACA,IAAIsB,CAAC,GAAG,EAAE;EACV,OAAOF,kBAAkB,CAACE,CAAC,EAAEd,CAAC,CAAC,EAAE;IAC/Bc,CAAC,IAAI,EAAE;EACT;EAEA,IAAIJ,CAAC,GAAGlB,CAAC;EACT,IAAIuB,CAAC,GAAGR,MAAM,CAACO,CAAC,EAAEnB,CAAC,EAAEK,CAAC,CAAC;EACvB,IAAIN,CAAC,GAAGa,MAAM,CAACrB,CAAC,EAAES,CAAC,EAAEK,CAAC,CAAC;EACvB,IAAIV,CAAC,GAAGiB,MAAM,CAACrB,CAAC,EAAE,CAACS,CAAC,GAAG,EAAE,IAAI,EAAE,EAAEK,CAAC,CAAC;EAEnC,OAAO,IAAI,EAAE;IACX,IAAIN,CAAC,KAAK,EAAE,EAAE,OAAOJ,CAAC;IACtB;IACA,IAAI0B,CAAC,GAAG,EAAE;IACV,IAAIC,IAAI,GAAIvB,CAAC,GAAGA,CAAC,GAAIM,CAAC;IACtB,OAAOiB,IAAI,KAAK,EAAE,EAAE;MAClBA,IAAI,GAAIA,IAAI,GAAGA,IAAI,GAAIjB,CAAC;MACxBgB,CAAC,IAAI,EAAE;IACT;IACA;IACA,IAAM7B,CAAC,GAAGoB,MAAM,CAACQ,CAAC,EAAE,EAAE,IAAKL,CAAC,GAAGM,CAAC,GAAG,EAAG,EAAEhB,CAAC,CAAC;IAC1CU,CAAC,GAAGM,CAAC;IACLD,CAAC,GAAI5B,CAAC,GAAGA,CAAC,GAAIa,CAAC;IACfN,CAAC,GAAIA,CAAC,GAAGqB,CAAC,GAAIf,CAAC;IACfV,CAAC,GAAIA,CAAC,GAAGH,CAAC,GAAIa,CAAC;EACjB;AACF","ignoreList":[]}