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.
130 lines (127 loc) • 17.5 kB
JavaScript
;
Object.defineProperty(exports, "__esModule", {
value: true
});
exports.affineAdd = affineAdd;
exports.affineDouble = affineDouble;
exports.affineMul = affineMul;
var _math = require("../../utils/math.js");
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; } /**
* Elliptic curve arithmetic in affine coordinates.
*
* In affine coordinates a point on the curve y² = x³ + ax + b (mod p) is
* represented directly by its (x, y) pair. Each addition or doubling
* requires one modular inversion, making this system straightforward but
* slower than projective alternatives for scalar multiplication.
*
* Note: these routines are NOT constant-time and should not be used in
* production contexts where timing side-channels are a concern.
* See RFC 6090, Section 4 for background on secure implementation
* considerations.
*/
/**
* Double a point in affine coordinates.
*
* Computes 2P using the tangent-line formula:
*
* λ = (3x₁² + a) · (2y₁)⁻¹ (mod p)
* x₃ = λ² - 2x₁ (mod p)
* y₃ = λ(x₁ - x₃) - y₁ (mod p)
*
* Returns [null, null] (identity) if the input is the identity or if
* 2y₁ ≡ 0 (mod p) (vertical tangent).
*
* @param {BigInt|null} px - x-coordinate (null for identity).
* @param {BigInt|null} py - y-coordinate (null for identity).
* @param {CurveParams} curve
* @returns {[BigInt|null, BigInt|null]}
*/
function affineDouble(px, py, curve) {
if (px === null || py === null) return [null, null];
var p = curve.p;
var num = (0, _math.modulus)(3n * px * px + curve.a, p);
var den = (0, _math.modulus)(2n * py, p);
if (den === 0n) return [null, null];
var inv = (0, _math.modInverse)(den, p);
var s = num * inv % p;
var x3 = (0, _math.modulus)(s * s - 2n * px, p);
var y3 = (0, _math.modulus)(s * (px - x3) - py, p);
return [x3, y3];
}
/**
* Add two distinct points in affine coordinates.
*
* Given P₁ = (x₁, y₁) and P₂ = (x₂, y₂) with P₁ ≠ P₂, the chord-line
* formula is:
*
* λ = (y₂ - y₁) · (x₂ - x₁)⁻¹ (mod p)
* x₃ = λ² - x₁ - x₂ (mod p)
* y₃ = λ(x₁ - x₃) - y₁ (mod p)
*
* If P₁ = P₂ the call is forwarded to {@link affineDouble}.
*
* @param {BigInt|null} p1x
* @param {BigInt|null} p1y
* @param {BigInt|null} p2x
* @param {BigInt|null} p2y
* @param {CurveParams} curve
* @returns {[BigInt|null, BigInt|null]}
*/
function affineAdd(p1x, p1y, p2x, p2y, curve) {
if (p1x === null || p1y === null) return [p2x, p2y];
if (p2x === null || p2y === null) return [p1x, p1y];
if (p1x === p2x && p1y === p2y) return affineDouble(p1x, p1y, curve);
var p = curve.p;
var num = (0, _math.modulus)(p2y - p1y, p);
var den = (0, _math.modulus)(p2x - p1x, p);
if (den === 0n) return [null, null];
var inv = (0, _math.modInverse)(den, p);
var s = num * inv % p;
var x3 = (0, _math.modulus)(s * s - p1x - p2x, p);
var y3 = (0, _math.modulus)(s * (p1x - x3) - p1y, p);
return [x3, y3];
}
/**
* Scalar multiplication in affine coordinates (double-and-add).
*
* Computes k·P by scanning the bits of k from LSB to MSB,
* accumulating the result and doubling the base at each step.
* Runs in O(log k) doublings and at most O(log k) additions.
*
* Warning: the double-and-add algorithm is NOT constant-time: the number
* of additions depends on the Hamming weight of k. For
* constant-time requirements see RFC 6090, Section 4.
*
* @param {BigInt} k - Scalar multiplier.
* @param {BigInt|null} px - x-coordinate of the base point.
* @param {BigInt|null} py - y-coordinate of the base point.
* @param {CurveParams} curve
* @returns {[BigInt|null, BigInt|null]}
*/
function affineMul(k, px, py, curve) {
if (px === null || py === null || k === 0n) return [null, null];
var rx = null,
ry = null;
while (k > 0n) {
if (k & 1n) {
;
var _affineAdd = affineAdd(rx, ry, px, py, curve);
var _affineAdd2 = _slicedToArray(_affineAdd, 2);
rx = _affineAdd2[0];
ry = _affineAdd2[1];
}
;
var _affineDouble = affineDouble(px, py, curve);
var _affineDouble2 = _slicedToArray(_affineDouble, 2);
px = _affineDouble2[0];
py = _affineDouble2[1];
k >>= 1n;
}
return [rx, ry];
}
//# sourceMappingURL=data:application/json;charset=utf-8;base64,{"version":3,"names":["_math","require","_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","affineDouble","px","py","curve","p","num","modulus","den","inv","modInverse","s","x3","y3","affineAdd","p1x","p1y","p2x","p2y","affineMul","k","rx","ry","_affineAdd","_affineAdd2","_affineDouble","_affineDouble2"],"sources":["../../../../src/core/arithmetic/affine.js"],"sourcesContent":["/**\n * Elliptic curve arithmetic in affine coordinates.\n *\n * In affine coordinates a point on the curve y² = x³ + ax + b (mod p) is\n * represented directly by its (x, y) pair.  Each addition or doubling\n * requires one modular inversion, making this system straightforward but\n * slower than projective alternatives for scalar multiplication.\n *\n * Note: these routines are NOT constant-time and should not be used in\n * production contexts where timing side-channels are a concern.\n * See RFC 6090, Section 4 for background on secure implementation\n * considerations.\n */\n\nimport { modulus, modInverse } from '../../utils/math.js'\n\n/**\n * Double a point in affine coordinates.\n *\n * Computes 2P using the tangent-line formula:\n *\n *     λ  = (3x₁² + a) · (2y₁)⁻¹  (mod p)\n *     x₃ = λ² - 2x₁              (mod p)\n *     y₃ = λ(x₁ - x₃) - y₁      (mod p)\n *\n * Returns [null, null] (identity) if the input is the identity or if\n * 2y₁ ≡ 0 (mod p) (vertical tangent).\n *\n * @param {BigInt|null} px - x-coordinate (null for identity).\n * @param {BigInt|null} py - y-coordinate (null for identity).\n * @param {CurveParams} curve\n * @returns {[BigInt|null, BigInt|null]}\n */\nexport function affineDouble(px, py, curve) {\n  if (px === null || py === null) return [null, null]\n  const p = curve.p\n  const num = modulus(3n * px * px + curve.a, p)\n  const den = modulus(2n * py, p)\n  if (den === 0n) return [null, null]\n  const inv = modInverse(den, p)\n  const s = (num * inv) % p\n  const x3 = modulus(s * s - 2n * px, p)\n  const y3 = modulus(s * (px - x3) - py, p)\n  return [x3, y3]\n}\n\n/**\n * Add two distinct points in affine coordinates.\n *\n * Given P₁ = (x₁, y₁) and P₂ = (x₂, y₂) with P₁ ≠ P₂, the chord-line\n * formula is:\n *\n *     λ  = (y₂ - y₁) · (x₂ - x₁)⁻¹  (mod p)\n *     x₃ = λ² - x₁ - x₂              (mod p)\n *     y₃ = λ(x₁ - x₃) - y₁           (mod p)\n *\n * If P₁ = P₂ the call is forwarded to {@link affineDouble}.\n *\n * @param {BigInt|null} p1x\n * @param {BigInt|null} p1y\n * @param {BigInt|null} p2x\n * @param {BigInt|null} p2y\n * @param {CurveParams} curve\n * @returns {[BigInt|null, BigInt|null]}\n */\nexport function affineAdd(p1x, p1y, p2x, p2y, curve) {\n  if (p1x === null || p1y === null) return [p2x, p2y]\n  if (p2x === null || p2y === null) return [p1x, p1y]\n  if (p1x === p2x && p1y === p2y) return affineDouble(p1x, p1y, curve)\n  const p = curve.p\n  const num = modulus(p2y - p1y, p)\n  const den = modulus(p2x - p1x, p)\n  if (den === 0n) return [null, null]\n  const inv = modInverse(den, p)\n  const s = (num * inv) % p\n  const x3 = modulus(s * s - p1x - p2x, p)\n  const y3 = modulus(s * (p1x - x3) - p1y, p)\n  return [x3, y3]\n}\n\n/**\n * Scalar multiplication in affine coordinates (double-and-add).\n *\n * Computes k·P by scanning the bits of k from LSB to MSB,\n * accumulating the result and doubling the base at each step.\n * Runs in O(log k) doublings and at most O(log k) additions.\n *\n * Warning: the double-and-add algorithm is NOT constant-time: the number\n * of additions depends on the Hamming weight of k.  For\n * constant-time requirements see RFC 6090, Section 4.\n *\n * @param {BigInt} k   - Scalar multiplier.\n * @param {BigInt|null} px - x-coordinate of the base point.\n * @param {BigInt|null} py - y-coordinate of the base point.\n * @param {CurveParams} curve\n * @returns {[BigInt|null, BigInt|null]}\n */\nexport function affineMul(k, px, py, curve) {\n  if (px === null || py === null || k === 0n) return [null, null]\n  let rx = null,\n    ry = null\n  while (k > 0n) {\n    if (k & 1n) {\n      ;[rx, ry] = affineAdd(rx, ry, px, py, curve)\n    }\n    ;[px, py] = affineDouble(px, py, curve)\n    k >>= 1n\n  }\n  return [rx, ry]\n}\n"],"mappings":";;;;;;;;AAcA,IAAAA,KAAA,GAAAC,OAAA;AAAyD,SAAAC,eAAAC,CAAA,EAAAC,CAAA,WAAAC,eAAA,CAAAF,CAAA,KAAAG,qBAAA,CAAAH,CAAA,EAAAC,CAAA,KAAAG,2BAAA,CAAAJ,CAAA,EAAAC,CAAA,KAAAI,gBAAA;AAAA,SAAAA,iBAAA,cAAAC,SAAA;AAAA,SAAAF,4BAAAJ,CAAA,EAAAO,CAAA,QAAAP,CAAA,2BAAAA,CAAA,SAAAQ,iBAAA,CAAAR,CAAA,EAAAO,CAAA,OAAAE,CAAA,MAAAC,QAAA,CAAAC,IAAA,CAAAX,CAAA,EAAAY,KAAA,6BAAAH,CAAA,IAAAT,CAAA,CAAAa,WAAA,KAAAJ,CAAA,GAAAT,CAAA,CAAAa,WAAA,CAAAC,IAAA,aAAAL,CAAA,cAAAA,CAAA,GAAAM,KAAA,CAAAC,IAAA,CAAAhB,CAAA,oBAAAS,CAAA,+CAAAQ,IAAA,CAAAR,CAAA,IAAAD,iBAAA,CAAAR,CAAA,EAAAO,CAAA;AAAA,SAAAC,kBAAAR,CAAA,EAAAO,CAAA,aAAAA,CAAA,IAAAA,CAAA,GAAAP,CAAA,CAAAkB,MAAA,MAAAX,CAAA,GAAAP,CAAA,CAAAkB,MAAA,YAAAjB,CAAA,MAAAkB,CAAA,GAAAJ,KAAA,CAAAR,CAAA,GAAAN,CAAA,GAAAM,CAAA,EAAAN,CAAA,IAAAkB,CAAA,CAAAlB,CAAA,IAAAD,CAAA,CAAAC,CAAA,UAAAkB,CAAA;AAAA,SAAAhB,sBAAAH,CAAA,EAAAoB,CAAA,QAAAX,CAAA,WAAAT,CAAA,gCAAAqB,MAAA,IAAArB,CAAA,CAAAqB,MAAA,CAAAC,QAAA,KAAAtB,CAAA,4BAAAS,CAAA,QAAAR,CAAA,EAAAkB,CAAA,EAAAI,CAAA,EAAAC,CAAA,EAAAjB,CAAA,OAAAkB,CAAA,OAAAC,CAAA,iBAAAH,CAAA,IAAAd,CAAA,GAAAA,CAAA,CAAAE,IAAA,CAAAX,CAAA,GAAA2B,IAAA,QAAAP,CAAA,QAAAQ,MAAA,CAAAnB,CAAA,MAAAA,CAAA,UAAAgB,CAAA,uBAAAA,CAAA,IAAAxB,CAAA,GAAAsB,CAAA,CAAAZ,IAAA,CAAAF,CAAA,GAAAoB,IAAA,MAAAtB,CAAA,CAAAuB,IAAA,CAAA7B,CAAA,CAAA8B,KAAA,GAAAxB,CAAA,CAAAW,MAAA,KAAAE,CAAA,GAAAK,CAAA,iBAAAzB,CAAA,IAAA0B,CAAA,OAAAP,CAAA,GAAAnB,CAAA,yBAAAyB,CAAA,YAAAhB,CAAA,eAAAe,CAAA,GAAAf,CAAA,cAAAmB,MAAA,CAAAJ,CAAA,MAAAA,CAAA,2BAAAE,CAAA,QAAAP,CAAA,aAAAZ,CAAA;AAAA,SAAAL,gBAAAF,CAAA,QAAAe,KAAA,CAAAiB,OAAA,CAAAhC,CAAA,UAAAA,CAAA,IAdzD;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AAIA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASiC,YAAYA,CAACC,EAAE,EAAEC,EAAE,EAAEC,KAAK,EAAE;EAC1C,IAAIF,EAAE,KAAK,IAAI,IAAIC,EAAE,KAAK,IAAI,EAAE,OAAO,CAAC,IAAI,EAAE,IAAI,CAAC;EACnD,IAAME,CAAC,GAAGD,KAAK,CAACC,CAAC;EACjB,IAAMC,GAAG,GAAG,IAAAC,aAAO,EAAC,EAAE,GAAGL,EAAE,GAAGA,EAAE,GAAGE,KAAK,CAAC7B,CAAC,EAAE8B,CAAC,CAAC;EAC9C,IAAMG,GAAG,GAAG,IAAAD,aAAO,EAAC,EAAE,GAAGJ,EAAE,EAAEE,CAAC,CAAC;EAC/B,IAAIG,GAAG,KAAK,EAAE,EAAE,OAAO,CAAC,IAAI,EAAE,IAAI,CAAC;EACnC,IAAMC,GAAG,GAAG,IAAAC,gBAAU,EAACF,GAAG,EAAEH,CAAC,CAAC;EAC9B,IAAMM,CAAC,GAAIL,GAAG,GAAGG,GAAG,GAAIJ,CAAC;EACzB,IAAMO,EAAE,GAAG,IAAAL,aAAO,EAACI,CAAC,GAAGA,CAAC,GAAG,EAAE,GAAGT,EAAE,EAAEG,CAAC,CAAC;EACtC,IAAMQ,EAAE,GAAG,IAAAN,aAAO,EAACI,CAAC,IAAIT,EAAE,GAAGU,EAAE,CAAC,GAAGT,EAAE,EAAEE,CAAC,CAAC;EACzC,OAAO,CAACO,EAAE,EAAEC,EAAE,CAAC;AACjB;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASC,SAASA,CAACC,GAAG,EAAEC,GAAG,EAAEC,GAAG,EAAEC,GAAG,EAAEd,KAAK,EAAE;EACnD,IAAIW,GAAG,KAAK,IAAI,IAAIC,GAAG,KAAK,IAAI,EAAE,OAAO,CAACC,GAAG,EAAEC,GAAG,CAAC;EACnD,IAAID,GAAG,KAAK,IAAI,IAAIC,GAAG,KAAK,IAAI,EAAE,OAAO,CAACH,GAAG,EAAEC,GAAG,CAAC;EACnD,IAAID,GAAG,KAAKE,GAAG,IAAID,GAAG,KAAKE,GAAG,EAAE,OAAOjB,YAAY,CAACc,GAAG,EAAEC,GAAG,EAAEZ,KAAK,CAAC;EACpE,IAAMC,CAAC,GAAGD,KAAK,CAACC,CAAC;EACjB,IAAMC,GAAG,GAAG,IAAAC,aAAO,EAACW,GAAG,GAAGF,GAAG,EAAEX,CAAC,CAAC;EACjC,IAAMG,GAAG,GAAG,IAAAD,aAAO,EAACU,GAAG,GAAGF,GAAG,EAAEV,CAAC,CAAC;EACjC,IAAIG,GAAG,KAAK,EAAE,EAAE,OAAO,CAAC,IAAI,EAAE,IAAI,CAAC;EACnC,IAAMC,GAAG,GAAG,IAAAC,gBAAU,EAACF,GAAG,EAAEH,CAAC,CAAC;EAC9B,IAAMM,CAAC,GAAIL,GAAG,GAAGG,GAAG,GAAIJ,CAAC;EACzB,IAAMO,EAAE,GAAG,IAAAL,aAAO,EAACI,CAAC,GAAGA,CAAC,GAAGI,GAAG,GAAGE,GAAG,EAAEZ,CAAC,CAAC;EACxC,IAAMQ,EAAE,GAAG,IAAAN,aAAO,EAACI,CAAC,IAAII,GAAG,GAAGH,EAAE,CAAC,GAAGI,GAAG,EAAEX,CAAC,CAAC;EAC3C,OAAO,CAACO,EAAE,EAAEC,EAAE,CAAC;AACjB;;AAEA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACA;AACO,SAASM,SAASA,CAACC,CAAC,EAAElB,EAAE,EAAEC,EAAE,EAAEC,KAAK,EAAE;EAC1C,IAAIF,EAAE,KAAK,IAAI,IAAIC,EAAE,KAAK,IAAI,IAAIiB,CAAC,KAAK,EAAE,EAAE,OAAO,CAAC,IAAI,EAAE,IAAI,CAAC;EAC/D,IAAIC,EAAE,GAAG,IAAI;IACXC,EAAE,GAAG,IAAI;EACX,OAAOF,CAAC,GAAG,EAAE,EAAE;IACb,IAAIA,CAAC,GAAG,EAAE,EAAE;MACV;MAAC,IAAAG,UAAA,GAAWT,SAAS,CAACO,EAAE,EAAEC,EAAE,EAAEpB,EAAE,EAAEC,EAAE,EAAEC,KAAK,CAAC;MAAA,IAAAoB,WAAA,GAAAzD,cAAA,CAAAwD,UAAA;MAA1CF,EAAE,GAAAG,WAAA;MAAEF,EAAE,GAAAE,WAAA;IACV;IACA;IAAC,IAAAC,aAAA,GAAWxB,YAAY,CAACC,EAAE,EAAEC,EAAE,EAAEC,KAAK,CAAC;IAAA,IAAAsB,cAAA,GAAA3D,cAAA,CAAA0D,aAAA;IAArCvB,EAAE,GAAAwB,cAAA;IAAEvB,EAAE,GAAAuB,cAAA;IACRN,CAAC,KAAK,EAAE;EACV;EACA,OAAO,CAACC,EAAE,EAAEC,EAAE,CAAC;AACjB","ignoreList":[]}