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emergent-agent-e1
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122 KiB
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1 line
122 KiB
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{"dependencies":[{"name":"@babel/runtime/helpers/classCallCheck","data":{"asyncType":null,"isESMImport":false,"locs":[],"key":"yg7e6laZwmpbIvId5jovq9ugXp8=","exportNames":["*"],"imports":1}},{"name":"@babel/runtime/helpers/createClass","data":{"asyncType":null,"isESMImport":false,"locs":[],"key":"Z6pzkVZ2fvxBLkFTgVVOy4UDj30=","exportNames":["*"],"imports":1}},{"name":"../utils.js","data":{"asyncType":null,"isESMImport":false,"locs":[{"start":{"line":14,"column":19,"index":540},"end":{"line":14,"column":41,"index":562}}],"key":"Yc7DmwhweSDBIC4bv+r2fO8xp6U=","exportNames":["*"],"imports":1}},{"name":"./curve.js","data":{"asyncType":null,"isESMImport":false,"locs":[{"start":{"line":15,"column":19,"index":583},"end":{"line":15,"column":40,"index":604}}],"key":"D2lpvogjUpmMFXMnxIh5QgGQVQM=","exportNames":["*"],"imports":1}},{"name":"./modular.js","data":{"asyncType":null,"isESMImport":false,"locs":[{"start":{"line":16,"column":21,"index":627},"end":{"line":16,"column":44,"index":650}}],"key":"pkHxIsiyj9LvPZma2E+OjOIbg7k=","exportNames":["*"],"imports":1}}],"output":[{"data":{"code":"__d(function (global, require, _$$_IMPORT_DEFAULT, _$$_IMPORT_ALL, module, exports, _dependencyMap) {\n \"use strict\";\n\n var _classCallCheck = require(_dependencyMap[0], \"@babel/runtime/helpers/classCallCheck\").default;\n var _createClass = require(_dependencyMap[1], \"@babel/runtime/helpers/createClass\").default;\n Object.defineProperty(exports, \"__esModule\", {\n value: true\n });\n exports.PrimeEdwardsPoint = void 0;\n exports.edwards = edwards;\n exports.eddsa = eddsa;\n exports.twistedEdwards = twistedEdwards;\n /**\n * Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y².\n * For design rationale of types / exports, see weierstrass module documentation.\n * Untwisted Edwards curves exist, but they aren't used in real-world protocols.\n * @module\n */\n /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n var utils_ts_1 = require(_dependencyMap[2], \"../utils.js\");\n var curve_ts_1 = require(_dependencyMap[3], \"./curve.js\");\n var modular_ts_1 = require(_dependencyMap[4], \"./modular.js\");\n // Be friendly to bad ECMAScript parsers by not using bigint literals\n // prettier-ignore\n var _0n = BigInt(0),\n _1n = BigInt(1),\n _2n = BigInt(2),\n _8n = BigInt(8);\n function isEdValidXY(Fp, CURVE, x, y) {\n var x2 = Fp.sqr(x);\n var y2 = Fp.sqr(y);\n var left = Fp.add(Fp.mul(CURVE.a, x2), y2);\n var right = Fp.add(Fp.ONE, Fp.mul(CURVE.d, Fp.mul(x2, y2)));\n return Fp.eql(left, right);\n }\n function edwards(params) {\n var extraOpts = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};\n var validated = (0, curve_ts_1._createCurveFields)('edwards', params, extraOpts, extraOpts.FpFnLE);\n var Fp = validated.Fp,\n Fn = validated.Fn;\n var _CURVE = validated.CURVE;\n var cofactor = _CURVE.h;\n (0, utils_ts_1._validateObject)(extraOpts, {}, {\n uvRatio: 'function'\n });\n // Important:\n // There are some places where Fp.BYTES is used instead of nByteLength.\n // So far, everything has been tested with curves of Fp.BYTES == nByteLength.\n // TODO: test and find curves which behave otherwise.\n var MASK = _2n << BigInt(Fn.BYTES * 8) - _1n;\n var modP = n => Fp.create(n); // Function overrides\n // sqrt(u/v)\n var uvRatio = extraOpts.uvRatio || ((u, v) => {\n try {\n return {\n isValid: true,\n value: Fp.sqrt(Fp.div(u, v))\n };\n } catch (e) {\n return {\n isValid: false,\n value: _0n\n };\n }\n });\n // Validate whether the passed curve params are valid.\n // equation ax² + y² = 1 + dx²y² should work for generator point.\n if (!isEdValidXY(Fp, _CURVE, _CURVE.Gx, _CURVE.Gy)) throw new Error('bad curve params: generator point');\n /**\n * Asserts coordinate is valid: 0 <= n < MASK.\n * Coordinates >= Fp.ORDER are allowed for zip215.\n */\n function acoord(title, n) {\n var banZero = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : false;\n var min = banZero ? _1n : _0n;\n (0, utils_ts_1.aInRange)('coordinate ' + title, n, min, MASK);\n return n;\n }\n function aextpoint(other) {\n if (!(other instanceof Point)) throw new Error('ExtendedPoint expected');\n }\n // Converts Extended point to default (x, y) coordinates.\n // Can accept precomputed Z^-1 - for example, from invertBatch.\n var toAffineMemo = (0, utils_ts_1.memoized)((p, iz) => {\n var X = p.X,\n Y = p.Y,\n Z = p.Z;\n var is0 = p.is0();\n if (iz == null) iz = is0 ? _8n : Fp.inv(Z); // 8 was chosen arbitrarily\n var x = modP(X * iz);\n var y = modP(Y * iz);\n var zz = Fp.mul(Z, iz);\n if (is0) return {\n x: _0n,\n y: _1n\n };\n if (zz !== _1n) throw new Error('invZ was invalid');\n return {\n x,\n y\n };\n });\n var assertValidMemo = (0, utils_ts_1.memoized)(p => {\n var a = _CURVE.a,\n d = _CURVE.d;\n if (p.is0()) throw new Error('bad point: ZERO'); // TODO: optimize, with vars below?\n // Equation in affine coordinates: ax² + y² = 1 + dx²y²\n // Equation in projective coordinates (X/Z, Y/Z, Z): (aX² + Y²)Z² = Z⁴ + dX²Y²\n var X = p.X,\n Y = p.Y,\n Z = p.Z,\n T = p.T;\n var X2 = modP(X * X); // X²\n var Y2 = modP(Y * Y); // Y²\n var Z2 = modP(Z * Z); // Z²\n var Z4 = modP(Z2 * Z2); // Z⁴\n var aX2 = modP(X2 * a); // aX²\n var left = modP(Z2 * modP(aX2 + Y2)); // (aX² + Y²)Z²\n var right = modP(Z4 + modP(d * modP(X2 * Y2))); // Z⁴ + dX²Y²\n if (left !== right) throw new Error('bad point: equation left != right (1)');\n // In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T\n var XY = modP(X * Y);\n var ZT = modP(Z * T);\n if (XY !== ZT) throw new Error('bad point: equation left != right (2)');\n return true;\n });\n // Extended Point works in extended coordinates: (X, Y, Z, T) ∋ (x=X/Z, y=Y/Z, T=xy).\n // https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates\n var Point = /*#__PURE__*/function () {\n function Point(X, Y, Z, T) {\n _classCallCheck(this, Point);\n this.X = acoord('x', X);\n this.Y = acoord('y', Y);\n this.Z = acoord('z', Z, true);\n this.T = acoord('t', T);\n Object.freeze(this);\n }\n return _createClass(Point, [{\n key: \"x\",\n get: function () {\n return this.toAffine().x;\n }\n }, {\n key: \"y\",\n get: function () {\n return this.toAffine().y;\n }\n }, {\n key: \"precompute\",\n value: function precompute() {\n var windowSize = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 8;\n var isLazy = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : true;\n wnaf.createCache(this, windowSize);\n if (!isLazy) this.multiply(_2n); // random number\n return this;\n }\n // Useful in fromAffine() - not for fromBytes(), which always created valid points.\n }, {\n key: \"assertValidity\",\n value: function assertValidity() {\n assertValidMemo(this);\n }\n // Compare one point to another.\n }, {\n key: \"equals\",\n value: function equals(other) {\n aextpoint(other);\n var X1 = this.X,\n Y1 = this.Y,\n Z1 = this.Z;\n var X2 = other.X,\n Y2 = other.Y,\n Z2 = other.Z;\n var X1Z2 = modP(X1 * Z2);\n var X2Z1 = modP(X2 * Z1);\n var Y1Z2 = modP(Y1 * Z2);\n var Y2Z1 = modP(Y2 * Z1);\n return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;\n }\n }, {\n key: \"is0\",\n value: function is0() {\n return this.equals(Point.ZERO);\n }\n }, {\n key: \"negate\",\n value: function negate() {\n // Flips point sign to a negative one (-x, y in affine coords)\n return new Point(modP(-this.X), this.Y, this.Z, modP(-this.T));\n }\n // Fast algo for doubling Extended Point.\n // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd\n // Cost: 4M + 4S + 1*a + 6add + 1*2.\n }, {\n key: \"double\",\n value: function double() {\n var a = _CURVE.a;\n var X1 = this.X,\n Y1 = this.Y,\n Z1 = this.Z;\n var A = modP(X1 * X1); // A = X12\n var B = modP(Y1 * Y1); // B = Y12\n var C = modP(_2n * modP(Z1 * Z1)); // C = 2*Z12\n var D = modP(a * A); // D = a*A\n var x1y1 = X1 + Y1;\n var E = modP(modP(x1y1 * x1y1) - A - B); // E = (X1+Y1)2-A-B\n var G = D + B; // G = D+B\n var F = G - C; // F = G-C\n var H = D - B; // H = D-B\n var X3 = modP(E * F); // X3 = E*F\n var Y3 = modP(G * H); // Y3 = G*H\n var T3 = modP(E * H); // T3 = E*H\n var Z3 = modP(F * G); // Z3 = F*G\n return new Point(X3, Y3, Z3, T3);\n }\n // Fast algo for adding 2 Extended Points.\n // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd\n // Cost: 9M + 1*a + 1*d + 7add.\n }, {\n key: \"add\",\n value: function add(other) {\n aextpoint(other);\n var a = _CURVE.a,\n d = _CURVE.d;\n var X1 = this.X,\n Y1 = this.Y,\n Z1 = this.Z,\n T1 = this.T;\n var X2 = other.X,\n Y2 = other.Y,\n Z2 = other.Z,\n T2 = other.T;\n var A = modP(X1 * X2); // A = X1*X2\n var B = modP(Y1 * Y2); // B = Y1*Y2\n var C = modP(T1 * d * T2); // C = T1*d*T2\n var D = modP(Z1 * Z2); // D = Z1*Z2\n var E = modP((X1 + Y1) * (X2 + Y2) - A - B); // E = (X1+Y1)*(X2+Y2)-A-B\n var F = D - C; // F = D-C\n var G = D + C; // G = D+C\n var H = modP(B - a * A); // H = B-a*A\n var X3 = modP(E * F); // X3 = E*F\n var Y3 = modP(G * H); // Y3 = G*H\n var T3 = modP(E * H); // T3 = E*H\n var Z3 = modP(F * G); // Z3 = F*G\n return new Point(X3, Y3, Z3, T3);\n }\n }, {\n key: \"subtract\",\n value: function subtract(other) {\n return this.add(other.negate());\n }\n // Constant-time multiplication.\n }, {\n key: \"multiply\",\n value: function multiply(scalar) {\n // 1 <= scalar < L\n if (!Fn.isValidNot0(scalar)) throw new Error('invalid scalar: expected 1 <= sc < curve.n');\n var _wnaf$cached = wnaf.cached(this, scalar, p => (0, curve_ts_1.normalizeZ)(Point, p)),\n p = _wnaf$cached.p,\n f = _wnaf$cached.f;\n return (0, curve_ts_1.normalizeZ)(Point, [p, f])[0];\n }\n // Non-constant-time multiplication. Uses double-and-add algorithm.\n // It's faster, but should only be used when you don't care about\n // an exposed private key e.g. sig verification.\n // Does NOT allow scalars higher than CURVE.n.\n // Accepts optional accumulator to merge with multiply (important for sparse scalars)\n }, {\n key: \"multiplyUnsafe\",\n value: function multiplyUnsafe(scalar) {\n var acc = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : Point.ZERO;\n // 0 <= scalar < L\n if (!Fn.isValid(scalar)) throw new Error('invalid scalar: expected 0 <= sc < curve.n');\n if (scalar === _0n) return Point.ZERO;\n if (this.is0() || scalar === _1n) return this;\n return wnaf.unsafe(this, scalar, p => (0, curve_ts_1.normalizeZ)(Point, p), acc);\n }\n // Checks if point is of small order.\n // If you add something to small order point, you will have \"dirty\"\n // point with torsion component.\n // Multiplies point by cofactor and checks if the result is 0.\n }, {\n key: \"isSmallOrder\",\n value: function isSmallOrder() {\n return this.multiplyUnsafe(cofactor).is0();\n }\n // Multiplies point by curve order and checks if the result is 0.\n // Returns `false` is the point is dirty.\n }, {\n key: \"isTorsionFree\",\n value: function isTorsionFree() {\n return wnaf.unsafe(this, _CURVE.n).is0();\n }\n // Converts Extended point to default (x, y) coordinates.\n // Can accept precomputed Z^-1 - for example, from invertBatch.\n }, {\n key: \"toAffine\",\n value: function toAffine(invertedZ) {\n return toAffineMemo(this, invertedZ);\n }\n }, {\n key: \"clearCofactor\",\n value: function clearCofactor() {\n if (cofactor === _1n) return this;\n return this.multiplyUnsafe(cofactor);\n }\n }, {\n key: \"toBytes\",\n value: function toBytes() {\n var _this$toAffine = this.toAffine(),\n x = _this$toAffine.x,\n y = _this$toAffine.y;\n // Fp.toBytes() allows non-canonical encoding of y (>= p).\n var bytes = Fp.toBytes(y);\n // Each y has 2 valid points: (x, y), (x,-y).\n // When compressing, it's enough to store y and use the last byte to encode sign of x\n bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;\n return bytes;\n }\n }, {\n key: \"toHex\",\n value: function toHex() {\n return (0, utils_ts_1.bytesToHex)(this.toBytes());\n }\n }, {\n key: \"toString\",\n value: function toString() {\n return `<Point ${this.is0() ? 'ZERO' : this.toHex()}>`;\n }\n // TODO: remove\n }, {\n key: \"ex\",\n get: function () {\n return this.X;\n }\n }, {\n key: \"ey\",\n get: function () {\n return this.Y;\n }\n }, {\n key: \"ez\",\n get: function () {\n return this.Z;\n }\n }, {\n key: \"et\",\n get: function () {\n return this.T;\n }\n }, {\n key: \"_setWindowSize\",\n value: function _setWindowSize(windowSize) {\n this.precompute(windowSize);\n }\n }, {\n key: \"toRawBytes\",\n value: function toRawBytes() {\n return this.toBytes();\n }\n }], [{\n key: \"CURVE\",\n value: function CURVE() {\n return _CURVE;\n }\n }, {\n key: \"fromAffine\",\n value: function fromAffine(p) {\n if (p instanceof Point) throw new Error('extended point not allowed');\n var _ref = p || {},\n x = _ref.x,\n y = _ref.y;\n acoord('x', x);\n acoord('y', y);\n return new Point(x, y, _1n, modP(x * y));\n }\n // Uses algo from RFC8032 5.1.3.\n }, {\n key: \"fromBytes\",\n value: function fromBytes(bytes) {\n var zip215 = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;\n var len = Fp.BYTES;\n var a = _CURVE.a,\n d = _CURVE.d;\n bytes = (0, utils_ts_1.copyBytes)((0, utils_ts_1._abytes2)(bytes, len, 'point'));\n (0, utils_ts_1._abool2)(zip215, 'zip215');\n var normed = (0, utils_ts_1.copyBytes)(bytes); // copy again, we'll manipulate it\n var lastByte = bytes[len - 1]; // select last byte\n normed[len - 1] = lastByte & ~0x80; // clear last bit\n var y = (0, utils_ts_1.bytesToNumberLE)(normed);\n // zip215=true is good for consensus-critical apps. =false follows RFC8032 / NIST186-5.\n // RFC8032 prohibits >= p, but ZIP215 doesn't\n // zip215=true: 0 <= y < MASK (2^256 for ed25519)\n // zip215=false: 0 <= y < P (2^255-19 for ed25519)\n var max = zip215 ? MASK : Fp.ORDER;\n (0, utils_ts_1.aInRange)('point.y', y, _0n, max);\n // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:\n // ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)\n var y2 = modP(y * y); // denominator is always non-0 mod p.\n var u = modP(y2 - _1n); // u = y² - 1\n var v = modP(d * y2 - a); // v = d y² + 1.\n var _uvRatio = uvRatio(u, v),\n isValid = _uvRatio.isValid,\n x = _uvRatio.value; // √(u/v)\n if (!isValid) throw new Error('bad point: invalid y coordinate');\n var isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper\n var isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit\n if (!zip215 && x === _0n && isLastByteOdd)\n // if x=0 and x_0 = 1, fail\n throw new Error('bad point: x=0 and x_0=1');\n if (isLastByteOdd !== isXOdd) x = modP(-x); // if x_0 != x mod 2, set x = p-x\n return Point.fromAffine({\n x,\n y\n });\n }\n }, {\n key: \"fromHex\",\n value: function fromHex(bytes) {\n var zip215 = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : false;\n return Point.fromBytes((0, utils_ts_1.ensureBytes)('point', bytes), zip215);\n }\n }, {\n key: \"normalizeZ\",\n value: function normalizeZ(points) {\n return (0, curve_ts_1.normalizeZ)(Point, points);\n }\n }, {\n key: \"msm\",\n value: function msm(points, scalars) {\n return (0, curve_ts_1.pippenger)(Point, Fn, points, scalars);\n }\n }]);\n }(); // base / generator point\n Point.BASE = new Point(_CURVE.Gx, _CURVE.Gy, _1n, modP(_CURVE.Gx * _CURVE.Gy));\n // zero / infinity / identity point\n Point.ZERO = new Point(_0n, _1n, _1n, _0n); // 0, 1, 1, 0\n // math field\n Point.Fp = Fp;\n // scalar field\n Point.Fn = Fn;\n var wnaf = new curve_ts_1.wNAF(Point, Fn.BITS);\n Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.\n return Point;\n }\n /**\n * Base class for prime-order points like Ristretto255 and Decaf448.\n * These points eliminate cofactor issues by representing equivalence classes\n * of Edwards curve points.\n */\n var PrimeEdwardsPoint = /*#__PURE__*/function () {\n function PrimeEdwardsPoint(ep) {\n _classCallCheck(this, PrimeEdwardsPoint);\n this.ep = ep;\n }\n // Static methods that must be implemented by subclasses\n return _createClass(PrimeEdwardsPoint, [{\n key: \"x\",\n get: function () {\n return this.toAffine().x;\n }\n }, {\n key: \"y\",\n get: function () {\n return this.toAffine().y;\n }\n // Common implementations\n }, {\n key: \"clearCofactor\",\n value: function clearCofactor() {\n // no-op for prime-order groups\n return this;\n }\n }, {\n key: \"assertValidity\",\n value: function assertValidity() {\n this.ep.assertValidity();\n }\n }, {\n key: \"toAffine\",\n value: function toAffine(invertedZ) {\n return this.ep.toAffine(invertedZ);\n }\n }, {\n key: \"toHex\",\n value: function toHex() {\n return (0, utils_ts_1.bytesToHex)(this.toBytes());\n }\n }, {\n key: \"toString\",\n value: function toString() {\n return this.toHex();\n }\n }, {\n key: \"isTorsionFree\",\n value: function isTorsionFree() {\n return true;\n }\n }, {\n key: \"isSmallOrder\",\n value: function isSmallOrder() {\n return false;\n }\n }, {\n key: \"add\",\n value: function add(other) {\n this.assertSame(other);\n return this.init(this.ep.add(other.ep));\n }\n }, {\n key: \"subtract\",\n value: function subtract(other) {\n this.assertSame(other);\n return this.init(this.ep.subtract(other.ep));\n }\n }, {\n key: \"multiply\",\n value: function multiply(scalar) {\n return this.init(this.ep.multiply(scalar));\n }\n }, {\n key: \"multiplyUnsafe\",\n value: function multiplyUnsafe(scalar) {\n return this.init(this.ep.multiplyUnsafe(scalar));\n }\n }, {\n key: \"double\",\n value: function double() {\n return this.init(this.ep.double());\n }\n }, {\n key: \"negate\",\n value: function negate() {\n return this.init(this.ep.negate());\n }\n }, {\n key: \"precompute\",\n value: function precompute(windowSize, isLazy) {\n return this.init(this.ep.precompute(windowSize, isLazy));\n }\n /** @deprecated use `toBytes` */\n }, {\n key: \"toRawBytes\",\n value: function toRawBytes() {\n return this.toBytes();\n }\n }], [{\n key: \"fromBytes\",\n value: function fromBytes(_bytes) {\n (0, utils_ts_1.notImplemented)();\n }\n }, {\n key: \"fromHex\",\n value: function fromHex(_hex) {\n (0, utils_ts_1.notImplemented)();\n }\n }]);\n }();\n exports.PrimeEdwardsPoint = PrimeEdwardsPoint;\n /**\n * Initializes EdDSA signatures over given Edwards curve.\n */\n function eddsa(Point, cHash) {\n var eddsaOpts = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : {};\n if (typeof cHash !== 'function') throw new Error('\"hash\" function param is required');\n (0, utils_ts_1._validateObject)(eddsaOpts, {}, {\n adjustScalarBytes: 'function',\n randomBytes: 'function',\n domain: 'function',\n prehash: 'function',\n mapToCurve: 'function'\n });\n var prehash = eddsaOpts.prehash;\n var BASE = Point.BASE,\n Fp = Point.Fp,\n Fn = Point.Fn;\n var randomBytes = eddsaOpts.randomBytes || utils_ts_1.randomBytes;\n var adjustScalarBytes = eddsaOpts.adjustScalarBytes || (bytes => bytes);\n var domain = eddsaOpts.domain || ((data, ctx, phflag) => {\n (0, utils_ts_1._abool2)(phflag, 'phflag');\n if (ctx.length || phflag) throw new Error('Contexts/pre-hash are not supported');\n return data;\n }); // NOOP\n // Little-endian SHA512 with modulo n\n function modN_LE(hash) {\n return Fn.create((0, utils_ts_1.bytesToNumberLE)(hash)); // Not Fn.fromBytes: it has length limit\n }\n // Get the hashed private scalar per RFC8032 5.1.5\n function getPrivateScalar(key) {\n var len = lengths.secretKey;\n key = (0, utils_ts_1.ensureBytes)('private key', key, len);\n // Hash private key with curve's hash function to produce uniformingly random input\n // Check byte lengths: ensure(64, h(ensure(32, key)))\n var hashed = (0, utils_ts_1.ensureBytes)('hashed private key', cHash(key), 2 * len);\n var head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE\n var prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)\n var scalar = modN_LE(head); // The actual private scalar\n return {\n head,\n prefix,\n scalar\n };\n }\n /** Convenience method that creates public key from scalar. RFC8032 5.1.5 */\n function getExtendedPublicKey(secretKey) {\n var _getPrivateScalar = getPrivateScalar(secretKey),\n head = _getPrivateScalar.head,\n prefix = _getPrivateScalar.prefix,\n scalar = _getPrivateScalar.scalar;\n var point = BASE.multiply(scalar); // Point on Edwards curve aka public key\n var pointBytes = point.toBytes();\n return {\n head,\n prefix,\n scalar,\n point,\n pointBytes\n };\n }\n /** Calculates EdDSA pub key. RFC8032 5.1.5. */\n function getPublicKey(secretKey) {\n return getExtendedPublicKey(secretKey).pointBytes;\n }\n // int('LE', SHA512(dom2(F, C) || msgs)) mod N\n function hashDomainToScalar() {\n var context = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : Uint8Array.of();\n for (var _len = arguments.length, msgs = new Array(_len > 1 ? _len - 1 : 0), _key = 1; _key < _len; _key++) {\n msgs[_key - 1] = arguments[_key];\n }\n var msg = (0, utils_ts_1.concatBytes)(...msgs);\n return modN_LE(cHash(domain(msg, (0, utils_ts_1.ensureBytes)('context', context), !!prehash)));\n }\n /** Signs message with privateKey. RFC8032 5.1.6 */\n function sign(msg, secretKey) {\n var options = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : {};\n msg = (0, utils_ts_1.ensureBytes)('message', msg);\n if (prehash) msg = prehash(msg); // for ed25519ph etc.\n var _getExtendedPublicKey = getExtendedPublicKey(secretKey),\n prefix = _getExtendedPublicKey.prefix,\n scalar = _getExtendedPublicKey.scalar,\n pointBytes = _getExtendedPublicKey.pointBytes;\n var r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)\n var R = BASE.multiply(r).toBytes(); // R = rG\n var k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)\n var s = Fn.create(r + k * scalar); // S = (r + k * s) mod L\n if (!Fn.isValid(s)) throw new Error('sign failed: invalid s'); // 0 <= s < L\n var rs = (0, utils_ts_1.concatBytes)(R, Fn.toBytes(s));\n return (0, utils_ts_1._abytes2)(rs, lengths.signature, 'result');\n }\n // verification rule is either zip215 or rfc8032 / nist186-5. Consult fromHex:\n var verifyOpts = {\n zip215: true\n };\n /**\n * Verifies EdDSA signature against message and public key. RFC8032 5.1.7.\n * An extended group equation is checked.\n */\n function verify(sig, msg, publicKey) {\n var options = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : verifyOpts;\n var context = options.context,\n zip215 = options.zip215;\n var len = lengths.signature;\n sig = (0, utils_ts_1.ensureBytes)('signature', sig, len);\n msg = (0, utils_ts_1.ensureBytes)('message', msg);\n publicKey = (0, utils_ts_1.ensureBytes)('publicKey', publicKey, lengths.publicKey);\n if (zip215 !== undefined) (0, utils_ts_1._abool2)(zip215, 'zip215');\n if (prehash) msg = prehash(msg); // for ed25519ph, etc\n var mid = len / 2;\n var r = sig.subarray(0, mid);\n var s = (0, utils_ts_1.bytesToNumberLE)(sig.subarray(mid, len));\n var A, R, SB;\n try {\n // zip215=true is good for consensus-critical apps. =false follows RFC8032 / NIST186-5.\n // zip215=true: 0 <= y < MASK (2^256 for ed25519)\n // zip215=false: 0 <= y < P (2^255-19 for ed25519)\n A = Point.fromBytes(publicKey, zip215);\n R = Point.fromBytes(r, zip215);\n SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside\n } catch (error) {\n return false;\n }\n if (!zip215 && A.isSmallOrder()) return false; // zip215 allows public keys of small order\n var k = hashDomainToScalar(context, R.toBytes(), A.toBytes(), msg);\n var RkA = R.add(A.multiplyUnsafe(k));\n // Extended group equation\n // [8][S]B = [8]R + [8][k]A'\n return RkA.subtract(SB).clearCofactor().is0();\n }\n var _size = Fp.BYTES; // 32 for ed25519, 57 for ed448\n var lengths = {\n secretKey: _size,\n publicKey: _size,\n signature: 2 * _size,\n seed: _size\n };\n function randomSecretKey() {\n var seed = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : randomBytes(lengths.seed);\n return (0, utils_ts_1._abytes2)(seed, lengths.seed, 'seed');\n }\n function keygen(seed) {\n var secretKey = utils.randomSecretKey(seed);\n return {\n secretKey,\n publicKey: getPublicKey(secretKey)\n };\n }\n function isValidSecretKey(key) {\n return (0, utils_ts_1.isBytes)(key) && key.length === Fn.BYTES;\n }\n function isValidPublicKey(key, zip215) {\n try {\n return !!Point.fromBytes(key, zip215);\n } catch (error) {\n return false;\n }\n }\n var utils = {\n getExtendedPublicKey,\n randomSecretKey,\n isValidSecretKey,\n isValidPublicKey,\n /**\n * Converts ed public key to x public key. Uses formula:\n * - ed25519:\n * - `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`\n * - `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`\n * - ed448:\n * - `(u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)`\n * - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`\n */\n toMontgomery(publicKey) {\n var _Point$fromBytes = Point.fromBytes(publicKey),\n y = _Point$fromBytes.y;\n var size = lengths.publicKey;\n var is25519 = size === 32;\n if (!is25519 && size !== 57) throw new Error('only defined for 25519 and 448');\n var u = is25519 ? Fp.div(_1n + y, _1n - y) : Fp.div(y - _1n, y + _1n);\n return Fp.toBytes(u);\n },\n toMontgomerySecret(secretKey) {\n var size = lengths.secretKey;\n (0, utils_ts_1._abytes2)(secretKey, size);\n var hashed = cHash(secretKey.subarray(0, size));\n return adjustScalarBytes(hashed).subarray(0, size);\n },\n /** @deprecated */\n randomPrivateKey: randomSecretKey,\n /** @deprecated */\n precompute() {\n var windowSize = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : 8;\n var point = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : Point.BASE;\n return point.precompute(windowSize, false);\n }\n };\n return Object.freeze({\n keygen,\n getPublicKey,\n sign,\n verify,\n utils,\n Point,\n lengths\n });\n }\n function _eddsa_legacy_opts_to_new(c) {\n var CURVE = {\n a: c.a,\n d: c.d,\n p: c.Fp.ORDER,\n n: c.n,\n h: c.h,\n Gx: c.Gx,\n Gy: c.Gy\n };\n var Fp = c.Fp;\n var Fn = (0, modular_ts_1.Field)(CURVE.n, c.nBitLength, true);\n var curveOpts = {\n Fp,\n Fn,\n uvRatio: c.uvRatio\n };\n var eddsaOpts = {\n randomBytes: c.randomBytes,\n adjustScalarBytes: c.adjustScalarBytes,\n domain: c.domain,\n prehash: c.prehash,\n mapToCurve: c.mapToCurve\n };\n return {\n CURVE,\n curveOpts,\n hash: c.hash,\n eddsaOpts\n };\n }\n function _eddsa_new_output_to_legacy(c, eddsa) {\n var Point = eddsa.Point;\n var legacy = Object.assign({}, eddsa, {\n ExtendedPoint: Point,\n CURVE: c,\n nBitLength: Point.Fn.BITS,\n nByteLength: Point.Fn.BYTES\n });\n return legacy;\n }\n // TODO: remove. Use eddsa\n function twistedEdwards(c) {\n var _eddsa_legacy_opts_to = _eddsa_legacy_opts_to_new(c),\n CURVE = _eddsa_legacy_opts_to.CURVE,\n curveOpts = _eddsa_legacy_opts_to.curveOpts,\n hash = _eddsa_legacy_opts_to.hash,\n eddsaOpts = _eddsa_legacy_opts_to.eddsaOpts;\n var Point = edwards(CURVE, curveOpts);\n var EDDSA = eddsa(Point, hash, eddsaOpts);\n return _eddsa_new_output_to_legacy(c, EDDSA);\n 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