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emergent-agent-e1
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81 KiB
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1 line
81 KiB
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{"dependencies":[{"name":"../utils.js","data":{"asyncType":null,"isESMImport":false,"locs":[{"start":{"line":31,"column":19,"index":1057},"end":{"line":31,"column":41,"index":1079}}],"key":"Yc7DmwhweSDBIC4bv+r2fO8xp6U=","exportNames":["*"],"imports":1}}],"output":[{"data":{"code":"__d(function (global, require, _$$_IMPORT_DEFAULT, _$$_IMPORT_ALL, module, exports, _dependencyMap) {\n \"use strict\";\n\n Object.defineProperty(exports, \"__esModule\", {\n value: true\n });\n exports.isNegativeLE = void 0;\n exports.mod = mod;\n exports.pow = pow;\n exports.pow2 = pow2;\n exports.invert = invert;\n exports.tonelliShanks = tonelliShanks;\n exports.FpSqrt = FpSqrt;\n exports.validateField = validateField;\n exports.FpPow = FpPow;\n exports.FpInvertBatch = FpInvertBatch;\n exports.FpDiv = FpDiv;\n exports.FpLegendre = FpLegendre;\n exports.FpIsSquare = FpIsSquare;\n exports.nLength = nLength;\n exports.Field = Field;\n exports.FpSqrtOdd = FpSqrtOdd;\n exports.FpSqrtEven = FpSqrtEven;\n exports.hashToPrivateScalar = hashToPrivateScalar;\n exports.getFieldBytesLength = getFieldBytesLength;\n exports.getMinHashLength = getMinHashLength;\n exports.mapHashToField = mapHashToField;\n /**\n * Utils for modular division and fields.\n * Field over 11 is a finite (Galois) field is integer number operations `mod 11`.\n * There is no division: it is replaced by modular multiplicative inverse.\n * @module\n */\n /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */\n const utils_ts_1 = require(_dependencyMap[0], \"../utils.js\");\n // prettier-ignore\n const _0n = BigInt(0),\n _1n = BigInt(1),\n _2n = /* @__PURE__ */BigInt(2),\n _3n = /* @__PURE__ */BigInt(3);\n // prettier-ignore\n const _4n = /* @__PURE__ */BigInt(4),\n _5n = /* @__PURE__ */BigInt(5),\n _7n = /* @__PURE__ */BigInt(7);\n // prettier-ignore\n const _8n = /* @__PURE__ */BigInt(8),\n _9n = /* @__PURE__ */BigInt(9),\n _16n = /* @__PURE__ */BigInt(16);\n // Calculates a modulo b\n function mod(a, b) {\n const result = a % b;\n return result >= _0n ? result : b + result;\n }\n /**\n * Efficiently raise num to power and do modular division.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n * @example\n * pow(2n, 6n, 11n) // 64n % 11n == 9n\n */\n function pow(num, power, modulo) {\n return FpPow(Field(modulo), num, power);\n }\n /** Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)` */\n function pow2(x, power, modulo) {\n let res = x;\n while (power-- > _0n) {\n res *= res;\n res %= modulo;\n }\n return res;\n }\n /**\n * Inverses number over modulo.\n * Implemented using [Euclidean GCD](https://brilliant.org/wiki/extended-euclidean-algorithm/).\n */\n function invert(number, modulo) {\n if (number === _0n) throw new Error('invert: expected non-zero number');\n if (modulo <= _0n) throw new Error('invert: expected positive modulus, got ' + modulo);\n // Fermat's little theorem \"CT-like\" version inv(n) = n^(m-2) mod m is 30x slower.\n let a = mod(number, modulo);\n let b = modulo;\n // prettier-ignore\n let x = _0n,\n y = _1n,\n u = _1n,\n v = _0n;\n while (a !== _0n) {\n // JIT applies optimization if those two lines follow each other\n const q = b / a;\n const r = b % a;\n const m = x - u * q;\n const n = y - v * q;\n // prettier-ignore\n b = a, a = r, x = u, y = v, u = m, v = n;\n }\n const gcd = b;\n if (gcd !== _1n) throw new Error('invert: does not exist');\n return mod(x, modulo);\n }\n function assertIsSquare(Fp, root, n) {\n if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');\n }\n // Not all roots are possible! Example which will throw:\n // const NUM =\n // n = 72057594037927816n;\n // Fp = Field(BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'));\n function sqrt3mod4(Fp, n) {\n const p1div4 = (Fp.ORDER + _1n) / _4n;\n const root = Fp.pow(n, p1div4);\n assertIsSquare(Fp, root, n);\n return root;\n }\n function sqrt5mod8(Fp, n) {\n const p5div8 = (Fp.ORDER - _5n) / _8n;\n const n2 = Fp.mul(n, _2n);\n const v = Fp.pow(n2, p5div8);\n const nv = Fp.mul(n, v);\n const i = Fp.mul(Fp.mul(nv, _2n), v);\n const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));\n assertIsSquare(Fp, root, n);\n return root;\n }\n // Based on RFC9380, Kong algorithm\n // prettier-ignore\n function sqrt9mod16(P) {\n const Fp_ = Field(P);\n const tn = tonelliShanks(P);\n const c1 = tn(Fp_, Fp_.neg(Fp_.ONE)); // 1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F\n const c2 = tn(Fp_, c1); // 2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F\n const c3 = tn(Fp_, Fp_.neg(c1)); // 3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F\n const c4 = (P + _7n) / _16n; // 4. c4 = (q + 7) / 16 # Integer arithmetic\n return (Fp, n) => {\n let tv1 = Fp.pow(n, c4); // 1. tv1 = x^c4\n let tv2 = Fp.mul(tv1, c1); // 2. tv2 = c1 * tv1\n const tv3 = Fp.mul(tv1, c2); // 3. tv3 = c2 * tv1\n const tv4 = Fp.mul(tv1, c3); // 4. tv4 = c3 * tv1\n const e1 = Fp.eql(Fp.sqr(tv2), n); // 5. e1 = (tv2^2) == x\n const e2 = Fp.eql(Fp.sqr(tv3), n); // 6. e2 = (tv3^2) == x\n tv1 = Fp.cmov(tv1, tv2, e1); // 7. tv1 = CMOV(tv1, tv2, e1) # Select tv2 if (tv2^2) == x\n tv2 = Fp.cmov(tv4, tv3, e2); // 8. tv2 = CMOV(tv4, tv3, e2) # Select tv3 if (tv3^2) == x\n const e3 = Fp.eql(Fp.sqr(tv2), n); // 9. e3 = (tv2^2) == x\n const root = Fp.cmov(tv1, tv2, e3); // 10. z = CMOV(tv1, tv2, e3) # Select sqrt from tv1 & tv2\n assertIsSquare(Fp, root, n);\n return root;\n };\n }\n /**\n * Tonelli-Shanks square root search algorithm.\n * 1. https://eprint.iacr.org/2012/685.pdf (page 12)\n * 2. Square Roots from 1; 24, 51, 10 to Dan Shanks\n * @param P field order\n * @returns function that takes field Fp (created from P) and number n\n */\n function tonelliShanks(P) {\n // Initialization (precomputation).\n // Caching initialization could boost perf by 7%.\n if (P < _3n) throw new Error('sqrt is not defined for small field');\n // Factor P - 1 = Q * 2^S, where Q is odd\n let Q = P - _1n;\n let S = 0;\n while (Q % _2n === _0n) {\n Q /= _2n;\n S++;\n }\n // Find the first quadratic non-residue Z >= 2\n let Z = _2n;\n const _Fp = Field(P);\n while (FpLegendre(_Fp, Z) === 1) {\n // Basic primality test for P. After x iterations, chance of\n // not finding quadratic non-residue is 2^x, so 2^1000.\n if (Z++ > 1000) throw new Error('Cannot find square root: probably non-prime P');\n }\n // Fast-path; usually done before Z, but we do \"primality test\".\n if (S === 1) return sqrt3mod4;\n // Slow-path\n // TODO: test on Fp2 and others\n let cc = _Fp.pow(Z, Q); // c = z^Q\n const Q1div2 = (Q + _1n) / _2n;\n return function tonelliSlow(Fp, n) {\n if (Fp.is0(n)) return n;\n // Check if n is a quadratic residue using Legendre symbol\n if (FpLegendre(Fp, n) !== 1) throw new Error('Cannot find square root');\n // Initialize variables for the main loop\n let M = S;\n let c = Fp.mul(Fp.ONE, cc); // c = z^Q, move cc from field _Fp into field Fp\n let t = Fp.pow(n, Q); // t = n^Q, first guess at the fudge factor\n let R = Fp.pow(n, Q1div2); // R = n^((Q+1)/2), first guess at the square root\n // Main loop\n // while t != 1\n while (!Fp.eql(t, Fp.ONE)) {\n if (Fp.is0(t)) return Fp.ZERO; // if t=0 return R=0\n let i = 1;\n // Find the smallest i >= 1 such that t^(2^i) ≡ 1 (mod P)\n let t_tmp = Fp.sqr(t); // t^(2^1)\n while (!Fp.eql(t_tmp, Fp.ONE)) {\n i++;\n t_tmp = Fp.sqr(t_tmp); // t^(2^2)...\n if (i === M) throw new Error('Cannot find square root');\n }\n // Calculate the exponent for b: 2^(M - i - 1)\n const exponent = _1n << BigInt(M - i - 1); // bigint is important\n const b = Fp.pow(c, exponent); // b = 2^(M - i - 1)\n // Update variables\n M = i;\n c = Fp.sqr(b); // c = b^2\n t = Fp.mul(t, c); // t = (t * b^2)\n R = Fp.mul(R, b); // R = R*b\n }\n return R;\n };\n }\n /**\n * Square root for a finite field. Will try optimized versions first:\n *\n * 1. P ≡ 3 (mod 4)\n * 2. P ≡ 5 (mod 8)\n * 3. P ≡ 9 (mod 16)\n * 4. Tonelli-Shanks algorithm\n *\n * Different algorithms can give different roots, it is up to user to decide which one they want.\n * For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).\n */\n function FpSqrt(P) {\n // P ≡ 3 (mod 4) => √n = n^((P+1)/4)\n if (P % _4n === _3n) return sqrt3mod4;\n // P ≡ 5 (mod 8) => Atkin algorithm, page 10 of https://eprint.iacr.org/2012/685.pdf\n if (P % _8n === _5n) return sqrt5mod8;\n // P ≡ 9 (mod 16) => Kong algorithm, page 11 of https://eprint.iacr.org/2012/685.pdf (algorithm 4)\n if (P % _16n === _9n) return sqrt9mod16(P);\n // Tonelli-Shanks algorithm\n return tonelliShanks(P);\n }\n // Little-endian check for first LE bit (last BE bit);\n const isNegativeLE = (num, modulo) => (mod(num, modulo) & _1n) === _1n;\n exports.isNegativeLE = isNegativeLE;\n // prettier-ignore\n const FIELD_FIELDS = ['create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr', 'eql', 'add', 'sub', 'mul', 'pow', 'div', 'addN', 'subN', 'mulN', 'sqrN'];\n function validateField(field) {\n const initial = {\n ORDER: 'bigint',\n MASK: 'bigint',\n BYTES: 'number',\n BITS: 'number'\n };\n const opts = FIELD_FIELDS.reduce((map, val) => {\n map[val] = 'function';\n return map;\n }, initial);\n (0, utils_ts_1._validateObject)(field, opts);\n // const max = 16384;\n // if (field.BYTES < 1 || field.BYTES > max) throw new Error('invalid field');\n // if (field.BITS < 1 || field.BITS > 8 * max) throw new Error('invalid field');\n return field;\n }\n // Generic field functions\n /**\n * Same as `pow` but for Fp: non-constant-time.\n * Unsafe in some contexts: uses ladder, so can expose bigint bits.\n */\n function FpPow(Fp, num, power) {\n if (power < _0n) throw new Error('invalid exponent, negatives unsupported');\n if (power === _0n) return Fp.ONE;\n if (power === _1n) return num;\n let p = Fp.ONE;\n let d = num;\n while (power > _0n) {\n if (power & _1n) p = Fp.mul(p, d);\n d = Fp.sqr(d);\n power >>= _1n;\n }\n return p;\n }\n /**\n * Efficiently invert an array of Field elements.\n * Exception-free. Will return `undefined` for 0 elements.\n * @param passZero map 0 to 0 (instead of undefined)\n */\n function FpInvertBatch(Fp, nums, passZero = false) {\n const inverted = new Array(nums.length).fill(passZero ? Fp.ZERO : undefined);\n // Walk from first to last, multiply them by each other MOD p\n const multipliedAcc = nums.reduce((acc, num, i) => {\n if (Fp.is0(num)) return acc;\n inverted[i] = acc;\n return Fp.mul(acc, num);\n }, Fp.ONE);\n // Invert last element\n const invertedAcc = Fp.inv(multipliedAcc);\n // Walk from last to first, multiply them by inverted each other MOD p\n nums.reduceRight((acc, num, i) => {\n if (Fp.is0(num)) return acc;\n inverted[i] = Fp.mul(acc, inverted[i]);\n return Fp.mul(acc, num);\n }, invertedAcc);\n return inverted;\n }\n // TODO: remove\n function FpDiv(Fp, lhs, rhs) {\n return Fp.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, Fp.ORDER) : Fp.inv(rhs));\n }\n /**\n * Legendre symbol.\n * Legendre constant is used to calculate Legendre symbol (a | p)\n * which denotes the value of a^((p-1)/2) (mod p).\n *\n * * (a | p) ≡ 1 if a is a square (mod p), quadratic residue\n * * (a | p) ≡ -1 if a is not a square (mod p), quadratic non residue\n * * (a | p) ≡ 0 if a ≡ 0 (mod p)\n */\n function FpLegendre(Fp, n) {\n // We can use 3rd argument as optional cache of this value\n // but seems unneeded for now. The operation is very fast.\n const p1mod2 = (Fp.ORDER - _1n) / _2n;\n const powered = Fp.pow(n, p1mod2);\n const yes = Fp.eql(powered, Fp.ONE);\n const zero = Fp.eql(powered, Fp.ZERO);\n const no = Fp.eql(powered, Fp.neg(Fp.ONE));\n if (!yes && !zero && !no) throw new Error('invalid Legendre symbol result');\n return yes ? 1 : zero ? 0 : -1;\n }\n // This function returns True whenever the value x is a square in the field F.\n function FpIsSquare(Fp, n) {\n const l = FpLegendre(Fp, n);\n return l === 1;\n }\n // CURVE.n lengths\n function nLength(n, nBitLength) {\n // Bit size, byte size of CURVE.n\n if (nBitLength !== undefined) (0, utils_ts_1.anumber)(nBitLength);\n const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;\n const nByteLength = Math.ceil(_nBitLength / 8);\n return {\n nBitLength: _nBitLength,\n nByteLength\n };\n }\n /**\n * Creates a finite field. Major performance optimizations:\n * * 1. Denormalized operations like mulN instead of mul.\n * * 2. Identical object shape: never add or remove keys.\n * * 3. `Object.freeze`.\n * Fragile: always run a benchmark on a change.\n * Security note: operations don't check 'isValid' for all elements for performance reasons,\n * it is caller responsibility to check this.\n * This is low-level code, please make sure you know what you're doing.\n *\n * Note about field properties:\n * * CHARACTERISTIC p = prime number, number of elements in main subgroup.\n * * ORDER q = similar to cofactor in curves, may be composite `q = p^m`.\n *\n * @param ORDER field order, probably prime, or could be composite\n * @param bitLen how many bits the field consumes\n * @param isLE (default: false) if encoding / decoding should be in little-endian\n * @param redef optional faster redefinitions of sqrt and other methods\n */\n function Field(ORDER, bitLenOrOpts,\n // TODO: use opts only in v2?\n isLE = false, opts = {}) {\n if (ORDER <= _0n) throw new Error('invalid field: expected ORDER > 0, got ' + ORDER);\n let _nbitLength = undefined;\n let _sqrt = undefined;\n let modFromBytes = false;\n let allowedLengths = undefined;\n if (typeof bitLenOrOpts === 'object' && bitLenOrOpts != null) {\n if (opts.sqrt || isLE) throw new Error('cannot specify opts in two arguments');\n const _opts = bitLenOrOpts;\n if (_opts.BITS) _nbitLength = _opts.BITS;\n if (_opts.sqrt) _sqrt = _opts.sqrt;\n if (typeof _opts.isLE === 'boolean') isLE = _opts.isLE;\n if (typeof _opts.modFromBytes === 'boolean') modFromBytes = _opts.modFromBytes;\n allowedLengths = _opts.allowedLengths;\n } else {\n if (typeof bitLenOrOpts === 'number') _nbitLength = bitLenOrOpts;\n if (opts.sqrt) _sqrt = opts.sqrt;\n }\n const {\n nBitLength: BITS,\n nByteLength: BYTES\n } = nLength(ORDER, _nbitLength);\n if (BYTES > 2048) throw new Error('invalid field: expected ORDER of <= 2048 bytes');\n let sqrtP; // cached sqrtP\n const f = Object.freeze({\n ORDER,\n isLE,\n BITS,\n BYTES,\n MASK: (0, utils_ts_1.bitMask)(BITS),\n ZERO: _0n,\n ONE: _1n,\n allowedLengths: allowedLengths,\n create: num => mod(num, ORDER),\n isValid: num => {\n if (typeof num !== 'bigint') throw new Error('invalid field element: expected bigint, got ' + typeof num);\n return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible\n },\n is0: num => num === _0n,\n // is valid and invertible\n isValidNot0: num => !f.is0(num) && f.isValid(num),\n isOdd: num => (num & _1n) === _1n,\n neg: num => mod(-num, ORDER),\n eql: (lhs, rhs) => lhs === rhs,\n sqr: num => mod(num * num, ORDER),\n add: (lhs, rhs) => mod(lhs + rhs, ORDER),\n sub: (lhs, rhs) => mod(lhs - rhs, ORDER),\n mul: (lhs, rhs) => mod(lhs * rhs, ORDER),\n pow: (num, power) => FpPow(f, num, power),\n div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),\n // Same as above, but doesn't normalize\n sqrN: num => num * num,\n addN: (lhs, rhs) => lhs + rhs,\n subN: (lhs, rhs) => lhs - rhs,\n mulN: (lhs, rhs) => lhs * rhs,\n inv: num => invert(num, ORDER),\n sqrt: _sqrt || (n => {\n if (!sqrtP) sqrtP = FpSqrt(ORDER);\n return sqrtP(f, n);\n }),\n toBytes: num => isLE ? (0, utils_ts_1.numberToBytesLE)(num, BYTES) : (0, utils_ts_1.numberToBytesBE)(num, BYTES),\n fromBytes: (bytes, skipValidation = true) => {\n if (allowedLengths) {\n if (!allowedLengths.includes(bytes.length) || bytes.length > BYTES) {\n throw new Error('Field.fromBytes: expected ' + allowedLengths + ' bytes, got ' + bytes.length);\n }\n const padded = new Uint8Array(BYTES);\n // isLE add 0 to right, !isLE to the left.\n padded.set(bytes, isLE ? 0 : padded.length - bytes.length);\n bytes = padded;\n }\n if (bytes.length !== BYTES) throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);\n let scalar = isLE ? (0, utils_ts_1.bytesToNumberLE)(bytes) : (0, utils_ts_1.bytesToNumberBE)(bytes);\n if (modFromBytes) scalar = mod(scalar, ORDER);\n if (!skipValidation) if (!f.isValid(scalar)) throw new Error('invalid field element: outside of range 0..ORDER');\n // NOTE: we don't validate scalar here, please use isValid. This done such way because some\n // protocol may allow non-reduced scalar that reduced later or changed some other way.\n return scalar;\n },\n // TODO: we don't need it here, move out to separate fn\n invertBatch: lst => FpInvertBatch(f, lst),\n // We can't move this out because Fp6, Fp12 implement it\n // and it's unclear what to return in there.\n cmov: (a, b, c) => c ? b : a\n });\n return Object.freeze(f);\n }\n // Generic random scalar, we can do same for other fields if via Fp2.mul(Fp2.ONE, Fp2.random)?\n // This allows unsafe methods like ignore bias or zero. These unsafe, but often used in different protocols (if deterministic RNG).\n // which mean we cannot force this via opts.\n // Not sure what to do with randomBytes, we can accept it inside opts if wanted.\n // Probably need to export getMinHashLength somewhere?\n // random(bytes?: Uint8Array, unsafeAllowZero = false, unsafeAllowBias = false) {\n // const LEN = !unsafeAllowBias ? getMinHashLength(ORDER) : BYTES;\n // if (bytes === undefined) bytes = randomBytes(LEN); // _opts.randomBytes?\n // const num = isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);\n // // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0\n // const reduced = unsafeAllowZero ? mod(num, ORDER) : mod(num, ORDER - _1n) + _1n;\n // return reduced;\n // },\n function FpSqrtOdd(Fp, elm) {\n if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n const root = Fp.sqrt(elm);\n return Fp.isOdd(root) ? root : Fp.neg(root);\n }\n function FpSqrtEven(Fp, elm) {\n if (!Fp.isOdd) throw new Error(\"Field doesn't have isOdd\");\n const root = Fp.sqrt(elm);\n return Fp.isOdd(root) ? Fp.neg(root) : root;\n }\n /**\n * \"Constant-time\" private key generation utility.\n * Same as mapKeyToField, but accepts less bytes (40 instead of 48 for 32-byte field).\n * Which makes it slightly more biased, less secure.\n * @deprecated use `mapKeyToField` instead\n */\n function hashToPrivateScalar(hash, groupOrder, isLE = false) {\n hash = (0, utils_ts_1.ensureBytes)('privateHash', hash);\n const hashLen = hash.length;\n const minLen = nLength(groupOrder).nByteLength + 8;\n if (minLen < 24 || hashLen < minLen || hashLen > 1024) throw new Error('hashToPrivateScalar: expected ' + minLen + '-1024 bytes of input, got ' + hashLen);\n const num = isLE ? (0, utils_ts_1.bytesToNumberLE)(hash) : (0, utils_ts_1.bytesToNumberBE)(hash);\n return mod(num, groupOrder - _1n) + _1n;\n }\n /**\n * Returns total number of bytes consumed by the field element.\n * For example, 32 bytes for usual 256-bit weierstrass curve.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of field\n */\n function getFieldBytesLength(fieldOrder) {\n if (typeof fieldOrder !== 'bigint') throw new Error('field order must be bigint');\n const bitLength = fieldOrder.toString(2).length;\n return Math.ceil(bitLength / 8);\n }\n /**\n * Returns minimal amount of bytes that can be safely reduced\n * by field order.\n * Should be 2^-128 for 128-bit curve such as P256.\n * @param fieldOrder number of field elements, usually CURVE.n\n * @returns byte length of target hash\n */\n function getMinHashLength(fieldOrder) {\n const length = getFieldBytesLength(fieldOrder);\n return length + Math.ceil(length / 2);\n }\n /**\n * \"Constant-time\" private key generation utility.\n * Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF\n * and convert them into private scalar, with the modulo bias being negligible.\n * Needs at least 48 bytes of input for 32-byte private key.\n * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/\n * FIPS 186-5, A.2 https://csrc.nist.gov/publications/detail/fips/186/5/final\n * RFC 9380, https://www.rfc-editor.org/rfc/rfc9380#section-5\n * @param hash hash output from SHA3 or a similar function\n * @param groupOrder size of subgroup - (e.g. secp256k1.CURVE.n)\n * @param isLE interpret hash bytes as LE num\n * @returns valid private scalar\n */\n function mapHashToField(key, fieldOrder, isLE = false) {\n const len = key.length;\n const fieldLen = getFieldBytesLength(fieldOrder);\n const minLen = getMinHashLength(fieldOrder);\n // No small numbers: need to understand bias story. No huge numbers: easier to detect JS timings.\n if (len < 16 || len < minLen || len > 1024) throw new Error('expected ' + minLen + '-1024 bytes of input, got ' + len);\n const num = isLE ? (0, utils_ts_1.bytesToNumberLE)(key) : (0, utils_ts_1.bytesToNumberBE)(key);\n // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0\n const reduced = mod(num, fieldOrder - _1n) + _1n;\n return isLE ? (0, utils_ts_1.numberToBytesLE)(reduced, fieldLen) : (0, utils_ts_1.numberToBytesBE)(reduced, fieldLen);\n 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