5faa06fc143c884d50fa8914fc21d23be45a68ef76ea86c738215c39b6392c0b.json raw

   1  {"ast":null,"code":"\"use strict\";\n\nObject.defineProperty(exports, \"__esModule\", {\n  value: true\n});\nexports.isNegativeLE = void 0;\nexports.mod = mod;\nexports.pow = pow;\nexports.pow2 = pow2;\nexports.invert = invert;\nexports.tonelliShanks = tonelliShanks;\nexports.FpSqrt = FpSqrt;\nexports.validateField = validateField;\nexports.FpPow = FpPow;\nexports.FpInvertBatch = FpInvertBatch;\nexports.FpDiv = FpDiv;\nexports.FpLegendre = FpLegendre;\nexports.FpIsSquare = FpIsSquare;\nexports.nLength = nLength;\nexports.Field = Field;\nexports.FpSqrtOdd = FpSqrtOdd;\nexports.FpSqrtEven = FpSqrtEven;\nexports.hashToPrivateScalar = hashToPrivateScalar;\nexports.getFieldBytesLength = getFieldBytesLength;\nexports.getMinHashLength = getMinHashLength;\nexports.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) */\nconst utils_ts_1 = require(\"../utils.js\");\n// prettier-ignore\nconst _0n = BigInt(0),\n  _1n = BigInt(1),\n  _2n = /* @__PURE__ */BigInt(2),\n  _3n = /* @__PURE__ */BigInt(3);\n// prettier-ignore\nconst _4n = /* @__PURE__ */BigInt(4),\n  _5n = /* @__PURE__ */BigInt(5),\n  _7n = /* @__PURE__ */BigInt(7);\n// prettier-ignore\nconst _8n = /* @__PURE__ */BigInt(8),\n  _9n = /* @__PURE__ */BigInt(9),\n  _16n = /* @__PURE__ */BigInt(16);\n// Calculates a modulo b\nfunction 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 */\nfunction 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)` */\nfunction 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 */\nfunction 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}\nfunction 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'));\nfunction 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}\nfunction 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\nfunction 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 */\nfunction 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 */\nfunction 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);\nconst isNegativeLE = (num, modulo) => (mod(num, modulo) & _1n) === _1n;\nexports.isNegativeLE = isNegativeLE;\n// prettier-ignore\nconst FIELD_FIELDS = ['create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr', 'eql', 'add', 'sub', 'mul', 'pow', 'div', 'addN', 'subN', 'mulN', 'sqrN'];\nfunction 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 */\nfunction 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 */\nfunction 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\nfunction 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 */\nfunction 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.\nfunction FpIsSquare(Fp, n) {\n  const l = FpLegendre(Fp, n);\n  return l === 1;\n}\n// CURVE.n lengths\nfunction 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 */\nfunction Field(ORDER, bitLenOrOpts,\n// TODO: use opts only in v2?\nisLE = 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// },\nfunction 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}\nfunction 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 */\nfunction 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 */\nfunction 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 */\nfunction 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 */\nfunction 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}\n//# sourceMappingURL=modular.js.map","map":null,"metadata":{},"sourceType":"script","externalDependencies":[]}