bigint-crypto-utils/lib/index.node.js

'use strict'

Object.defineProperty(exports, '__esModule', { value: true })

const _ZERO = BigInt(0)
const _ONE = BigInt(1)
const _TWO = BigInt(2)

/**
 * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
 *
 * @param {number|bigint} a
 *
 * @returns {bigint} the absolute value of a
 */
function abs (a) {
  a = BigInt(a)
  return (a >= _ZERO) ? a : -a
}

/**
 * Returns the bitlength of a number
 *
 * @param {number|bigint} a
 * @returns {number} - the bit length
 */
function bitLength (a) {
  a = BigInt(a)
  if (a === _ONE) { return 1 }
  let bits = 1
  do {
    bits++
  } while ((a >>= _ONE) > _ONE)
  return bits
}

/**
 * @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
 * @property {bigint} g
 * @property {bigint} x
 * @property {bigint} y
 */
/**
 * An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
 * Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
 *
 * @param {number|bigint} a
 * @param {number|bigint} b
 *
 * @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
 */
function eGcd (a, b) {
  a = BigInt(a)
  b = BigInt(b)
  if (a <= _ZERO | b <= _ZERO) { return NaN } // a and b MUST be positive

  let x = _ZERO
  let y = _ONE
  let u = _ONE
  let v = _ZERO

  while (a !== _ZERO) {
    const q = b / a
    const r = b % a
    const m = x - (u * q)
    const n = y - (v * q)
    b = a
    a = r
    x = u
    y = v
    u = m
    v = n
  }
  return {
    b: b,
    x: x,
    y: y
  }
}

/**
 * Greatest-common divisor of two integers based on the iterative binary algorithm.
 *
 * @param {number|bigint} a
 * @param {number|bigint} b
 *
 * @returns {bigint} The greatest common divisor of a and b
 */
function gcd (a, b) {
  a = abs(a)
  b = abs(b)
  if (a === _ZERO) { return b } else if (b === _ZERO) { return a }

  let shift = _ZERO
  while (!((a | b) & _ONE)) {
    a >>= _ONE
    b >>= _ONE
    shift++
  }
  while (!(a & _ONE)) a >>= _ONE
  do {
    while (!(b & _ONE)) b >>= _ONE
    if (a > b) {
      const x = a
      a = b
      b = x
    }
    b -= a
  } while (b)

  // rescale
  return a << shift
}

/**
 * The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
 * iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
 *
 * @param {number|bigint} w An integer to be tested for primality
 * @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
 *
 * @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
 */
async function isProbablyPrime (w, iterations = 16) {
  if (typeof w === 'number') {
    w = BigInt(w)
  }
  /* eslint-disable no-lone-blocks */
  { // Node.js
    if (_useWorkers) {
      const { Worker } = require('worker_threads')
      return new Promise((resolve, reject) => {
        const worker = new Worker(__filename)

        worker.on('message', (data) => {
          worker.terminate()
          resolve(data.isPrime)
        })

        worker.on('error', reject)

        worker.postMessage({
          rnd: w,
          iterations: iterations,
          id: 0

        })
      })
    } else {
      return new Promise((resolve) => {
        resolve(_isProbablyPrime(w, iterations))
      })
    }
  }
  /* eslint-enable no-lone-blocks */
}

/**
 * The least common multiple computed as abs(a*b)/gcd(a,b)
 * @param {number|bigint} a
 * @param {number|bigint} b
 *
 * @returns {bigint} The least common multiple of a and b
 */
function lcm (a, b) {
  a = BigInt(a)
  b = BigInt(b)
  if (a === _ZERO && b === _ZERO) { return _ZERO }
  return abs(a * b) / gcd(a, b)
}

/**
 * Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
 *
 * @param {number|bigint} a
 * @param {number|bigint} b
 *
 * @returns {bigint} maximum of numbers a and b
 */
function max (a, b) {
  a = BigInt(a)
  b = BigInt(b)
  return (a >= b) ? a : b
}

/**
 * Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
 *
 * @param {number|bigint} a
 * @param {number|bigint} b
 *
 * @returns {bigint} minimum of numbers a and b
 */
function min (a, b) {
  a = BigInt(a)
  b = BigInt(b)
  return (a >= b) ? b : a
}

/**
 * Modular inverse.
 *
 * @param {number|bigint} a The number to find an inverse for
 * @param {number|bigint} n The modulo
 *
 * @returns {bigint} the inverse modulo n or NaN if it does not exist
 */
function modInv (a, n) {
  const egcd = eGcd(toZn(a, n), n)
  if (egcd.b !== _ONE) {
    return NaN // modular inverse does not exist
  } else {
    return toZn(egcd.x, n)
  }
}

/**
 * Modular exponentiation b**e mod n. Currently using the right-to-left binary method
 *
 * @param {number|bigint} b base
 * @param {number|bigint} e exponent
 * @param {number|bigint} n modulo
 *
 * @returns {bigint} b**e mod n
 */
function modPow (b, e, n) {
  n = BigInt(n)
  if (n === _ZERO) { return NaN } else if (n === _ONE) { return _ZERO }

  b = toZn(b, n)

  e = BigInt(e)
  if (e < _ZERO) {
    return modInv(modPow(b, abs(e), n), n)
  }

  let r = _ONE
  while (e > 0) {
    if ((e % _TWO) === _ONE) {
      r = (r * b) % n
    }
    e = e / _TWO
    b = b ** _TWO % n
  }
  return r
}

/**
 * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
 * The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
 * main process, and it can be much faster (if several cores or cpu are available).
 * The node version can also use worker_threads if they are available (enabled by default with Node 11 and
 * and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
 *
 * @param {number} bitLength The required bit length for the generated prime
 * @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
 *
 * @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
 */
function prime (bitLength, iterations = 16) {
  if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }

  if (!_useWorkers) {
    let rnd = _ZERO
    do {
      rnd = fromBuffer(randBytesSync(bitLength / 8, true))
    } while (!_isProbablyPrime(rnd, iterations))
    return new Promise((resolve) => { resolve(rnd) })
  }
  return new Promise((resolve) => {
    const workerList = []
    const _onmessage = (msg, newWorker) => {
      if (msg.isPrime) {
        // if a prime number has been found, stop all the workers, and return it
        for (let j = 0; j < workerList.length; j++) {
          workerList[j].terminate()
        }
        while (workerList.length) {
          workerList.pop()
        }
        resolve(msg.value)
      } else { // if a composite is found, make the worker test another random number
        const buf = randBits(bitLength, true)
        const rnd = fromBuffer(buf)
        try {
          newWorker.postMessage({
            rnd: rnd,
            iterations: iterations,
            id: msg.id
          })
        } catch (error) {
          // The worker has already terminated. There is nothing to handle here
        }
      }
    }
    /* eslint-disable no-lone-blocks */
    { // Node.js
      const { cpus } = require('os')
      const { Worker } = require('worker_threads')
      for (let i = 0; i < cpus().length; i++) {
        const newWorker = new Worker(__filename)
        newWorker.on('message', (msg) => _onmessage(msg, newWorker))
        workerList.push(newWorker)
      }
    }
    /* eslint-enable no-lone-blocks */
    for (let i = 0; i < workerList.length; i++) {
      const buf = randBits(bitLength, true)
      const rnd = fromBuffer(buf)
      workerList[i].postMessage({
        rnd: rnd,
        iterations: iterations,
        id: i
      })
    }
  })
}

/**
 * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
 * The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
 *
 * @param {number} bitLength The required bit length for the generated prime
 * @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
 *
 * @returns {bigint} A bigint probable prime of bitLength bits.
 */
function primeSync (bitLength, iterations = 16) {
  if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
  let rnd = _ZERO
  do {
    rnd = fromBuffer(randBytesSync(bitLength / 8, true))
  } while (!_isProbablyPrime(rnd, iterations))
  return rnd
}

/**
 * Returns a cryptographically secure random integer between [min,max]
 * @param {bigint} max Returned value will be <= max
 * @param {bigint} [min = BigInt(1)] Returned value will be >= min
 *
 * @returns {bigint} A cryptographically secure random bigint between [min,max]
 */
function randBetween (max, min = _ONE) {
  if (max <= min) throw new Error('max must be > min')
  const interval = max - min
  const bitLen = bitLength(interval)
  let rnd
  do {
    const buf = randBits(bitLen)
    rnd = fromBuffer(buf)
  } while (rnd > interval)
  return rnd + min
}

/**
 * Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 *
 * @param {number} bitLength The desired number of random bits
 * @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
 *
 * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
 */
function randBits (bitLength, forceLength = false) {
  if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }

  const byteLength = Math.ceil(bitLength / 8)
  const rndBytes = randBytesSync(byteLength, false)
  // Fill with 0's the extra bits
  rndBytes[0] = rndBytes[0] & (2 ** (bitLength % 8) - 1)
  if (forceLength) {
    const mask = (bitLength % 8) ? 2 ** ((bitLength % 8) - 1) : 128
    rndBytes[0] = rndBytes[0] | mask
  }
  return rndBytes
}

/**
 * Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 *
 * @param {number} byteLength The desired number of random bytes
 * @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
 *
 * @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
 */
function randBytes (byteLength, forceLength = false) {
  if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }

  let buf
  /* eslint-disable no-lone-blocks */
  { // node
    const crypto = require('crypto')
    buf = Buffer.alloc(byteLength)
    return crypto.randomFill(buf, function (resolve) {
      // If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
      if (forceLength) { buf[0] = buf[0] | 128 }
      resolve(buf)
    })
  }
  /* eslint-disable no-lone-blocks */
}

/**
 * Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
 *
 * @param {number} byteLength The desired number of random bytes
 * @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
 *
 * @returns {Buffer|Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
 */
function randBytesSync (byteLength, forceLength = false) {
  if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }

  let buf
  { // node
    const crypto = require('crypto')
    buf = Buffer.alloc(byteLength)
    crypto.randomFillSync(buf)
  }
  // If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
  if (forceLength) { buf[0] = buf[0] | 128 }
  return buf
}

/**
 * Finds the smallest positive element that is congruent to a in modulo n
 * @param {number|bigint} a An integer
 * @param {number|bigint} n The modulo
 *
 * @returns {bigint} The smallest positive representation of a in modulo n
 */
function toZn (a, n) {
  n = BigInt(n)
  if (n <= 0) { return NaN }

  a = BigInt(a) % n
  return (a < 0) ? a + n : a
}

/* HELPER FUNCTIONS */

function fromBuffer (buf) {
  let ret = _ZERO
  for (const i of buf.values()) {
    const bi = BigInt(i)
    ret = (ret << BigInt(8)) + bi
  }
  return ret
}

function _isProbablyPrime (w, iterations = 16) {
  /*
  PREFILTERING. Even values but 2 are not primes, so don't test.
  1 is not a prime and the M-R algorithm needs w>1.
  */
  if (w === _TWO) { return true } else if ((w & _ONE) === _ZERO || w === _ONE) { return false }

  /*
    Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
    */
  const firstPrimes = [
    3,
    5,
    7,
    11,
    13,
    17,
    19,
    23,
    29,
    31,
    37,
    41,
    43,
    47,
    53,
    59,
    61,
    67,
    71,
    73,
    79,
    83,
    89,
    97,
    101,
    103,
    107,
    109,
    113,
    127,
    131,
    137,
    139,
    149,
    151,
    157,
    163,
    167,
    173,
    179,
    181,
    191,
    193,
    197,
    199,
    211,
    223,
    227,
    229,
    233,
    239,
    241,
    251,
    257,
    263,
    269,
    271,
    277,
    281,
    283,
    293,
    307,
    311,
    313,
    317,
    331,
    337,
    347,
    349,
    353,
    359,
    367,
    373,
    379,
    383,
    389,
    397,
    401,
    409,
    419,
    421,
    431,
    433,
    439,
    443,
    449,
    457,
    461,
    463,
    467,
    479,
    487,
    491,
    499,
    503,
    509,
    521,
    523,
    541,
    547,
    557,
    563,
    569,
    571,
    577,
    587,
    593,
    599,
    601,
    607,
    613,
    617,
    619,
    631,
    641,
    643,
    647,
    653,
    659,
    661,
    673,
    677,
    683,
    691,
    701,
    709,
    719,
    727,
    733,
    739,
    743,
    751,
    757,
    761,
    769,
    773,
    787,
    797,
    809,
    811,
    821,
    823,
    827,
    829,
    839,
    853,
    857,
    859,
    863,
    877,
    881,
    883,
    887,
    907,
    911,
    919,
    929,
    937,
    941,
    947,
    953,
    967,
    971,
    977,
    983,
    991,
    997,
    1009,
    1013,
    1019,
    1021,
    1031,
    1033,
    1039,
    1049,
    1051,
    1061,
    1063,
    1069,
    1087,
    1091,
    1093,
    1097,
    1103,
    1109,
    1117,
    1123,
    1129,
    1151,
    1153,
    1163,
    1171,
    1181,
    1187,
    1193,
    1201,
    1213,
    1217,
    1223,
    1229,
    1231,
    1237,
    1249,
    1259,
    1277,
    1279,
    1283,
    1289,
    1291,
    1297,
    1301,
    1303,
    1307,
    1319,
    1321,
    1327,
    1361,
    1367,
    1373,
    1381,
    1399,
    1409,
    1423,
    1427,
    1429,
    1433,
    1439,
    1447,
    1451,
    1453,
    1459,
    1471,
    1481,
    1483,
    1487,
    1489,
    1493,
    1499,
    1511,
    1523,
    1531,
    1543,
    1549,
    1553,
    1559,
    1567,
    1571,
    1579,
    1583,
    1597
  ]
  for (let i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) {
    const p = BigInt(firstPrimes[i])
    if (w === p) { return true } else if (w % p === _ZERO) { return false }
  }

  /*
    1. Let a be the largest integer such that 2**a divides w−1.
    2. m = (w−1) / 2**a.
    3. wlen = len (w).
    4. For i = 1 to iterations do
        4.1 Obtain a string b of wlen bits from an RBG.
        Comment: Ensure that 1 < b < w−1.
        4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
        4.3 z = b**m mod w.
        4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
        4.5 For j = 1 to a − 1 do.
        4.5.1 z = z**2 mod w.
        4.5.2 If (z = w−1), then go to step 4.7.
        4.5.3 If (z = 1), then go to step 4.6.
        4.6 Return COMPOSITE.
        4.7 Continue.
        Comment: Increment i for the do-loop in step 4.
    5. Return PROBABLY PRIME.
    */
  let a = _ZERO; let d = w - _ONE
  while (d % _TWO === _ZERO) {
    d /= _TWO
    ++a
  }

  const m = (w - _ONE) / (_TWO ** a)

  /* eslint-disable no-labels */
  loop: do {
    const b = randBetween(w - _ONE, _TWO)
    let z = modPow(b, m, w)
    if (z === _ONE || z === w - _ONE) { continue }

    for (let j = 1; j < a; j++) {
      z = modPow(z, _TWO, w)
      if (z === w - _ONE) { continue loop }
      if (z === _ONE) { break }
    }
    return false
  } while (--iterations)
  /* eslint-enable no-labels */

  return true
}

let _useWorkers = true // The following is just to check whether Node.js can use workers
{ // Node.js
  _useWorkers = (function _workers () {
    try {
      require.resolve('worker_threads')
      return true
    } catch (e) {
      console.log(`[bigint-crypto-utils] WARNING:
This node version doesn't support worker_threads. You should enable them in order to greatly speedup the generation of big prime numbers.
    · With Node 11 it is enabled by default (consider upgrading).
    · With Node 10, starting with 10.5.0, you can enable worker_threads at runtime executing node --experimental-worker `)
      return false
    }
  })()
}

if (_useWorkers) { // node.js with support for workers
  const { parentPort, isMainThread } = require('worker_threads')
  if (!isMainThread) { // worker
    parentPort.on('message', function (data) { // Let's start once we are called
      // data = {rnd: <bigint>, iterations: <number>}
      const isPrime = _isProbablyPrime(data.rnd, data.iterations)
      parentPort.postMessage({
        isPrime: isPrime,
        value: data.rnd,
        id: data.id
      })
    })
  }
}

exports.abs = abs
exports.bitLength = bitLength
exports.eGcd = eGcd
exports.gcd = gcd
exports.isProbablyPrime = isProbablyPrime
exports.lcm = lcm
exports.max = max
exports.min = min
exports.modInv = modInv
exports.modPow = modPow
exports.prime = prime
exports.primeSync = primeSync
exports.randBetween = randBetween
exports.randBits = randBits
exports.randBytes = randBytes
exports.randBytesSync = randBytesSync
exports.toZn = toZn