bigint-utils

Some extra functions to work with modular arithmetics along with secure random numbers and probable prime (Miller-Rabin primality test) generation/testing using native JS (stage 3) implementation of BigInt. It can be used with Node.js (>=10.4.0) and Web Browsers supporting BigInt.

The operations supported on BigInts are not constant time. BigInt can be therefore unsuitable for use in cryptography

Many platforms provide native support for cryptography, such as webcrypto or node crypto.

Installation

bigint-utils is distributed as both an ES6 and a CJS module.

The ES6 module is built for any web browser supporting BigInt. The module only uses native javascript implementations and no polyfills had been applied.

The CJS module is built as a standard node module.

bigint-utils can be imported to your project with npm:

npm install bigint-utils

For web browsers, you can also download the bundle from GitHub.

Usage example

With node js:

const bigintUtils = require('bigint-utils');

// Stage 3 BigInts with value 666 can be declared as BigInt('666')
// or the shorter new no-so-linter-friendly syntax 666n
let a = BigInt('5');
let b = BigInt('2');
let n = BigInt('19');

console.log(bigintModArith.modPow(a, b, n)); // prints 6

console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3

console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2

// Generation of a probable prime of 2048 bits
const prime = await bigintUtils.prime(2048);

// Testing if a prime is a probable prime (Miller-Rabin)
if ( await bigintUtils.isProbablyPrime(prime) )
    // code if is prime

// Get a cryptographically secure random number between 1 and 2**256 bits.
const rnd = bigintUtils.randBetween(BigInt(2)**256);

From a browser, you can just load the module in a html page as:

  <script type="module">
    import * as bigintUtils from 'bigint-utils-latest.browser.mod.min.js';

    let a = BigInt('5');
    let b = BigInt('2');
    let n = BigInt('19');

    console.log(bigintModArith.modPow(a, b, n)); // prints 6

    console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3

    console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2

    (async function () {
      // Generation of a probable prime of 2018 bits
      const p = await bigintSecrets.prime(2048);

      // Testing if a prime is a probable prime (Miller-Rabin)
      const isPrime = await bigintSecrets.isProbablyPrime(p);
      alert(p.toString() + '\nIs prime?\n' + isPrime);

      // Get a cryptographically secure random number between 1 and 2**256 bits.
      const rnd = await bigintSecrets.randBetween(BigInt(2)**256);
      alert(rnd);
    })();
  </script>

bigint-utils JS Doc

Constants

abs ⇒ bigint

Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

gcd ⇒ bigint

Greatest-common divisor of two integers based on the iterative binary algorithm.

lcm ⇒ bigint

The least common multiple computed as abs(a*b)/gcd(a,b)

toZn ⇒ bigint

Finds the smallest positive element that is congruent to a in modulo n

eGcd ⇒ egcdReturn

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).

modInv ⇒ bigint

Modular inverse.

modPow ⇒ bigint

Modular exponentiation a**b mod n

randBytes ⇒ Promise

Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process

randBetween ⇒ Promise

Returns a cryptographically secure random integer between [min,max]

isProbablyPrime ⇒ Promise

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)

prime ⇒ Promise

A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator

Typedefs

egcdReturn : Object

A triple (g, x, y), such that ax + by = g = gcd(a, b).

abs ⇒ bigint

Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

Kind: global constant
Returns: bigint - the absolute value of a

Param	Type
a	number | bigint

gcd ⇒ bigint

Greatest-common divisor of two integers based on the iterative binary algorithm.

Kind: global constant
Returns: bigint - The greatest common divisor of a and b

Param	Type
a	number | bigint
b	number | bigint

lcm ⇒ bigint

The least common multiple computed as abs(a*b)/gcd(a,b)

Kind: global constant
Returns: bigint - The least common multiple of a and b

Param	Type
a	number | bigint
b	number | bigint

toZn ⇒ bigint

Finds the smallest positive element that is congruent to a in modulo n

Kind: global constant
Returns: bigint - The smallest positive representation of a in modulo n

Param	Type	Description
a	number | bigint	An integer
n	number | bigint	The modulo

eGcd ⇒ egcdReturn

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).

Kind: global constant

Param	Type
a	number | bigint
b	number | bigint

modInv ⇒ bigint

Modular inverse.

Kind: global constant
Returns: bigint - the inverse modulo n

Param	Type	Description
a	number | bigint	The number to find an inverse for
n	number | bigint	The modulo

modPow ⇒ bigint

Modular exponentiation a**b mod n

Kind: global constant
Returns: bigint - a**b mod n

Param	Type	Description
a	number | bigint	base
b	number | bigint	exponent
n	number | bigint	modulo

randBytes ⇒ Promise

Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process

Kind: global constant
Returns: Promise - A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes

Param	Type	Description
byteLength	number	The desired number of random bytes
forceLength	boolean	If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1

randBetween ⇒ Promise

Returns a cryptographically secure random integer between [min,max]

Kind: global constant
Returns: Promise - A promise that resolves to a cryptographically secure random bigint between [min,max]

Param	Type	Description
max	bigint	Returned value will be <= max
min	bigint	Returned value will be >= min

isProbablyPrime ⇒ Promise

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)

Kind: global constant
Returns: Promise - A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)

Param	Type	Description
w	bigint	An integer to be tested for primality
iterations	number	The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3

prime ⇒ Promise

A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator

Kind: global constant
Returns: Promise - A promise that resolves to a bigint probable prime of bitLength bits

Param	Type	Description
bitLength	number	The required bit length for the generated prime
iterations	number	The number of iterations for the Miller-Rabin Probabilistic Primality Test

egcdReturn : Object

A triple (g, x, y), such that ax + by = g = gcd(a, b).

Kind: global typedef
Properties

Name	Type
g	bigint
x	bigint
y	bigint

---