bigint-crypto-utils

Utils for working with cryptography using native JS (stage 3) implementation of BigInt. It includes some extra functions to work with modular arithmetics along with secure random numbers and a fast strong probable prime generator/tester (parallelised multi-threaded Miller-Rabin primality test). It can be used by any Web Browser or webview supporting BigInt and with Node.js (>=10.4.0). In the latter case, for multi-threaded primality tests, you should use Node.js 11 or enable at runtime with node --experimental-worker with Node.js >=10.5.0.

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 Web Cryptography API or Node.js Crypto.

Installation

bigint-crypto-utils is distributed for web browsers and/or webviews supporting BigInt as an ES6 module or an IIFE file; and for Node.js (>=10.4.0), as a CJS module.

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

npm install bigint-crypto-utils

NPM installation defaults to the ES6 module for browsers and the CJS one for Node.js.

For web browsers, you can also directly download the minimised version of the IIFE file or the ES6 module from GitHub.

Usage example

With node js:

const bigintCryptoUtils = require('bigint-crypto-utils');

/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter new no-so-linter-friendly syntax 666n.
Notice that you can also pass a number, e.g. BigInt(666), but it is not
recommended since values over 2**53 - 1 won't be safe but no warning will
be raised.
*/
let a = BigInt('5');
let b = BigInt('2');
let n = BigInt('19');

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bigint-crypto-utils JS Doc

Functions

abs(a) ⇒ bigint

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

bitLength(a) ⇒ number

Returns the bitlength of a number

eGcd(a, b) ⇒ 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).

gcd(a, b) ⇒ bigint

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

isProbablyPrime(w, iterations) ⇒ 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)

lcm(a, b) ⇒ bigint

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

max(a, b) ⇒ bigint

Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b

min(a, b) ⇒ bigint

Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b

modInv(a, n) ⇒ bigint

Modular inverse.

modPow(b, e, n) ⇒ bigint

Modular exponentiation b**e mod n. Currently using the right-to-left binary method

prime(bitLength, [iterations]) ⇒ Promise

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).

primeSync(bitLength, [iterations]) ⇒ bigint

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.

randBetween(max, [min]) ⇒ bigint

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

randBits(bitLength, [forceLength]) ⇒ Buffer | Uint8Array

Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

randBytes(byteLength, [forceLength]) ⇒ Promise

Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

randBytesSync(byteLength, [forceLength]) ⇒ Buffer | Uint8Array

Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

toZn(a, n) ⇒ bigint

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

Typedefs

egcdReturn : Object

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

abs(a) ⇒ bigint

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

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

Param	Type
a	number | bigint

bitLength(a) ⇒ number

Returns the bitlength of a number

Kind: global function
Returns: number - - the bit length

Param	Type
a	number | bigint

eGcd(a, b) ⇒ 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 function
Returns: egcdReturn - A triple (g, x, y), such that ax + by = g = gcd(a, b).

Param	Type
a	number | bigint
b	number | bigint

gcd(a, b) ⇒ bigint

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

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

Param	Type
a	number | bigint
b	number | bigint

isProbablyPrime(w, iterations) ⇒ 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 function
Returns: Promise - A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)

Param	Type	Description
w	number | 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

lcm(a, b) ⇒ bigint

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

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

Param	Type
a	number | bigint
b	number | bigint

max(a, b) ⇒ bigint

Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b

Kind: global function
Returns: bigint - maximum of numbers a and b

Param	Type
a	number | bigint
b	number | bigint

min(a, b) ⇒ bigint

Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b

Kind: global function
Returns: bigint - minimum of numbers a and b

Param	Type
a	number | bigint
b	number | bigint

modInv(a, n) ⇒ bigint

Modular inverse.

Kind: global function
Returns: bigint - the inverse modulo n or NaN if it does not exist

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

modPow(b, e, n) ⇒ bigint

Modular exponentiation b**e mod n. Currently using the right-to-left binary method

Kind: global function
Returns: bigint - b**e mod n

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

prime(bitLength, [iterations]) ⇒ Promise

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).

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

Param	Type	Default	Description
bitLength	number		The required bit length for the generated prime
[iterations]	number	16	The number of iterations for the Miller-Rabin Probabilistic Primality Test

primeSync(bitLength, [iterations]) ⇒ bigint

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.

Kind: global function
Returns: bigint - A bigint probable prime of bitLength bits.

Param	Type	Default	Description
bitLength	number		The required bit length for the generated prime
[iterations]	number	16	The number of iterations for the Miller-Rabin Probabilistic Primality Test

randBetween(max, [min]) ⇒ bigint

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

Kind: global function
Returns: bigint - A cryptographically secure random bigint between [min,max]

Param	Type	Default	Description
max	bigint		Returned value will be <= max
[min]	bigint	BigInt(1)	Returned value will be >= min

randBits(bitLength, [forceLength]) ⇒ Buffer | Uint8Array

Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

Kind: global function
Returns: Buffer | Uint8Array - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits

Param	Type	Default	Description
bitLength	number		The desired number of random bits
[forceLength]	boolean	false	If we want to force the output to have a specific bit length. It basically forces the msb to be 1

randBytes(byteLength, [forceLength]) ⇒ Promise

Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

Kind: global function
Returns: Promise - A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes

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

randBytesSync(byteLength, [forceLength]) ⇒ Buffer | Uint8Array

Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

Kind: global function
Returns: Buffer | Uint8Array - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes

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

toZn(a, n) ⇒ bigint

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

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

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

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

---