bigint-mod-arith

Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used by any Web Browser or webview supporting BigInt and with Node.js (>=10.4.0).

If you are looking for a cryptographically-secure random generator and for strong probable primes (generation and testing), you may be interested in bigint-secrets

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-mod-arith 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-mod-arith can be imported to your project with npm:

npm install bigint-mod-arith

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 bigintModArith = require('bigint-mod-arith');

/* 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

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

<script type="module">
    import * as bigintModArith from 'bigint-mod-arith-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
</script>

bigint-mod-arith JS Doc

Functions

abs(a) ⇒ bigint

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

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.

lcm(a, b) ⇒ bigint

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

modInv(a, n) ⇒ bigint

Modular inverse.

modPow(a, b, n) ⇒ bigint

Modular exponentiation a**b mod n

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

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

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

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

modInv(a, n) ⇒ bigint

Modular inverse.

Kind: global function
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(a, b, n) ⇒ bigint

Modular exponentiation a**b mod n

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

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

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

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