bigint-mod-arith/README.md

bigint-mod-arith

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

If you are looking for a cryptographically secure random generator and for probale 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 webcrypto or node crypto.

Installation

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

npm install bigint-mod-arith

For web browsers, you can also download the bundle from GitHub or just hotlink to it:

<script type="module" src="https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js"></script>

Usage examples

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

// Stage 3 BigInts with value 666 can be declared as BigInt('666') 
// or the shorter no-linter-friendly new 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

bigint-mod-arith JS Doc

Functions

abs(a) ⇒ bigint

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

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)

toZn(a, n) ⇒ bigint

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

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).

modInv(a, n) ⇒ bigint

Modular inverse.

modPow(a, b, n) ⇒ bigint

Modular exponentiation a**b mod 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

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

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

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

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

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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