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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 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 |