291 lines
10 KiB
Markdown
291 lines
10 KiB
Markdown
|
# 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](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility).
|
||
|
|
|
||
|
|
_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html)**_
|
||
|
|
|
||
|
|
Many platforms provide native support for cryptography, such as [webcrypto](https://w3c.github.io/webcrypto/Overview.html) or [node crypto](https://nodejs.org/dist/latest/docs/api/crypto.html).
|
||
|
|
|
||
|
|
## Installation
|
||
|
|
bigint-utils is distributed as both an ES6 and a CJS module.
|
||
|
|
|
||
|
|
The ES6 module is built for any [web browser supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). 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`:
|
||
|
|
```bash
|
||
|
|
npm install bigint-utils
|
||
|
|
```
|
||
|
|
|
||
|
|
For web browsers, you can also [download the bundle from GitHub](https://raw.githubusercontent.com/juanelas/bigint-utils/master/dist/bigint-utils-latest.browser.mod.min.js).
|
||
|
|
|
||
|
|
## Usage example
|
||
|
|
|
||
|
|
With node js:
|
||
|
|
```javascript
|
||
|
|
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:
|
||
|
|
```html
|
||
|
|
<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
|
||
|
|
|
||
|
|
<dl>
|
||
|
|
<dt><a href="#abs">abs</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#gcd">gcd</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#lcm">lcm</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#toZn">toZn</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#eGcd">eGcd</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
|
||
|
|
<dd><p>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).</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#modInv">modInv</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>Modular inverse.</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#modPow">modPow</a> ⇒ <code>bigint</code></dt>
|
||
|
|
<dd><p>Modular exponentiation a**b mod n</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#randBytes">randBytes</a> ⇒ <code>Promise</code></dt>
|
||
|
|
<dd><p>Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#randBetween">randBetween</a> ⇒ <code>Promise</code></dt>
|
||
|
|
<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#isProbablyPrime">isProbablyPrime</a> ⇒ <code>Promise</code></dt>
|
||
|
|
<dd><p>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)</p>
|
||
|
|
</dd>
|
||
|
|
<dt><a href="#prime">prime</a> ⇒ <code>Promise</code></dt>
|
||
|
|
<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator</p>
|
||
|
|
</dd>
|
||
|
|
</dl>
|
||
|
|
|
||
|
|
## Typedefs
|
||
|
|
|
||
|
|
<dl>
|
||
|
|
<dt><a href="#egcdReturn">egcdReturn</a> : <code>Object</code></dt>
|
||
|
|
<dd><p>A triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
|
||
|
|
</dd>
|
||
|
|
</dl>
|
||
|
|
|
||
|
|
<a name="abs"></a>
|
||
|
|
|
||
|
|
## abs ⇒ <code>bigint</code>
|
||
|
|
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - the absolute value of a
|
||
|
|
|
||
|
|
| Param | Type |
|
||
|
|
| --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> |
|
||
|
|
|
||
|
|
<a name="gcd"></a>
|
||
|
|
|
||
|
|
## gcd ⇒ <code>bigint</code>
|
||
|
|
Greatest-common divisor of two integers based on the iterative binary algorithm.
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - The greatest common divisor of a and b
|
||
|
|
|
||
|
|
| Param | Type |
|
||
|
|
| --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> |
|
||
|
|
| b | <code>number</code> \| <code>bigint</code> |
|
||
|
|
|
||
|
|
<a name="lcm"></a>
|
||
|
|
|
||
|
|
## lcm ⇒ <code>bigint</code>
|
||
|
|
The least common multiple computed as abs(a*b)/gcd(a,b)
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - The least common multiple of a and b
|
||
|
|
|
||
|
|
| Param | Type |
|
||
|
|
| --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> |
|
||
|
|
| b | <code>number</code> \| <code>bigint</code> |
|
||
|
|
|
||
|
|
<a name="toZn"></a>
|
||
|
|
|
||
|
|
## toZn ⇒ <code>bigint</code>
|
||
|
|
Finds the smallest positive element that is congruent to a in modulo n
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> | An integer |
|
||
|
|
| n | <code>number</code> \| <code>bigint</code> | The modulo |
|
||
|
|
|
||
|
|
<a name="eGcd"></a>
|
||
|
|
|
||
|
|
## eGcd ⇒ [<code>egcdReturn</code>](#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 | <code>number</code> \| <code>bigint</code> |
|
||
|
|
| b | <code>number</code> \| <code>bigint</code> |
|
||
|
|
|
||
|
|
<a name="modInv"></a>
|
||
|
|
|
||
|
|
## modInv ⇒ <code>bigint</code>
|
||
|
|
Modular inverse.
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - the inverse modulo n
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> | The number to find an inverse for |
|
||
|
|
| n | <code>number</code> \| <code>bigint</code> | The modulo |
|
||
|
|
|
||
|
|
<a name="modPow"></a>
|
||
|
|
|
||
|
|
## modPow ⇒ <code>bigint</code>
|
||
|
|
Modular exponentiation a**b mod n
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>bigint</code> - a**b mod n
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| a | <code>number</code> \| <code>bigint</code> | base |
|
||
|
|
| b | <code>number</code> \| <code>bigint</code> | exponent |
|
||
|
|
| n | <code>number</code> \| <code>bigint</code> | modulo |
|
||
|
|
|
||
|
|
<a name="randBytes"></a>
|
||
|
|
|
||
|
|
## randBytes ⇒ <code>Promise</code>
|
||
|
|
Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>Promise</code> - A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| byteLength | <code>number</code> | The desired number of random bytes |
|
||
|
|
| forceLength | <code>boolean</code> | If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 |
|
||
|
|
|
||
|
|
<a name="randBetween"></a>
|
||
|
|
|
||
|
|
## randBetween ⇒ <code>Promise</code>
|
||
|
|
Returns a cryptographically secure random integer between [min,max]
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>Promise</code> - A promise that resolves to a cryptographically secure random bigint between [min,max]
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| max | <code>bigint</code> | Returned value will be <= max |
|
||
|
|
| min | <code>bigint</code> | Returned value will be >= min |
|
||
|
|
|
||
|
|
<a name="isProbablyPrime"></a>
|
||
|
|
|
||
|
|
## isProbablyPrime ⇒ <code>Promise</code>
|
||
|
|
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**: <code>Promise</code> - A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| w | <code>bigint</code> | An integer to be tested for primality |
|
||
|
|
| iterations | <code>number</code> | The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 |
|
||
|
|
|
||
|
|
<a name="prime"></a>
|
||
|
|
|
||
|
|
## prime ⇒ <code>Promise</code>
|
||
|
|
A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator
|
||
|
|
|
||
|
|
**Kind**: global constant
|
||
|
|
**Returns**: <code>Promise</code> - A promise that resolves to a bigint probable prime of bitLength bits
|
||
|
|
|
||
|
|
| Param | Type | Description |
|
||
|
|
| --- | --- | --- |
|
||
|
|
| bitLength | <code>number</code> | The required bit length for the generated prime |
|
||
|
|
| iterations | <code>number</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
|
||
|
|
|
||
|
|
<a name="egcdReturn"></a>
|
||
|
|
|
||
|
|
## egcdReturn : <code>Object</code>
|
||
|
|
A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
||
|
|
|
||
|
|
**Kind**: global typedef
|
||
|
|
**Properties**
|
||
|
|
|
||
|
|
| Name | Type |
|
||
|
|
| --- | --- |
|
||
|
|
| g | <code>bigint</code> |
|
||
|
|
| x | <code>bigint</code> |
|
||
|
|
| y | <code>bigint</code> |
|
||
|
|
|
||
|
|
|
||
|
|
* * *
|