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Now the bundle can be mangled. Multi-threaded uses all CPUs but 1. Readme improvements

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juanelas 2020-04-07 17:03:30 +02:00
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@ -16,9 +16,9 @@ bigint-crypto-utils can be imported to your project with `npm`:
npm install bigint-crypto-utils
```
NPM installation defaults to the minified ES6 module for browsers and the CJS one for Node.js.
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 [IIFE file](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.js) or the [ES6 module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.mod.js) from GitHub.
For web browsers, you can also directly download the [IIFE bundle](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.js) or the [ES6 bundle module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.mod.js) from GitHub.
## Usage examples
@ -29,26 +29,25 @@ Import your module as :
const bigintCryptoUtils = require('bigint-crypto-utils')
... // your code here
```
- Javascript native project
- JavaScript native project
```javascript
import * as bigintCryptoUtils from 'bigint-crypto-utils'
... // your code here
```
- Javascript native browser ES6 mod
- JavaScript native browser ES6 mod
```html
<script type="module">
import * as bigintCryptoUtils from 'lib/index.browser.bundle.mod.js' // Use you actual path to the broser mod bundle
... // your code here
</script>
import as bcu from 'bigint-crypto-utils'
... // your code here
```
- Javascript native browser IIFE
- JavaScript native browser IIFE
```html
<script src="../../lib/index.browser.bundle.js"></script>
<script src="../../lib/index.browser.bundle.js"></script> <!-- Use you actual path to the browser bundle -->
<script>
... // your code here
</script>
```
- TypeScript
```typescript
import * as bigintCryptoUtils from 'bigint-crypto-utils'
@ -56,6 +55,8 @@ Import your module as :
```
> BigInt is [ES-2020](https://tc39.es/ecma262/#sec-bigint-objects). In order to use it with TypeScript you should set `lib` (and probably also `target` and `module`) to `esnext` in `tsconfig.json`.
And you could use it like in the following:
```javascript
/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter new no-so-linter-friendly syntax 666n.
@ -65,22 +66,22 @@ be raised.
*/
const a = BigInt('5')
const b = BigInt('2')
const n = BigInt('19')
const n = 19n
console.log(bigintCryptoUtils.modPow(a, b, n)) // prints 6
console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))) // prints 3
console.log(bigintCryptoUtils.modInv(2n, 5n)) // prints 3
console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))) // prints 2
console.log(bigintCryptoUtils.randBetween(BigInt(2) ** BigInt(256))) // Prints a cryptographically secure random number between 1 and 2**256 bits.
console.log(bigintCryptoUtils.randBetween(2n ** 256n)) // Prints a cryptographically secure random number between 1 and 2**256 bits.
async function primeTesting () {
// Output of a probable prime of 2048 bits
console.log(await bigintCryptoUtils.prime(2048))
// Testing if a number is a probable prime (Miller-Rabin)
const number = 27
const number = 27n
const isPrime = await bigintCryptoUtils.isProbablyPrime(number)
if (isPrime) {
console.log(`${number} is prime`)
@ -93,78 +94,7 @@ primeTesting()
```
## bigint-crypto-utils JS Doc
### Functions
<dl>
<dt><a href="#abs">abs(a)</a> ⇒ <code>bigint</code></dt>
<dd><p>Absolute value. abs(a)==a if a&gt;=0. abs(a)==-a if a&lt;0</p>
</dd>
<dt><a href="#bitLength">bitLength(a)</a> ⇒ <code>number</code></dt>
<dd><p>Returns the bitlength of a number</p>
</dd>
<dt><a href="#eGcd">eGcd(a, b)</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="#gcd">gcd(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
</dd>
<dt><a href="#isProbablyPrime">isProbablyPrime(w, [iterations])</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="#lcm">lcm(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
</dd>
<dt><a href="#max">max(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>Maximum. max(a,b)==a if a&gt;=b. max(a,b)==b if a&lt;=b</p>
</dd>
<dt><a href="#min">min(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>Minimum. min(a,b)==b if a&gt;=b. min(a,b)==a if a&lt;=b</p>
</dd>
<dt><a href="#modInv">modInv(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular inverse.</p>
</dd>
<dt><a href="#modPow">modPow(b, e, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular exponentiation b**e mod n. Currently using the right-to-left binary method</p>
</dd>
<dt><a href="#prime">prime(bitLength, [iterations])</a> ⇒ <code>Promise</code></dt>
<dd><p>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 &gt;=10.5.0).</p>
</dd>
<dt><a href="#primeSync">primeSync(bitLength, [iterations])</a> ⇒ <code>bigint</code></dt>
<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
The sync version is NOT RECOMMENDED since it won&#39;t use workers and thus it&#39;ll be slower and may freeze thw window in browser&#39;s javascript. Please consider using prime() instead.</p>
</dd>
<dt><a href="#randBetween">randBetween(max, [min])</a> ⇒ <code>bigint</code></dt>
<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
</dd>
<dt><a href="#randBits">randBits(bitLength, [forceLength])</a> ⇒ <code>Buffer</code> | <code>Uint8Array</code></dt>
<dd><p>Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
</dd>
<dt><a href="#randBytes">randBytes(byteLength, [forceLength])</a> ⇒ <code>Promise</code></dt>
<dd><p>Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
</dd>
<dt><a href="#randBytesSync">randBytesSync(byteLength, [forceLength])</a> ⇒ <code>Buffer</code> | <code>Uint8Array</code></dt>
<dd><p>Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
</dd>
<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Finds the smallest positive element that is congruent to a in modulo n</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>
## API reference documentation
<a name="abs"></a>
@ -217,20 +147,6 @@ Greatest-common divisor of two integers based on the iterative binary algorithm.
| a | <code>number</code> \| <code>bigint</code> |
| b | <code>number</code> \| <code>bigint</code> |
<a name="isProbablyPrime"></a>
### isProbablyPrime(w, [iterations]) ⇒ <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 function
**Returns**: <code>Promise</code> - A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| w | <code>number</code> \| <code>bigint</code> | | An integer to be tested for primality |
| [iterations] | <code>number</code> | <code>16</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="lcm"></a>
### lcm(a, b) ⇒ <code>bigint</code>
@ -297,89 +213,6 @@ Modular exponentiation b**e mod n. Currently using the right-to-left binary meth
| e | <code>number</code> \| <code>bigint</code> | exponent |
| n | <code>number</code> \| <code>bigint</code> | modulo |
<a name="prime"></a>
### prime(bitLength, [iterations]) ⇒ <code>Promise</code>
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**: <code>Promise</code> - A promise that resolves to a bigint probable prime of bitLength bits.
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| bitLength | <code>number</code> | | The required bit length for the generated prime |
| [iterations] | <code>number</code> | <code>16</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
<a name="primeSync"></a>
### primeSync(bitLength, [iterations]) ⇒ <code>bigint</code>
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**: <code>bigint</code> - A bigint probable prime of bitLength bits.
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| bitLength | <code>number</code> | | The required bit length for the generated prime |
| [iterations] | <code>number</code> | <code>16</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
<a name="randBetween"></a>
### randBetween(max, [min]) ⇒ <code>bigint</code>
Returns a cryptographically secure random integer between [min,max]
**Kind**: global function
**Returns**: <code>bigint</code> - A cryptographically secure random bigint between [min,max]
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| max | <code>bigint</code> | | Returned value will be <= max |
| [min] | <code>bigint</code> | <code>BigInt(1)</code> | Returned value will be >= min |
<a name="randBits"></a>
### randBits(bitLength, [forceLength]) ⇒ <code>Buffer</code> \| <code>Uint8Array</code>
Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
**Kind**: global function
**Returns**: <code>Buffer</code> \| <code>Uint8Array</code> - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| bitLength | <code>number</code> | | The desired number of random bits |
| [forceLength] | <code>boolean</code> | <code>false</code> | If we want to force the output to have a specific bit length. It basically forces the msb to be 1 |
<a name="randBytes"></a>
### randBytes(byteLength, [forceLength]) ⇒ <code>Promise</code>
Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
**Kind**: global function
**Returns**: <code>Promise</code> - A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| byteLength | <code>number</code> | | The desired number of random bytes |
| [forceLength] | <code>boolean</code> | <code>false</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="randBytesSync"></a>
### randBytesSync(byteLength, [forceLength]) ⇒ <code>Buffer</code> \| <code>Uint8Array</code>
Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
**Kind**: global function
**Returns**: <code>Buffer</code> \| <code>Uint8Array</code> - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
| Param | Type | Default | Description |
| --- | --- | --- | --- |
| byteLength | <code>number</code> | | The desired number of random bytes |
| [forceLength] | <code>boolean</code> | <code>false</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="toZn"></a>
### toZn(a, n) ⇒ <code>bigint</code>

24
build/build.docs.js Normal file
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@ -0,0 +1,24 @@
'use strict'
const fs = require('fs')
const jsdoc2md = require('jsdoc-to-markdown')
const path = require('path')
const pkgJson = require('../package.json')
const rootDir = path.join(__dirname, '..')
const template = path.join(rootDir, pkgJson.directories.src, 'doc', 'readme-template.md')
const input = path.join(rootDir, pkgJson.directories.lib, 'index.node.js')
const options = {
source: fs.readFileSync(input, { encoding: 'UTF-8' }), // we need to use this instead of files in order to avoid issues with esnext features
template: fs.readFileSync(template, { encoding: 'UTF-8' }),
'heading-depth': 3, // The initial heading depth. For example, with a value of 2 the top-level markdown headings look like "## The heading"
'global-index-format': 'none' // none, grouped, table, dl.
}
const readmeContents = jsdoc2md.renderSync(options)
const readmeFile = path.join(rootDir, 'README.md')
fs.writeFileSync(readmeFile, readmeContents)

12
build/rollup.config.js
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@ -37,8 +37,8 @@ module.exports = [
replace({
'process.browser': true
})
]
// external: ['bigint-crypto-utils']
],
external: ['bigint-mod-arith']
},
{ // Browser bundles
input: input,
@ -61,8 +61,8 @@ module.exports = [
browser: true
}),
terser({
mangle: false,
compress: false
// mangle: false,
// compress: false
})
]
},
@ -76,7 +76,7 @@ module.exports = [
output: {
file: path.join(dstDir, 'index.node.js'),
format: 'cjs'
}
// external: ['bigint-crypto-utils']
},
external: ['bigint-mod-arith']
}
]

2
lib/index.browser.bundle.js
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2
lib/index.browser.bundle.mod.js
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792
lib/index.browser.mod.js
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@ -1,112 +1,5 @@
const _ZERO = BigInt(0)
const _ONE = BigInt(1)
const _TWO = BigInt(2)
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
* @param {number|bigint} a
*
* @returns {bigint} the absolute value of a
*/
function abs (a) {
a = BigInt(a)
return (a >= _ZERO) ? a : -a
}
/**
* Returns the bitlength of a number
*
* @param {number|bigint} a
* @returns {number} - the bit length
*/
function bitLength (a) {
a = BigInt(a)
if (a === _ONE) { return 1 }
let bits = 1
do {
bits++
} while ((a >>= _ONE) > _ONE)
return bits
}
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
* @property {bigint} g
* @property {bigint} x
* @property {bigint} y
*/
/**
* 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).
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
function eGcd (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a <= _ZERO | b <= _ZERO) { return NaN } // a and b MUST be positive
let x = _ZERO
let y = _ONE
let u = _ONE
let v = _ZERO
while (a !== _ZERO) {
const q = b / a
const r = b % a
const m = x - (u * q)
const n = y - (v * q)
b = a
a = r
x = u
y = v
u = m
v = n
}
return {
b: b,
x: x,
y: y
}
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
function gcd (a, b) {
a = abs(a)
b = abs(b)
if (a === _ZERO) { return b } else if (b === _ZERO) { return a }
let shift = _ZERO
while (!((a | b) & _ONE)) {
a >>= _ONE
b >>= _ONE
shift++
}
while (!(a & _ONE)) a >>= _ONE
do {
while (!(b & _ONE)) b >>= _ONE
if (a > b) {
const x = a
a = b
b = x
}
b -= a
} while (b)
// rescale
return a << shift
}
import { bitLength, eGcd, modInv, modPow, toZn } from 'bigint-mod-arith'
export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn } from 'bigint-mod-arith'
/**
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
@ -115,7 +8,7 @@ function gcd (a, b) {
* @param {number | bigint} w An integer to be tested for primality
* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
*
* @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
* @return {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
*/
async function isProbablyPrime (w, iterations = 16) {
if (typeof w === 'number') {
@ -145,96 +38,6 @@ async function isProbablyPrime (w, iterations = 16) {
/* eslint-enable no-lone-blocks */
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
function lcm (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a === _ZERO && b === _ZERO) { return _ZERO }
return abs(a * b) / gcd(a, b)
}
/**
* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} maximum of numbers a and b
*/
function max (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? a : b
}
/**
* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} minimum of numbers a and b
*/
function min (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? b : a
}
/**
* Modular inverse.
*
* @param {number|bigint} a The number to find an inverse for
* @param {number|bigint} n The modulo
*
* @returns {bigint} the inverse modulo n or NaN if it does not exist
*/
function modInv (a, n) {
const egcd = eGcd(toZn(a, n), n)
if (egcd.b !== _ONE) {
return NaN // modular inverse does not exist
} else {
return toZn(egcd.x, n)
}
}
/**
* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
*
* @param {number|bigint} b base
* @param {number|bigint} e exponent
* @param {number|bigint} n modulo
*
* @returns {bigint} b**e mod n
*/
function modPow (b, e, n) {
n = BigInt(n)
if (n === _ZERO) { return NaN } else if (n === _ONE) { return _ZERO }
b = toZn(b, n)
e = BigInt(e)
if (e < _ZERO) {
return modInv(modPow(b, abs(e), n), n)
}
let r = _ONE
while (e > 0) {
if ((e % _TWO) === _ONE) {
r = (r * b) % n
}
e = e / _TWO
b = b ** _TWO % n
}
return r
}
/**
* 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
@ -245,7 +48,7 @@ function modPow (b, e, n) {
* @param {number} bitLength The required bit length for the generated prime
* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
*/
function prime (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
@ -278,7 +81,7 @@ function prime (bitLength, iterations = 16) {
/* eslint-disable no-lone-blocks */
{ // browser
const workerURL = _isProbablyPrimeWorkerUrl()
for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) {
const newWorker = new Worker(workerURL)
newWorker.onmessage = (event) => _onmessage(event.data, newWorker)
workerList.push(newWorker)
@ -308,7 +111,7 @@ function prime (bitLength, iterations = 16) {
*/
function primeSync (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
let rnd = _ZERO
let rnd = 0n
do {
rnd = fromBuffer(randBytesSync(bitLength / 8, true))
} while (!_isProbablyPrime(rnd, iterations))
@ -322,7 +125,7 @@ function primeSync (bitLength, iterations = 16) {
*
* @returns {bigint} A cryptographically secure random bigint between [min,max]
*/
function randBetween (max, min = _ONE) {
function randBetween (max, min = 1n) {
if (max <= min) throw new Error('max must be > min')
const interval = max - min
const bitLen = bitLength(interval)
@ -367,7 +170,7 @@ function randBits (bitLength, forceLength = false) {
* @param {number} byteLength The desired number of random bytes
* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
*/
function randBytes (byteLength, forceLength = false) {
if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
@ -407,25 +210,10 @@ function randBytesSync (byteLength, forceLength = false) {
return buf
}
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
function toZn (a, n) {
n = BigInt(n)
if (n <= 0) { return NaN }
a = BigInt(a) % n
return (a < 0) ? a + n : a
}
/* HELPER FUNCTIONS */
function fromBuffer (buf) {
let ret = _ZERO
let ret = 0n
for (const i of buf.values()) {
const bi = BigInt(i)
ret = (ret << BigInt(8)) + bi
@ -435,7 +223,7 @@ function fromBuffer (buf) {
function _isProbablyPrimeWorkerUrl () {
// Let's us first add all the required functions
let workerCode = `'use strict';const _ZERO = BigInt(0);const _ONE = BigInt(1);const _TWO = BigInt(2);const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBits = ${randBits.toString()};const randBytesSync = ${randBytesSync.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`
let workerCode = `'use strict';const ${eGcd.name}=${eGcd.toString()};const ${modInv.name}=${modInv.toString()};const ${modPow.name}=${modPow.toString()};const ${toZn.name}=${toZn.toString()};const ${randBits.name}=${randBits.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`
const onmessage = async function (event) { // Let's start once we are called
// event.data = {rnd: <bigint>, iterations: <number>}
@ -463,269 +251,269 @@ function _isProbablyPrime (w, iterations = 16) {
PREFILTERING. Even values but 2 are not primes, so don't test.
1 is not a prime and the M-R algorithm needs w>1.
*/
if (w === _TWO) { return true } else if ((w & _ONE) === _ZERO || w === _ONE) { return false }
if (w === 2n) { return true } else if ((w & 1n) === 0n || w === 1n) { return false }
/*
Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
*/
const firstPrimes = [
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
43,
47,
53,
59,
61,
67,
71,
73,
79,
83,
89,
97,
101,
103,
107,
109,
113,
127,
131,
137,
139,
149,
151,
157,
163,
167,
173,
179,
181,
191,
193,
197,
199,
211,
223,
227,
229,
233,
239,
241,
251,
257,
263,
269,
271,
277,
281,
283,
293,
307,
311,
313,
317,
331,
337,
347,
349,
353,
359,
367,
373,
379,
383,
389,
397,
401,
409,
419,
421,
431,
433,
439,
443,
449,
457,
461,
463,
467,
479,
487,
491,
499,
503,
509,
521,
523,
541,
547,
557,
563,
569,
571,
577,
587,
593,
599,
601,
607,
613,
617,
619,
631,
641,
643,
647,
653,
659,
661,
673,
677,
683,
691,
701,
709,
719,
727,
733,
739,
743,
751,
757,
761,
769,
773,
787,
797,
809,
811,
821,
823,
827,
829,
839,
853,
857,
859,
863,
877,
881,
883,
887,
907,
911,
919,
929,
937,
941,
947,
953,
967,
971,
977,
983,
991,
997,
1009,
1013,
1019,
1021,
1031,
1033,
1039,
1049,
1051,
1061,
1063,
1069,
1087,
1091,
1093,
1097,
1103,
1109,
1117,
1123,
1129,
1151,
1153,
1163,
1171,
1181,
1187,
1193,
1201,
1213,
1217,
1223,
1229,
1231,
1237,
1249,
1259,
1277,
1279,
1283,
1289,
1291,
1297,
1301,
1303,
1307,
1319,
1321,
1327,
1361,
1367,
1373,
1381,
1399,
1409,
1423,
1427,
1429,
1433,
1439,
1447,
1451,
1453,
1459,
1471,
1481,
1483,
1487,
1489,
1493,
1499,
1511,
1523,
1531,
1543,
1549,
1553,
1559,
1567,
1571,
1579,
1583,
1597
3n,
5n,
7n,
11n,
13n,
17n,
19n,
23n,
29n,
31n,
37n,
41n,
43n,
47n,
53n,
59n,
61n,
67n,
71n,
73n,
79n,
83n,
89n,
97n,
101n,
103n,
107n,
109n,
113n,
127n,
131n,
137n,
139n,
149n,
151n,
157n,
163n,
167n,
173n,
179n,
181n,
191n,
193n,
197n,
199n,
211n,
223n,
227n,
229n,
233n,
239n,
241n,
251n,
257n,
263n,
269n,
271n,
277n,
281n,
283n,
293n,
307n,
311n,
313n,
317n,
331n,
337n,
347n,
349n,
353n,
359n,
367n,
373n,
379n,
383n,
389n,
397n,
401n,
409n,
419n,
421n,
431n,
433n,
439n,
443n,
449n,
457n,
461n,
463n,
467n,
479n,
487n,
491n,
499n,
503n,
509n,
521n,
523n,
541n,
547n,
557n,
563n,
569n,
571n,
577n,
587n,
593n,
599n,
601n,
607n,
613n,
617n,
619n,
631n,
641n,
643n,
647n,
653n,
659n,
661n,
673n,
677n,
683n,
691n,
701n,
709n,
719n,
727n,
733n,
739n,
743n,
751n,
757n,
761n,
769n,
773n,
787n,
797n,
809n,
811n,
821n,
823n,
827n,
829n,
839n,
853n,
857n,
859n,
863n,
877n,
881n,
883n,
887n,
907n,
911n,
919n,
929n,
937n,
941n,
947n,
953n,
967n,
971n,
977n,
983n,
991n,
997n,
1009n,
1013n,
1019n,
1021n,
1031n,
1033n,
1039n,
1049n,
1051n,
1061n,
1063n,
1069n,
1087n,
1091n,
1093n,
1097n,
1103n,
1109n,
1117n,
1123n,
1129n,
1151n,
1153n,
1163n,
1171n,
1181n,
1187n,
1193n,
1201n,
1213n,
1217n,
1223n,
1229n,
1231n,
1237n,
1249n,
1259n,
1277n,
1279n,
1283n,
1289n,
1291n,
1297n,
1301n,
1303n,
1307n,
1319n,
1321n,
1327n,
1361n,
1367n,
1373n,
1381n,
1399n,
1409n,
1423n,
1427n,
1429n,
1433n,
1439n,
1447n,
1451n,
1453n,
1459n,
1471n,
1481n,
1483n,
1487n,
1489n,
1493n,
1499n,
1511n,
1523n,
1531n,
1543n,
1549n,
1553n,
1559n,
1567n,
1571n,
1579n,
1583n,
1597n
]
let p = _ZERO
for (let i = 0; i < firstPrimes.length && (p <= w); i++) {
p = BigInt(firstPrimes[i])
for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
const p = firstPrimes[i]
if (w === p) {
return true
} else if (w % p === _ZERO) {
} else if (w % p === 0n) {
return false
}
}
@ -749,30 +537,48 @@ function _isProbablyPrime (w, iterations = 16) {
Comment: Increment i for the do-loop in step 4.
5. Return PROBABLY PRIME.
*/
let a = _ZERO; let d = w - _ONE
while (d % _TWO === _ZERO) {
d /= _TWO
let a = 0n
const d = w - 1n
let aux = d
while (aux % 2n === 0n) {
aux /= 2n
++a
}
const m = (w - _ONE) / (_TWO ** a)
const m = d / (2n ** a)
/* eslint-disable no-labels */
loop: do {
const b = randBetween(w - _ONE, _TWO)
// /* eslint-disable no-labels */
// loop: do {
// const b = randBetween(w - 1n, 2n)
// let z = modPow(b, m, w)
// if (z === 1n || z === w - 1n) { continue }
// for (let j = 1; j < a; j++) {
// z = modPow(z, 2n, w)
// if (z === w - 1n) { continue loop }
// if (z === 1n) { break }
// }
// return false
// } while (--iterations)
// /* eslint-enable no-labels */
// return true
do {
const b = randBetween(d, 2n)
let z = modPow(b, m, w)
if (z === _ONE || z === w - _ONE) { continue }
for (let j = 1; j < a; j++) {
z = modPow(z, _TWO, w)
if (z === w - _ONE) { continue loop }
if (z === _ONE) { break }
if (z === 1n || z === d) { continue }
let j = 1
while (j < a) {
z = modPow(z, 2n, w)
if (z === d) { break }
if (z === 1n) { return false }
j++
}
if (z !== d) {
return false
}
} while (--iterations)
/* eslint-enable no-labels */
return true
}
export { abs, bitLength, eGcd, gcd, isProbablyPrime, lcm, max, min, modInv, modPow, prime, primeSync, randBetween, randBits, randBytes, randBytesSync, toZn }
export { isProbablyPrime, prime, primeSync, randBetween, randBits, randBytes, randBytesSync }

861
lib/index.node.js
View File

@ -2,115 +2,7 @@
Object.defineProperty(exports, '__esModule', { value: true })
const _ZERO = BigInt(0)
const _ONE = BigInt(1)
const _TWO = BigInt(2)
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
* @param {number|bigint} a
*
* @returns {bigint} the absolute value of a
*/
function abs (a) {
a = BigInt(a)
return (a >= _ZERO) ? a : -a
}
/**
* Returns the bitlength of a number
*
* @param {number|bigint} a
* @returns {number} - the bit length
*/
function bitLength (a) {
a = BigInt(a)
if (a === _ONE) { return 1 }
let bits = 1
do {
bits++
} while ((a >>= _ONE) > _ONE)
return bits
}
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
* @property {bigint} g
* @property {bigint} x
* @property {bigint} y
*/
/**
* 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).
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
function eGcd (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a <= _ZERO | b <= _ZERO) { return NaN } // a and b MUST be positive
let x = _ZERO
let y = _ONE
let u = _ONE
let v = _ZERO
while (a !== _ZERO) {
const q = b / a
const r = b % a
const m = x - (u * q)
const n = y - (v * q)
b = a
a = r
x = u
y = v
u = m
v = n
}
return {
b: b,
x: x,
y: y
}
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
function gcd (a, b) {
a = abs(a)
b = abs(b)
if (a === _ZERO) { return b } else if (b === _ZERO) { return a }
let shift = _ZERO
while (!((a | b) & _ONE)) {
a >>= _ONE
b >>= _ONE
shift++
}
while (!(a & _ONE)) a >>= _ONE
do {
while (!(b & _ONE)) b >>= _ONE
if (a > b) {
const x = a
a = b
b = x
}
b -= a
} while (b)
// rescale
return a << shift
}
var bigintModArith = require('bigint-mod-arith')
/**
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
@ -119,7 +11,7 @@ function gcd (a, b) {
* @param {number | bigint} w An integer to be tested for primality
* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
*
* @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
* @return {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
*/
async function isProbablyPrime (w, iterations = 16) {
if (typeof w === 'number') {
@ -155,96 +47,6 @@ async function isProbablyPrime (w, iterations = 16) {
/* eslint-enable no-lone-blocks */
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
function lcm (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a === _ZERO && b === _ZERO) { return _ZERO }
return abs(a * b) / gcd(a, b)
}
/**
* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} maximum of numbers a and b
*/
function max (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? a : b
}
/**
* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} minimum of numbers a and b
*/
function min (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? b : a
}
/**
* Modular inverse.
*
* @param {number|bigint} a The number to find an inverse for
* @param {number|bigint} n The modulo
*
* @returns {bigint} the inverse modulo n or NaN if it does not exist
*/
function modInv (a, n) {
const egcd = eGcd(toZn(a, n), n)
if (egcd.b !== _ONE) {
return NaN // modular inverse does not exist
} else {
return toZn(egcd.x, n)
}
}
/**
* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
*
* @param {number|bigint} b base
* @param {number|bigint} e exponent
* @param {number|bigint} n modulo
*
* @returns {bigint} b**e mod n
*/
function modPow (b, e, n) {
n = BigInt(n)
if (n === _ZERO) { return NaN } else if (n === _ONE) { return _ZERO }
b = toZn(b, n)
e = BigInt(e)
if (e < _ZERO) {
return modInv(modPow(b, abs(e), n), n)
}
let r = _ONE
while (e > 0) {
if ((e % _TWO) === _ONE) {
r = (r * b) % n
}
e = e / _TWO
b = b ** _TWO % n
}
return r
}
/**
* 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
@ -255,13 +57,13 @@ function modPow (b, e, n) {
* @param {number} bitLength The required bit length for the generated prime
* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
*/
function prime (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
if (!_useWorkers) {
let rnd = _ZERO
let rnd = 0n
do {
rnd = fromBuffer(randBytesSync(bitLength / 8, true))
} while (!_isProbablyPrime(rnd, iterations))
@ -297,7 +99,7 @@ function prime (bitLength, iterations = 16) {
{ // Node.js
const { cpus } = require('os')
const { Worker } = require('worker_threads')
for (let i = 0; i < cpus().length; i++) {
for (let i = 0; i < cpus().length - 1; i++) {
const newWorker = new Worker(__filename)
newWorker.on('message', (msg) => _onmessage(msg, newWorker))
workerList.push(newWorker)
@ -327,7 +129,7 @@ function prime (bitLength, iterations = 16) {
*/
function primeSync (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
let rnd = _ZERO
let rnd = 0n
do {
rnd = fromBuffer(randBytesSync(bitLength / 8, true))
} while (!_isProbablyPrime(rnd, iterations))
@ -341,10 +143,10 @@ function primeSync (bitLength, iterations = 16) {
*
* @returns {bigint} A cryptographically secure random bigint between [min,max]
*/
function randBetween (max, min = _ONE) {
function randBetween (max, min = 1n) {
if (max <= min) throw new Error('max must be > min')
const interval = max - min
const bitLen = bitLength(interval)
const bitLen = bigintModArith.bitLength(interval)
let rnd
do {
const buf = randBits(bitLen)
@ -386,7 +188,7 @@ function randBits (bitLength, forceLength = false) {
* @param {number} byteLength The desired number of random bytes
* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
*/
function randBytes (byteLength, forceLength = false) {
if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
@ -427,25 +229,10 @@ function randBytesSync (byteLength, forceLength = false) {
return buf
}
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
function toZn (a, n) {
n = BigInt(n)
if (n <= 0) { return NaN }
a = BigInt(a) % n
return (a < 0) ? a + n : a
}
/* HELPER FUNCTIONS */
function fromBuffer (buf) {
let ret = _ZERO
let ret = 0n
for (const i of buf.values()) {
const bi = BigInt(i)
ret = (ret << BigInt(8)) + bi
@ -458,269 +245,269 @@ function _isProbablyPrime (w, iterations = 16) {
PREFILTERING. Even values but 2 are not primes, so don't test.
1 is not a prime and the M-R algorithm needs w>1.
*/
if (w === _TWO) { return true } else if ((w & _ONE) === _ZERO || w === _ONE) { return false }
if (w === 2n) { return true } else if ((w & 1n) === 0n || w === 1n) { return false }
/*
Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
*/
const firstPrimes = [
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
43,
47,
53,
59,
61,
67,
71,
73,
79,
83,
89,
97,
101,
103,
107,
109,
113,
127,
131,
137,
139,
149,
151,
157,
163,
167,
173,
179,
181,
191,
193,
197,
199,
211,
223,
227,
229,
233,
239,
241,
251,
257,
263,
269,
271,
277,
281,
283,
293,
307,
311,
313,
317,
331,
337,
347,
349,
353,
359,
367,
373,
379,
383,
389,
397,
401,
409,
419,
421,
431,
433,
439,
443,
449,
457,
461,
463,
467,
479,
487,
491,
499,
503,
509,
521,
523,
541,
547,
557,
563,
569,
571,
577,
587,
593,
599,
601,
607,
613,
617,
619,
631,
641,
643,
647,
653,
659,
661,
673,
677,
683,
691,
701,
709,
719,
727,
733,
739,
743,
751,
757,
761,
769,
773,
787,
797,
809,
811,
821,
823,
827,
829,
839,
853,
857,
859,
863,
877,
881,
883,
887,
907,
911,
919,
929,
937,
941,
947,
953,
967,
971,
977,
983,
991,
997,
1009,
1013,
1019,
1021,
1031,
1033,
1039,
1049,
1051,
1061,
1063,
1069,
1087,
1091,
1093,
1097,
1103,
1109,
1117,
1123,
1129,
1151,
1153,
1163,
1171,
1181,
1187,
1193,
1201,
1213,
1217,
1223,
1229,
1231,
1237,
1249,
1259,
1277,
1279,
1283,
1289,
1291,
1297,
1301,
1303,
1307,
1319,
1321,
1327,
1361,
1367,
1373,
1381,
1399,
1409,
1423,
1427,
1429,
1433,
1439,
1447,
1451,
1453,
1459,
1471,
1481,
1483,
1487,
1489,
1493,
1499,
1511,
1523,
1531,
1543,
1549,
1553,
1559,
1567,
1571,
1579,
1583,
1597
3n,
5n,
7n,
11n,
13n,
17n,
19n,
23n,
29n,
31n,
37n,
41n,
43n,
47n,
53n,
59n,
61n,
67n,
71n,
73n,
79n,
83n,
89n,
97n,
101n,
103n,
107n,
109n,
113n,
127n,
131n,
137n,
139n,
149n,
151n,
157n,
163n,
167n,
173n,
179n,
181n,
191n,
193n,
197n,
199n,
211n,
223n,
227n,
229n,
233n,
239n,
241n,
251n,
257n,
263n,
269n,
271n,
277n,
281n,
283n,
293n,
307n,
311n,
313n,
317n,
331n,
337n,
347n,
349n,
353n,
359n,
367n,
373n,
379n,
383n,
389n,
397n,
401n,
409n,
419n,
421n,
431n,
433n,
439n,
443n,
449n,
457n,
461n,
463n,
467n,
479n,
487n,
491n,
499n,
503n,
509n,
521n,
523n,
541n,
547n,
557n,
563n,
569n,
571n,
577n,
587n,
593n,
599n,
601n,
607n,
613n,
617n,
619n,
631n,
641n,
643n,
647n,
653n,
659n,
661n,
673n,
677n,
683n,
691n,
701n,
709n,
719n,
727n,
733n,
739n,
743n,
751n,
757n,
761n,
769n,
773n,
787n,
797n,
809n,
811n,
821n,
823n,
827n,
829n,
839n,
853n,
857n,
859n,
863n,
877n,
881n,
883n,
887n,
907n,
911n,
919n,
929n,
937n,
941n,
947n,
953n,
967n,
971n,
977n,
983n,
991n,
997n,
1009n,
1013n,
1019n,
1021n,
1031n,
1033n,
1039n,
1049n,
1051n,
1061n,
1063n,
1069n,
1087n,
1091n,
1093n,
1097n,
1103n,
1109n,
1117n,
1123n,
1129n,
1151n,
1153n,
1163n,
1171n,
1181n,
1187n,
1193n,
1201n,
1213n,
1217n,
1223n,
1229n,
1231n,
1237n,
1249n,
1259n,
1277n,
1279n,
1283n,
1289n,
1291n,
1297n,
1301n,
1303n,
1307n,
1319n,
1321n,
1327n,
1361n,
1367n,
1373n,
1381n,
1399n,
1409n,
1423n,
1427n,
1429n,
1433n,
1439n,
1447n,
1451n,
1453n,
1459n,
1471n,
1481n,
1483n,
1487n,
1489n,
1493n,
1499n,
1511n,
1523n,
1531n,
1543n,
1549n,
1553n,
1559n,
1567n,
1571n,
1579n,
1583n,
1597n
]
let p = _ZERO
for (let i = 0; i < firstPrimes.length && (p <= w); i++) {
p = BigInt(firstPrimes[i])
for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
const p = firstPrimes[i]
if (w === p) {
return true
} else if (w % p === _ZERO) {
} else if (w % p === 0n) {
return false
}
}
@ -744,29 +531,47 @@ function _isProbablyPrime (w, iterations = 16) {
Comment: Increment i for the do-loop in step 4.
5. Return PROBABLY PRIME.
*/
let a = _ZERO; let d = w - _ONE
while (d % _TWO === _ZERO) {
d /= _TWO
let a = 0n
const d = w - 1n
let aux = d
while (aux % 2n === 0n) {
aux /= 2n
++a
}
const m = (w - _ONE) / (_TWO ** a)
const m = d / (2n ** a)
/* eslint-disable no-labels */
loop: do {
const b = randBetween(w - _ONE, _TWO)
let z = modPow(b, m, w)
if (z === _ONE || z === w - _ONE) { continue }
// /* eslint-disable no-labels */
// loop: do {
// const b = randBetween(w - 1n, 2n)
// let z = modPow(b, m, w)
// if (z === 1n || z === w - 1n) { continue }
// for (let j = 1; j < a; j++) {
// z = modPow(z, 2n, w)
// if (z === w - 1n) { continue loop }
// if (z === 1n) { break }
// }
// return false
// } while (--iterations)
// /* eslint-enable no-labels */
for (let j = 1; j < a; j++) {
z = modPow(z, _TWO, w)
if (z === w - _ONE) { continue loop }
if (z === _ONE) { break }
// return true
do {
const b = randBetween(d, 2n)
let z = bigintModArith.modPow(b, m, w)
if (z === 1n || z === d) { continue }
let j = 1
while (j < a) {
z = bigintModArith.modPow(z, 2n, w)
if (z === d) { break }
if (z === 1n) { return false }
j++
}
if (z !== d) {
return false
}
} while (--iterations)
/* eslint-enable no-labels */
return true
}
@ -801,20 +606,70 @@ if (_useWorkers) { // node.js with support for workers
}
}
exports.abs = abs
exports.bitLength = bitLength
exports.eGcd = eGcd
exports.gcd = gcd
Object.defineProperty(exports, 'abs', {
enumerable: true,
get: function () {
return bigintModArith.abs
}
})
Object.defineProperty(exports, 'bitLength', {
enumerable: true,
get: function () {
return bigintModArith.bitLength
}
})
Object.defineProperty(exports, 'eGcd', {
enumerable: true,
get: function () {
return bigintModArith.eGcd
}
})
Object.defineProperty(exports, 'gcd', {
enumerable: true,
get: function () {
return bigintModArith.gcd
}
})
Object.defineProperty(exports, 'lcm', {
enumerable: true,
get: function () {
return bigintModArith.lcm
}
})
Object.defineProperty(exports, 'max', {
enumerable: true,
get: function () {
return bigintModArith.max
}
})
Object.defineProperty(exports, 'min', {
enumerable: true,
get: function () {
return bigintModArith.min
}
})
Object.defineProperty(exports, 'modInv', {
enumerable: true,
get: function () {
return bigintModArith.modInv
}
})
Object.defineProperty(exports, 'modPow', {
enumerable: true,
get: function () {
return bigintModArith.modPow
}
})
Object.defineProperty(exports, 'toZn', {
enumerable: true,
get: function () {
return bigintModArith.toZn
}
})
exports.isProbablyPrime = isProbablyPrime
exports.lcm = lcm
exports.max = max
exports.min = min
exports.modInv = modInv
exports.modPow = modPow
exports.prime = prime
exports.primeSync = primeSync
exports.randBetween = randBetween
exports.randBits = randBits
exports.randBytes = randBytes
exports.randBytesSync = randBytesSync
exports.toZn = toZn

8
package-lock.json generated
View File

@ -105,8 +105,7 @@
"@types/node": {
"version": "13.11.0",
"resolved": "https://registry.npmjs.org/@types/node/-/node-13.11.0.tgz",
"integrity": "sha512-uM4mnmsIIPK/yeO+42F2RQhGUIs39K2RFmugcJANppXe6J1nvH87PvzPZYpza7Xhhs8Yn9yIAVdLZ84z61+0xQ==",
"dev": true
"integrity": "sha512-uM4mnmsIIPK/yeO+42F2RQhGUIs39K2RFmugcJANppXe6J1nvH87PvzPZYpza7Xhhs8Yn9yIAVdLZ84z61+0xQ=="
},
"@types/resolve": {
"version": "0.0.8",
@ -262,6 +261,11 @@
"integrity": "sha1-ibTRmasr7kneFk6gK4nORi1xt2c=",
"dev": true
},
"bigint-mod-arith": {
"version": "2.0.4",
"resolved": "https://registry.npmjs.org/bigint-mod-arith/-/bigint-mod-arith-2.0.4.tgz",
"integrity": "sha512-sQyEj0XMU4hai3G/+uLwohrGjfUn8rGVWAYnnlFrQhw8YjilptTyJrx7NMimKwQvYr2eXGWGDlYVL3wfE4GIRg=="
},
"binary-extensions": {
"version": "2.0.0",
"resolved": "https://registry.npmjs.org/binary-extensions/-/binary-extensions-2.0.0.tgz",

6
package.json
View File

@ -34,7 +34,7 @@
"build:js": "rollup -c build/rollup.config.js",
"build:standard": "standard --fix",
"build:browserTests": "rollup -c build/rollup.tests.config.js",
"build:docs": "jsdoc2md --template=./src/doc/readme-template.md --files ./lib/index.browser.mod.js -d 3 > README.md",
"build:docs": "node build/build.docs.js",
"build:dts": "node build/build.dts.js",
"build": "run-s build:**",
"prepublishOnly": "npm run build"
@ -69,5 +69,9 @@
"rollup-plugin-terser": "^5.3.0",
"standard": "^14.3.3",
"typescript": "^3.8.3"
},
"dependencies": {
"@types/node": "^13.11.0",
"bigint-mod-arith": "^2.0.4"
}
}

27
src/doc/readme-template.md
View File

@ -16,9 +16,9 @@ bigint-crypto-utils can be imported to your project with `npm`:
npm install bigint-crypto-utils
```
NPM installation defaults to the minified ES6 module for browsers and the CJS one for Node.js.
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 [IIFE file](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.js) or the [ES6 module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.mod.js) from GitHub.
For web browsers, you can also directly download the [IIFE bundle](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.js) or the [ES6 bundle module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.mod.js) from GitHub.
## Usage examples
@ -29,26 +29,25 @@ Import your module as :
const bigintCryptoUtils = require('bigint-crypto-utils')
... // your code here
```
- Javascript native project
- JavaScript native project
```javascript
import * as bigintCryptoUtils from 'bigint-crypto-utils'
... // your code here
```
- Javascript native browser ES6 mod
- JavaScript native browser ES6 mod
```html
<script type="module">
import * as bigintCryptoUtils from 'lib/index.browser.bundle.mod.js' // Use you actual path to the broser mod bundle
... // your code here
</script>
import as bcu from 'bigint-crypto-utils'
... // your code here
```
- Javascript native browser IIFE
- JavaScript native browser IIFE
```html
<script src="../../lib/index.browser.bundle.js"></script>
<script src="../../lib/index.browser.bundle.js"></script> <!-- Use you actual path to the browser bundle -->
<script>
... // your code here
</script>
```
- TypeScript
```typescript
import * as bigintCryptoUtils from 'bigint-crypto-utils'
@ -56,6 +55,8 @@ Import your module as :
```
> BigInt is [ES-2020](https://tc39.es/ecma262/#sec-bigint-objects). In order to use it with TypeScript you should set `lib` (and probably also `target` and `module`) to `esnext` in `tsconfig.json`.
And you could use it like in the following:
```javascript
/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter new no-so-linter-friendly syntax 666n.
@ -65,22 +66,22 @@ be raised.
*/
const a = BigInt('5')
const b = BigInt('2')
const n = BigInt('19')
const n = 19n
console.log(bigintCryptoUtils.modPow(a, b, n)) // prints 6
console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))) // prints 3
console.log(bigintCryptoUtils.modInv(2n, 5n)) // prints 3
console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))) // prints 2
console.log(bigintCryptoUtils.randBetween(BigInt(2) ** BigInt(256))) // Prints a cryptographically secure random number between 1 and 2**256 bits.
console.log(bigintCryptoUtils.randBetween(2n ** 256n)) // Prints a cryptographically secure random number between 1 and 2**256 bits.
async function primeTesting () {
// Output of a probable prime of 2048 bits
console.log(await bigintCryptoUtils.prime(2048))
// Testing if a number is a probable prime (Miller-Rabin)
const number = 27
const number = 27n
const isPrime = await bigintCryptoUtils.isProbablyPrime(number)
if (isPrime) {
console.log(`${number} is prime`)
@ -93,6 +94,6 @@ primeTesting()
```
## bigint-crypto-utils JS Doc
## API reference documentation
{{>main}}

794
src/js/index.js
View File

@ -1,112 +1,5 @@
const _ZERO = BigInt(0)
const _ONE = BigInt(1)
const _TWO = BigInt(2)
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
* @param {number|bigint} a
*
* @returns {bigint} the absolute value of a
*/
export function abs (a) {
a = BigInt(a)
return (a >= _ZERO) ? a : -a
}
/**
* Returns the bitlength of a number
*
* @param {number|bigint} a
* @returns {number} - the bit length
*/
export function bitLength (a) {
a = BigInt(a)
if (a === _ONE) { return 1 }
let bits = 1
do {
bits++
} while ((a >>= _ONE) > _ONE)
return bits
}
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
* @property {bigint} g
* @property {bigint} x
* @property {bigint} y
*/
/**
* 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).
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
export function eGcd (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a <= _ZERO | b <= _ZERO) { return NaN } // a and b MUST be positive
let x = _ZERO
let y = _ONE
let u = _ONE
let v = _ZERO
while (a !== _ZERO) {
const q = b / a
const r = b % a
const m = x - (u * q)
const n = y - (v * q)
b = a
a = r
x = u
y = v
u = m
v = n
}
return {
b: b,
x: x,
y: y
}
}
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
export function gcd (a, b) {
a = abs(a)
b = abs(b)
if (a === _ZERO) { return b } else if (b === _ZERO) { return a }
let shift = _ZERO
while (!((a | b) & _ONE)) {
a >>= _ONE
b >>= _ONE
shift++
}
while (!(a & _ONE)) a >>= _ONE
do {
while (!(b & _ONE)) b >>= _ONE
if (a > b) {
const x = a
a = b
b = x
}
b -= a
} while (b)
// rescale
return a << shift
}
import { bitLength, eGcd, modInv, modPow, toZn } from 'bigint-mod-arith'
export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn } from 'bigint-mod-arith'
/**
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
@ -115,7 +8,7 @@ export function gcd (a, b) {
* @param {number | bigint} w An integer to be tested for primality
* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
*
* @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
* @return {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
*/
export async function isProbablyPrime (w, iterations = 16) {
if (typeof w === 'number') {
@ -170,96 +63,6 @@ export async function isProbablyPrime (w, iterations = 16) {
/* eslint-enable no-lone-blocks */
}
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
export function lcm (a, b) {
a = BigInt(a)
b = BigInt(b)
if (a === _ZERO && b === _ZERO) { return _ZERO }
return abs(a * b) / gcd(a, b)
}
/**
* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} maximum of numbers a and b
*/
export function max (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? a : b
}
/**
* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} minimum of numbers a and b
*/
export function min (a, b) {
a = BigInt(a)
b = BigInt(b)
return (a >= b) ? b : a
}
/**
* Modular inverse.
*
* @param {number|bigint} a The number to find an inverse for
* @param {number|bigint} n The modulo
*
* @returns {bigint} the inverse modulo n or NaN if it does not exist
*/
export function modInv (a, n) {
const egcd = eGcd(toZn(a, n), n)
if (egcd.b !== _ONE) {
return NaN // modular inverse does not exist
} else {
return toZn(egcd.x, n)
}
}
/**
* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
*
* @param {number|bigint} b base
* @param {number|bigint} e exponent
* @param {number|bigint} n modulo
*
* @returns {bigint} b**e mod n
*/
export function modPow (b, e, n) {
n = BigInt(n)
if (n === _ZERO) { return NaN } else if (n === _ONE) { return _ZERO }
b = toZn(b, n)
e = BigInt(e)
if (e < _ZERO) {
return modInv(modPow(b, abs(e), n), n)
}
let r = _ONE
while (e > 0) {
if ((e % _TWO) === _ONE) {
r = (r * b) % n
}
e = e / _TWO
b = b ** _TWO % n
}
return r
}
/**
* 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
@ -270,13 +73,13 @@ export function modPow (b, e, n) {
* @param {number} bitLength The required bit length for the generated prime
* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
*/
export function prime (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
if (!process.browser && !_useWorkers) {
let rnd = _ZERO
let rnd = 0n
do {
rnd = fromBuffer(randBytesSync(bitLength / 8, true))
} while (!_isProbablyPrime(rnd, iterations))
@ -311,7 +114,7 @@ export function prime (bitLength, iterations = 16) {
/* eslint-disable no-lone-blocks */
if (process.browser) { // browser
const workerURL = _isProbablyPrimeWorkerUrl()
for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) {
const newWorker = new Worker(workerURL)
newWorker.onmessage = (event) => _onmessage(event.data, newWorker)
workerList.push(newWorker)
@ -319,7 +122,7 @@ export function prime (bitLength, iterations = 16) {
} else { // Node.js
const { cpus } = require('os')
const { Worker } = require('worker_threads')
for (let i = 0; i < cpus().length; i++) {
for (let i = 0; i < cpus().length - 1; i++) {
const newWorker = new Worker(__filename)
newWorker.on('message', (msg) => _onmessage(msg, newWorker))
workerList.push(newWorker)
@ -349,7 +152,7 @@ export function prime (bitLength, iterations = 16) {
*/
export function primeSync (bitLength, iterations = 16) {
if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
let rnd = _ZERO
let rnd = 0n
do {
rnd = fromBuffer(randBytesSync(bitLength / 8, true))
} while (!_isProbablyPrime(rnd, iterations))
@ -363,7 +166,7 @@ export function primeSync (bitLength, iterations = 16) {
*
* @returns {bigint} A cryptographically secure random bigint between [min,max]
*/
export function randBetween (max, min = _ONE) {
export function randBetween (max, min = 1n) {
if (max <= min) throw new Error('max must be > min')
const interval = max - min
const bitLen = bitLength(interval)
@ -408,7 +211,7 @@ export function randBits (bitLength, forceLength = false) {
* @param {number} byteLength The desired number of random bytes
* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
*/
export function randBytes (byteLength, forceLength = false) {
if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
@ -460,25 +263,10 @@ export function randBytesSync (byteLength, forceLength = false) {
return buf
}
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
export function toZn (a, n) {
n = BigInt(n)
if (n <= 0) { return NaN }
a = BigInt(a) % n
return (a < 0) ? a + n : a
}
/* HELPER FUNCTIONS */
function fromBuffer (buf) {
let ret = _ZERO
let ret = 0n
for (const i of buf.values()) {
const bi = BigInt(i)
ret = (ret << BigInt(8)) + bi
@ -488,7 +276,7 @@ function fromBuffer (buf) {
function _isProbablyPrimeWorkerUrl () {
// Let's us first add all the required functions
let workerCode = `'use strict';const _ZERO = BigInt(0);const _ONE = BigInt(1);const _TWO = BigInt(2);const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBits = ${randBits.toString()};const randBytesSync = ${randBytesSync.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`
let workerCode = `'use strict';const ${eGcd.name}=${eGcd.toString()};const ${modInv.name}=${modInv.toString()};const ${modPow.name}=${modPow.toString()};const ${toZn.name}=${toZn.toString()};const ${randBits.name}=${randBits.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`
const onmessage = async function (event) { // Let's start once we are called
// event.data = {rnd: <bigint>, iterations: <number>}
@ -516,269 +304,269 @@ function _isProbablyPrime (w, iterations = 16) {
PREFILTERING. Even values but 2 are not primes, so don't test.
1 is not a prime and the M-R algorithm needs w>1.
*/
if (w === _TWO) { return true } else if ((w & _ONE) === _ZERO || w === _ONE) { return false }
if (w === 2n) { return true } else if ((w & 1n) === 0n || w === 1n) { return false }
/*
Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
*/
const firstPrimes = [
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
43,
47,
53,
59,
61,
67,
71,
73,
79,
83,
89,
97,
101,
103,
107,
109,
113,
127,
131,
137,
139,
149,
151,
157,
163,
167,
173,
179,
181,
191,
193,
197,
199,
211,
223,
227,
229,
233,
239,
241,
251,
257,
263,
269,
271,
277,
281,
283,
293,
307,
311,
313,
317,
331,
337,
347,
349,
353,
359,
367,
373,
379,
383,
389,
397,
401,
409,
419,
421,
431,
433,
439,
443,
449,
457,
461,
463,
467,
479,
487,
491,
499,
503,
509,
521,
523,
541,
547,
557,
563,
569,
571,
577,
587,
593,
599,
601,
607,
613,
617,
619,
631,
641,
643,
647,
653,
659,
661,
673,
677,
683,
691,
701,
709,
719,
727,
733,
739,
743,
751,
757,
761,
769,
773,
787,
797,
809,
811,
821,
823,
827,
829,
839,
853,
857,
859,
863,
877,
881,
883,
887,
907,
911,
919,
929,
937,
941,
947,
953,
967,
971,
977,
983,
991,
997,
1009,
1013,
1019,
1021,
1031,
1033,
1039,
1049,
1051,
1061,
1063,
1069,
1087,
1091,
1093,
1097,
1103,
1109,
1117,
1123,
1129,
1151,
1153,
1163,
1171,
1181,
1187,
1193,
1201,
1213,
1217,
1223,
1229,
1231,
1237,
1249,
1259,
1277,
1279,
1283,
1289,
1291,
1297,
1301,
1303,
1307,
1319,
1321,
1327,
1361,
1367,
1373,
1381,
1399,
1409,
1423,
1427,
1429,
1433,
1439,
1447,
1451,
1453,
1459,
1471,
1481,
1483,
1487,
1489,
1493,
1499,
1511,
1523,
1531,
1543,
1549,
1553,
1559,
1567,
1571,
1579,
1583,
1597
3n,
5n,
7n,
11n,
13n,
17n,
19n,
23n,
29n,
31n,
37n,
41n,
43n,
47n,
53n,
59n,
61n,
67n,
71n,
73n,
79n,
83n,
89n,
97n,
101n,
103n,
107n,
109n,
113n,
127n,
131n,
137n,
139n,
149n,
151n,
157n,
163n,
167n,
173n,
179n,
181n,
191n,
193n,
197n,
199n,
211n,
223n,
227n,
229n,
233n,
239n,
241n,
251n,
257n,
263n,
269n,
271n,
277n,
281n,
283n,
293n,
307n,
311n,
313n,
317n,
331n,
337n,
347n,
349n,
353n,
359n,
367n,
373n,
379n,
383n,
389n,
397n,
401n,
409n,
419n,
421n,
431n,
433n,
439n,
443n,
449n,
457n,
461n,
463n,
467n,
479n,
487n,
491n,
499n,
503n,
509n,
521n,
523n,
541n,
547n,
557n,
563n,
569n,
571n,
577n,
587n,
593n,
599n,
601n,
607n,
613n,
617n,
619n,
631n,
641n,
643n,
647n,
653n,
659n,
661n,
673n,
677n,
683n,
691n,
701n,
709n,
719n,
727n,
733n,
739n,
743n,
751n,
757n,
761n,
769n,
773n,
787n,
797n,
809n,
811n,
821n,
823n,
827n,
829n,
839n,
853n,
857n,
859n,
863n,
877n,
881n,
883n,
887n,
907n,
911n,
919n,
929n,
937n,
941n,
947n,
953n,
967n,
971n,
977n,
983n,
991n,
997n,
1009n,
1013n,
1019n,
1021n,
1031n,
1033n,
1039n,
1049n,
1051n,
1061n,
1063n,
1069n,
1087n,
1091n,
1093n,
1097n,
1103n,
1109n,
1117n,
1123n,
1129n,
1151n,
1153n,
1163n,
1171n,
1181n,
1187n,
1193n,
1201n,
1213n,
1217n,
1223n,
1229n,
1231n,
1237n,
1249n,
1259n,
1277n,
1279n,
1283n,
1289n,
1291n,
1297n,
1301n,
1303n,
1307n,
1319n,
1321n,
1327n,
1361n,
1367n,
1373n,
1381n,
1399n,
1409n,
1423n,
1427n,
1429n,
1433n,
1439n,
1447n,
1451n,
1453n,
1459n,
1471n,
1481n,
1483n,
1487n,
1489n,
1493n,
1499n,
1511n,
1523n,
1531n,
1543n,
1549n,
1553n,
1559n,
1567n,
1571n,
1579n,
1583n,
1597n
]
let p = _ZERO
for (let i = 0; i < firstPrimes.length && (p <= w); i++) {
p = BigInt(firstPrimes[i])
for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
const p = firstPrimes[i]
if (w === p) {
return true
} else if (w % p === _ZERO) {
} else if (w % p === 0n) {
return false
}
}
@ -802,29 +590,47 @@ function _isProbablyPrime (w, iterations = 16) {
Comment: Increment i for the do-loop in step 4.
5. Return PROBABLY PRIME.
*/
let a = _ZERO; let d = w - _ONE
while (d % _TWO === _ZERO) {
d /= _TWO
let a = 0n
const d = w - 1n
let aux = d
while (aux % 2n === 0n) {
aux /= 2n
++a
}
const m = (w - _ONE) / (_TWO ** a)
const m = d / (2n ** a)
/* eslint-disable no-labels */
loop: do {
const b = randBetween(w - _ONE, _TWO)
// /* eslint-disable no-labels */
// loop: do {
// const b = randBetween(w - 1n, 2n)
// let z = modPow(b, m, w)
// if (z === 1n || z === w - 1n) { continue }
// for (let j = 1; j < a; j++) {
// z = modPow(z, 2n, w)
// if (z === w - 1n) { continue loop }
// if (z === 1n) { break }
// }
// return false
// } while (--iterations)
// /* eslint-enable no-labels */
// return true
do {
const b = randBetween(d, 2n)
let z = modPow(b, m, w)
if (z === _ONE || z === w - _ONE) { continue }
for (let j = 1; j < a; j++) {
z = modPow(z, _TWO, w)
if (z === w - _ONE) { continue loop }
if (z === _ONE) { break }
if (z === 1n || z === d) { continue }
let j = 1
while (j < a) {
z = modPow(z, 2n, w)
if (z === d) { break }
if (z === 1n) { return false }
j++
}
if (z !== d) {
return false
}
} while (--iterations)
/* eslint-enable no-labels */
return true
}

114
types/index.d.ts vendored
View File

@ -1,51 +1,3 @@
/**
* A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
export type egcdReturn = {
g: bigint;
x: bigint;
y: bigint;
};
/**
* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
*
* @param {number|bigint} a
*
* @returns {bigint} the absolute value of a
*/
export function abs(a: number | bigint): bigint;
/**
* Returns the bitlength of a number
*
* @param {number|bigint} a
* @returns {number} - the bit length
*/
export function bitLength(a: number | bigint): number;
/**
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
* @property {bigint} g
* @property {bigint} x
* @property {bigint} y
*/
/**
* 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).
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
*/
export function eGcd(a: number | bigint, b: number | bigint): egcdReturn;
/**
* Greatest-common divisor of two integers based on the iterative binary algorithm.
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The greatest common divisor of a and b
*/
export function gcd(a: number | bigint, b: number | bigint): bigint;
/**
* 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)
@ -53,54 +5,9 @@ export function gcd(a: number | bigint, b: number | bigint): bigint;
* @param {number | bigint} w An integer to be tested for primality
* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
*
* @return {Promise} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
* @return {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
*/
export function isProbablyPrime(w: number | bigint, iterations?: number): Promise<any>;
/**
* The least common multiple computed as abs(a*b)/gcd(a,b)
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} The least common multiple of a and b
*/
export function lcm(a: number | bigint, b: number | bigint): bigint;
/**
* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} maximum of numbers a and b
*/
export function max(a: number | bigint, b: number | bigint): bigint;
/**
* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
*
* @param {number|bigint} a
* @param {number|bigint} b
*
* @returns {bigint} minimum of numbers a and b
*/
export function min(a: number | bigint, b: number | bigint): bigint;
/**
* Modular inverse.
*
* @param {number|bigint} a The number to find an inverse for
* @param {number|bigint} n The modulo
*
* @returns {bigint} the inverse modulo n or NaN if it does not exist
*/
export function modInv(a: number | bigint, n: number | bigint): bigint;
/**
* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
*
* @param {number|bigint} b base
* @param {number|bigint} e exponent
* @param {number|bigint} n modulo
*
* @returns {bigint} b**e mod n
*/
export function modPow(b: number | bigint, e: number | bigint, n: number | bigint): bigint;
export function isProbablyPrime(w: number | bigint, iterations?: number): Promise<boolean>;
/**
* 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
@ -111,9 +18,9 @@ export function modPow(b: number | bigint, e: number | bigint, n: number | bigin
* @param {number} bitLength The required bit length for the generated prime
* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
*
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits.
* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
*/
export function prime(bitLength: number, iterations?: number): Promise<any>;
export function prime(bitLength: number, iterations?: number): Promise<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.
@ -147,9 +54,9 @@ export function randBits(bitLength: number, forceLength?: boolean): Uint8Array |
* @param {number} byteLength The desired number of random bytes
* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
*
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
*/
export function randBytes(byteLength: number, forceLength?: boolean): Promise<any>;
export function randBytes(byteLength: number, forceLength?: boolean): Promise<Uint8Array | Buffer>;
/**
* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
*
@ -159,11 +66,4 @@ export function randBytes(byteLength: number, forceLength?: boolean): Promise<an
* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
*/
export function randBytesSync(byteLength: number, forceLength?: boolean): Uint8Array | Buffer;
/**
* Finds the smallest positive element that is congruent to a in modulo n
* @param {number|bigint} a An integer
* @param {number|bigint} n The modulo
*
* @returns {bigint} The smallest positive representation of a in modulo n
*/
export function toZn(a: number | bigint, n: number | bigint): bigint;
export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn } from "bigint-mod-arith";