191 lines
6.5 KiB
Markdown
191 lines
6.5 KiB
Markdown
# bigint-mod-arith
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Some extra functions to work with modular arithmetics using native JS (stage 3) implementation of BigInt. It can be used with Node.js (starting in version 10.4.0) and [Web Browsers supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility).
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If you are looking for a cryptographically secure random generator and for probale primes (generation and testing), you may be interested in [bigint-secrets](https://github.com/juanelas/bigint-secrets)
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_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)**_
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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).
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## Installation
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bigint-mod-arith is distributed as both an ES6 and a CJS module.
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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.
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The CJS module is built as a standard node module.
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bigint-mod-arith can be imported to your project with `npm`:
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```bash
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npm install bigint-mod-arith
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```
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For web brosers, you can also [download the bundle from GitHub](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js) or just hotlink to it:
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```html
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<script type="module" src="https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/dist/bigint-mod-arith-latest.browser.mod.min.js"></script>
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```
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## Usage examples
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```javascript
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const bigintModArith = require('bigint-mod-arith');
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// Stage 3 BigInts with value 666 can be declared as BigInt('666')
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// or the shorte no-linter-friendly new syntax 666n
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let a = BigInt('5');
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let b = BigInt('2');
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let n = BigInt('19');
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console.log(bigintModArith.modPow(a, b, n)); // prints 6
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console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
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```
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# bigint-mod-arith JS Doc
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## Functions
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<dl>
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<dt><a href="#abs">abs(a)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0</p>
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</dd>
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<dt><a href="#gcd">gcd(a, b)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
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</dd>
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<dt><a href="#lcm">lcm(a, b)</a> ⇒ <code>bigint</code></dt>
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<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
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</dd>
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<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
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</dd>
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<dt><a href="#eGcd">eGcd(a, b)</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
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<dd><p>An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
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</dd>
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<dt><a href="#modInv">modInv(a, n)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Modular inverse.</p>
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</dd>
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<dt><a href="#modPow">modPow(a, b, n)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Modular exponentiation a**b mod n</p>
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</dd>
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</dl>
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## Typedefs
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<dl>
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<dt><a href="#egcdReturn">egcdReturn</a> : <code>Object</code></dt>
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<dd><p>A triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
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</dd>
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</dl>
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<a name="abs"></a>
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## abs(a) ⇒ <code>bigint</code>
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Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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**Kind**: global function
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**Returns**: <code>bigint</code> - the absolute value of a
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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<a name="gcd"></a>
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## gcd(a, b) ⇒ <code>bigint</code>
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Greatest-common divisor of two integers based on the iterative binary algorithm.
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**Kind**: global function
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**Returns**: <code>bigint</code> - The greatest common divisor of a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="lcm"></a>
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## lcm(a, b) ⇒ <code>bigint</code>
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The least common multiple computed as abs(a*b)/gcd(a,b)
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**Kind**: global function
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**Returns**: <code>bigint</code> - The least common multiple of a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="toZn"></a>
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## toZn(a, n) ⇒ <code>bigint</code>
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Finds the smallest positive element that is congruent to a in modulo n
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**Kind**: global function
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**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
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| Param | Type | Description |
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| --- | --- | --- |
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| a | <code>number</code> \| <code>bigint</code> | An integer |
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| n | <code>number</code> \| <code>bigint</code> | The modulo |
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<a name="eGcd"></a>
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## eGcd(a, b) ⇒ [<code>egcdReturn</code>](#egcdReturn)
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An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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**Kind**: global function
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="modInv"></a>
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## modInv(a, n) ⇒ <code>bigint</code>
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Modular inverse.
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**Kind**: global function
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**Returns**: <code>bigint</code> - the inverse modulo n
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| Param | Type | Description |
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| --- | --- | --- |
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| a | <code>number</code> \| <code>bigint</code> | The number to find an inverse for |
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| n | <code>number</code> \| <code>bigint</code> | The modulo |
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<a name="modPow"></a>
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## modPow(a, b, n) ⇒ <code>bigint</code>
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Modular exponentiation a**b mod n
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**Kind**: global function
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**Returns**: <code>bigint</code> - a**b mod n
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| Param | Type | Description |
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| --- | --- | --- |
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| a | <code>number</code> \| <code>bigint</code> | base |
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| b | <code>number</code> \| <code>bigint</code> | exponent |
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| n | <code>number</code> \| <code>bigint</code> | modulo |
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<a name="egcdReturn"></a>
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## egcdReturn : <code>Object</code>
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A triple (g, x, y), such that ax + by = g = gcd(a, b).
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**Kind**: global typedef
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**Properties**
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| Name | Type |
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| --- | --- |
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| g | <code>bigint</code> |
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| x | <code>bigint</code> |
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| y | <code>bigint</code> |
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* * *
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