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94 lines
2.4 KiB
PHP
94 lines
2.4 KiB
PHP
<?php
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/**
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* PHP Montgomery Modular Exponentiation Engine
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*
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* PHP version 5 and 7
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*
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* @category Math
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* @package BigInteger
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright 2017 Jim Wigginton
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* @license http://www.opensource.org/licenses/mit-license.html MIT License
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* @link http://pear.php.net/package/Math_BigInteger
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*/
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namespace phpseclib3\Math\BigInteger\Engines\PHP;
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use phpseclib3\Math\BigInteger\Engines\Engine;
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use phpseclib3\Math\BigInteger\Engines\PHP;
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use phpseclib3\Math\BigInteger\Engines\PHP\Reductions\PowerOfTwo;
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/**
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* PHP Montgomery Modular Exponentiation Engine
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*
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* @package PHP
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* @author Jim Wigginton <terrafrost@php.net>
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* @access public
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*/
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abstract class Montgomery extends Base
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{
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/**
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* Test for engine validity
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*
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* @return bool
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*/
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public static function isValidEngine()
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{
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return static::class != __CLASS__;
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}
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/**
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* Performs modular exponentiation.
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*
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* @template T of Engine
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* @param Engine $x
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* @param Engine $e
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* @param Engine $n
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* @param class-string<T> $class
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* @return T
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*/
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protected static function slidingWindow(Engine $x, Engine $e, Engine $n, $class)
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{
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// is the modulo odd?
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if ($n->value[0] & 1) {
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return parent::slidingWindow($x, $e, $n, $class);
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}
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// if it's not, it's even
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// find the lowest set bit (eg. the max pow of 2 that divides $n)
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for ($i = 0; $i < count($n->value); ++$i) {
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if ($n->value[$i]) {
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$temp = decbin($n->value[$i]);
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$j = strlen($temp) - strrpos($temp, '1') - 1;
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$j += $class::BASE * $i;
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break;
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}
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}
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// at this point, 2^$j * $n/(2^$j) == $n
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$mod1 = clone $n;
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$mod1->rshift($j);
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$mod2 = new $class();
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$mod2->value = [1];
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$mod2->lshift($j);
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$part1 = $mod1->value != [1] ? parent::slidingWindow($x, $e, $mod1, $class) : new $class();
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$part2 = PowerOfTwo::slidingWindow($x, $e, $mod2, $class);
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$y1 = $mod2->modInverse($mod1);
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$y2 = $mod1->modInverse($mod2);
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$result = $part1->multiply($mod2);
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$result = $result->multiply($y1);
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$temp = $part2->multiply($mod1);
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$temp = $temp->multiply($y2);
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$result = $result->add($temp);
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list(, $result) = $result->divide($n);
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return $result;
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}
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}
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