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81 lines
2.9 KiB
PHP
81 lines
2.9 KiB
PHP
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<?php
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/**
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* PHP Montgomery Modular Exponentiation Engine with interleaved multiplication
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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 phpseclib\Math\BigInteger\Engines\PHP\Reductions;
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use phpseclib\Math\BigInteger\Engines\PHP\Base;
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/**
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* PHP Montgomery Modular Exponentiation Engine with interleaved multiplication
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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 MontgomeryMult extends Montgomery
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{
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/**
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* Montgomery Multiply
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*
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* Interleaves the montgomery reduction and long multiplication algorithms together as described in
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* {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36}
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*
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* @see self::_prepMontgomery()
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* @see self::_montgomery()
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* @access private
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* @param array $x
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* @param array $y
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* @param array $m
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* @param string $class
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* @return array
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*/
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public static function multiplyReduce(array $x, array $y, array $m, $class)
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{
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// the following code, although not callable, can be run independently of the above code
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// although the above code performed better in my benchmarks the following could might
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// perform better under different circumstances. in lieu of deleting it it's just been
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// made uncallable
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static $cache = [
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self::VARIABLE => [],
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self::DATA => []
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];
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if (($key = array_search($m, $cache[self::VARIABLE])) === false) {
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$key = count($cache[self::VARIABLE]);
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$cache[self::VARIABLE][] = $m;
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$cache[self::DATA][] = self::modInverse67108864($m, $class);
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}
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$n = max(count($x), count($y), count($m));
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$x = array_pad($x, $n, 0);
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$y = array_pad($y, $n, 0);
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$m = array_pad($m, $n, 0);
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$a = [self::VALUE => self::array_repeat(0, $n + 1)];
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for ($i = 0; $i < $n; ++$i) {
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$temp = $a[self::VALUE][0] + $x[$i] * $y[0];
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$temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
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$temp = $temp * $cache[self::DATA][$key];
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$temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
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$temp = $class::addHelper($class::regularMultiply([$x[$i]], $y), false, $class::regularMultiply([$temp], $m), false);
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$a = $class::addHelper($a[self::VALUE], false, $temp[self::VALUE], false);
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$a[self::VALUE] = array_slice($a[self::VALUE], 1);
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}
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if (self::compareHelper($a[self::VALUE], false, $m, false) >= 0) {
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$a = $class::subtractHelper($a[self::VALUE], false, $m, false);
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}
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return $a[self::VALUE];
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}
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}
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