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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 827 | daniel-mar | 1 | <?php |
| 2 | |||
| 3 | /** |
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| 4 | * PHP Montgomery Modular Exponentiation Engine with interleaved multiplication |
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| 5 | * |
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| 6 | * PHP version 5 and 7 |
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| 7 | * |
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| 874 | daniel-mar | 8 | * @category Math |
| 9 | * @package BigInteger |
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| 827 | daniel-mar | 10 | * @author Jim Wigginton <terrafrost@php.net> |
| 11 | * @copyright 2017 Jim Wigginton |
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| 12 | * @license http://www.opensource.org/licenses/mit-license.html MIT License |
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| 13 | * @link http://pear.php.net/package/Math_BigInteger |
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| 14 | */ |
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| 15 | |||
| 16 | namespace phpseclib3\Math\BigInteger\Engines\PHP\Reductions; |
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| 17 | |||
| 18 | use phpseclib3\Math\BigInteger\Engines\PHP; |
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| 19 | |||
| 20 | /** |
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| 21 | * PHP Montgomery Modular Exponentiation Engine with interleaved multiplication |
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| 22 | * |
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| 874 | daniel-mar | 23 | * @package PHP |
| 827 | daniel-mar | 24 | * @author Jim Wigginton <terrafrost@php.net> |
| 874 | daniel-mar | 25 | * @access public |
| 827 | daniel-mar | 26 | */ |
| 27 | abstract class MontgomeryMult extends Montgomery |
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| 28 | { |
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| 29 | /** |
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| 30 | * Montgomery Multiply |
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| 31 | * |
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| 32 | * Interleaves the montgomery reduction and long multiplication algorithms together as described in |
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| 33 | * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36} |
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| 34 | * |
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| 35 | * @see self::_prepMontgomery() |
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| 36 | * @see self::_montgomery() |
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| 874 | daniel-mar | 37 | * @access private |
| 827 | daniel-mar | 38 | * @param array $x |
| 39 | * @param array $y |
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| 40 | * @param array $m |
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| 41 | * @param class-string<PHP> $class |
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| 42 | * @return array |
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| 43 | */ |
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| 44 | public static function multiplyReduce(array $x, array $y, array $m, $class) |
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| 45 | { |
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| 46 | // the following code, although not callable, can be run independently of the above code |
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| 47 | // although the above code performed better in my benchmarks the following could might |
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| 48 | // perform better under different circumstances. in lieu of deleting it it's just been |
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| 49 | // made uncallable |
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| 50 | |||
| 51 | static $cache = [ |
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| 52 | self::VARIABLE => [], |
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| 53 | self::DATA => [] |
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| 54 | ]; |
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| 55 | |||
| 56 | if (($key = array_search($m, $cache[self::VARIABLE])) === false) { |
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| 57 | $key = count($cache[self::VARIABLE]); |
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| 58 | $cache[self::VARIABLE][] = $m; |
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| 59 | $cache[self::DATA][] = self::modInverse67108864($m, $class); |
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| 60 | } |
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| 61 | |||
| 62 | $n = max(count($x), count($y), count($m)); |
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| 63 | $x = array_pad($x, $n, 0); |
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| 64 | $y = array_pad($y, $n, 0); |
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| 65 | $m = array_pad($m, $n, 0); |
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| 66 | $a = [self::VALUE => self::array_repeat(0, $n + 1)]; |
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| 67 | for ($i = 0; $i < $n; ++$i) { |
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| 68 | $temp = $a[self::VALUE][0] + $x[$i] * $y[0]; |
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| 69 | $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31)); |
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| 70 | $temp = $temp * $cache[self::DATA][$key]; |
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| 71 | $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31)); |
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| 72 | $temp = $class::addHelper($class::regularMultiply([$x[$i]], $y), false, $class::regularMultiply([$temp], $m), false); |
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| 73 | $a = $class::addHelper($a[self::VALUE], false, $temp[self::VALUE], false); |
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| 74 | $a[self::VALUE] = array_slice($a[self::VALUE], 1); |
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| 75 | } |
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| 76 | if (self::compareHelper($a[self::VALUE], false, $m, false) >= 0) { |
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| 77 | $a = $class::subtractHelper($a[self::VALUE], false, $m, false); |
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| 78 | } |
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| 79 | return $a[self::VALUE]; |
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| 80 | } |
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| 81 | } |