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   1  <?php
   2  
   3  /**
   4   * PHP Montgomery Modular Exponentiation Engine with interleaved multiplication
   5   *
   6   * PHP version 5 and 7
   7   *
   8   * @author    Jim Wigginton <terrafrost@php.net>
   9   * @copyright 2017 Jim Wigginton
  10   * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
  11   * @link      http://pear.php.net/package/Math_BigInteger
  12   */
  13  
  14  namespace phpseclib3\Math\BigInteger\Engines\PHP\Reductions;
  15  
  16  use phpseclib3\Math\BigInteger\Engines\PHP;
  17  
  18  /**
  19   * PHP Montgomery Modular Exponentiation Engine with interleaved multiplication
  20   *
  21   * @author  Jim Wigginton <terrafrost@php.net>
  22   */
  23  abstract class MontgomeryMult extends Montgomery
  24  {
  25      /**
  26       * Montgomery Multiply
  27       *
  28       * Interleaves the montgomery reduction and long multiplication algorithms together as described in
  29       * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36}
  30       *
  31       * @see self::_prepMontgomery()
  32       * @see self::_montgomery()
  33       * @param array $x
  34       * @param array $y
  35       * @param array $m
  36       * @param class-string<PHP> $class
  37       * @return array
  38       */
  39      public static function multiplyReduce(array $x, array $y, array $m, $class)
  40      {
  41          // the following code, although not callable, can be run independently of the above code
  42          // although the above code performed better in my benchmarks the following could might
  43          // perform better under different circumstances. in lieu of deleting it it's just been
  44          // made uncallable
  45  
  46          static $cache = [
  47              self::VARIABLE => [],
  48              self::DATA => []
  49          ];
  50  
  51          if (($key = array_search($m, $cache[self::VARIABLE])) === false) {
  52              $key = count($cache[self::VARIABLE]);
  53              $cache[self::VARIABLE][] = $m;
  54              $cache[self::DATA][] = self::modInverse67108864($m, $class);
  55          }
  56  
  57          $n = max(count($x), count($y), count($m));
  58          $x = array_pad($x, $n, 0);
  59          $y = array_pad($y, $n, 0);
  60          $m = array_pad($m, $n, 0);
  61          $a = [self::VALUE => self::array_repeat(0, $n + 1)];
  62          for ($i = 0; $i < $n; ++$i) {
  63              $temp = $a[self::VALUE][0] + $x[$i] * $y[0];
  64              $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
  65              $temp = $temp * $cache[self::DATA][$key];
  66              $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
  67              $temp = $class::addHelper($class::regularMultiply([$x[$i]], $y), false, $class::regularMultiply([$temp], $m), false);
  68              $a = $class::addHelper($a[self::VALUE], false, $temp[self::VALUE], false);
  69              $a[self::VALUE] = array_slice($a[self::VALUE], 1);
  70          }
  71          if (self::compareHelper($a[self::VALUE], false, $m, false) >= 0) {
  72              $a = $class::subtractHelper($a[self::VALUE], false, $m, false);
  73          }
  74          return $a[self::VALUE];
  75      }
  76  }