* @copyright 2017-2026 Jim Wigginton * @license http://www.opensource.org/licenses/mit-license.html MIT License * @link https://phpseclib.com/ */ declare(strict_types=1); namespace phpseclib4\Math\BigInteger\Engines\PHP\Reductions; use phpseclib4\Math\BigInteger\Engines\PHP; /** * PHP Montgomery Modular Exponentiation Engine with interleaved multiplication * * @author Jim Wigginton * @psalm-api */ abstract class MontgomeryMult extends Montgomery { /** * Montgomery Multiply * * Interleaves the montgomery reduction and long multiplication algorithms together as described in * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=13 HAC 14.36} * * @param class-string $class * @see self::_prepMontgomery() * @see self::_montgomery() */ public static function multiplyReduce(array $x, array $y, array $n, string $class): array { // the following code, although not callable, can be run independently of the above code // although the above code performed better in my benchmarks the following could might // perform better under different circumstances. in lieu of deleting it it's just been // made uncallable static $cache = [ self::VARIABLE => [], self::DATA => [], ]; if (($key = array_search($n, $cache[self::VARIABLE])) === false) { $key = count($cache[self::VARIABLE]); $cache[self::VARIABLE][] = $n; $cache[self::DATA][] = self::modInverse67108864($n, $class); } $size = max(count($x), count($y), count($n)); $x = array_pad($x, $size, 0); $y = array_pad($y, $size, 0); $n = array_pad($n, $size, 0); $a = [self::VALUE => self::array_repeat(0, $size + 1)]; for ($i = 0; $i < $size; ++$i) { $temp = $a[self::VALUE][0] + $x[$i] * $y[0]; $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31)); $temp = $temp * $cache[self::DATA][$key]; $temp = $temp - $class::BASE_FULL * ($class::BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31)); $temp = $class::addHelper($class::regularMultiply([$x[$i]], $y), false, $class::regularMultiply([$temp], $n), false); $a = $class::addHelper($a[self::VALUE], false, $temp[self::VALUE], false); $a[self::VALUE] = array_slice($a[self::VALUE], 1); } if (self::compareHelper($a[self::VALUE], false, $n, false) >= 0) { $a = $class::subtractHelper($a[self::VALUE], false, $n, false); } return $a[self::VALUE]; } }