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Diffstat (limited to 'vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/Barrett.php')
-rw-r--r-- | vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/Barrett.php | 187 |
1 files changed, 187 insertions, 0 deletions
diff --git a/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/Barrett.php b/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/Barrett.php new file mode 100644 index 0000000..0fb7eae --- /dev/null +++ b/vendor/phpseclib/phpseclib/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/Barrett.php @@ -0,0 +1,187 @@ +<?php + +/** + * BCMath Barrett Modular Exponentiation Engine + * + * PHP version 5 and 7 + * + * @author Jim Wigginton <[email protected]> + * @copyright 2017 Jim Wigginton + * @license http://www.opensource.org/licenses/mit-license.html MIT License + * @link http://pear.php.net/package/Math_BigInteger + */ + +namespace phpseclib3\Math\BigInteger\Engines\BCMath\Reductions; + +use phpseclib3\Math\BigInteger\Engines\BCMath\Base; + +/** + * PHP Barrett Modular Exponentiation Engine + * + * @author Jim Wigginton <[email protected]> + */ +abstract class Barrett extends Base +{ + /** + * Cache constants + * + * $cache[self::VARIABLE] tells us whether or not the cached data is still valid. + * + */ + const VARIABLE = 0; + /** + * $cache[self::DATA] contains the cached data. + * + */ + const DATA = 1; + + /** + * Barrett Modular Reduction + * + * See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=14 HAC 14.3.3} / + * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=165 MPM 6.2.5} for more information. Modified slightly, + * so as not to require negative numbers (initially, this script didn't support negative numbers). + * + * Employs "folding", as described at + * {@link http://www.cosic.esat.kuleuven.be/publications/thesis-149.pdf#page=66 thesis-149.pdf#page=66}. To quote from + * it, "the idea [behind folding] is to find a value x' such that x (mod m) = x' (mod m), with x' being smaller than x." + * + * Unfortunately, the "Barrett Reduction with Folding" algorithm described in thesis-149.pdf is not, as written, all that + * usable on account of (1) its not using reasonable radix points as discussed in + * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=162 MPM 6.2.2} and (2) the fact that, even with reasonable + * radix points, it only works when there are an even number of digits in the denominator. The reason for (2) is that + * (x >> 1) + (x >> 1) != x / 2 + x / 2. If x is even, they're the same, but if x is odd, they're not. See the in-line + * comments for details. + * + * @param string $n + * @param string $m + * @return string + */ + protected static function reduce($n, $m) + { + static $cache = [ + self::VARIABLE => [], + self::DATA => [] + ]; + + $m_length = strlen($m); + + if (strlen($n) > 2 * $m_length) { + return bcmod($n, $m); + } + + // if (m.length >> 1) + 2 <= m.length then m is too small and n can't be reduced + if ($m_length < 5) { + return self::regularBarrett($n, $m); + } + // n = 2 * m.length + + if (($key = array_search($m, $cache[self::VARIABLE])) === false) { + $key = count($cache[self::VARIABLE]); + $cache[self::VARIABLE][] = $m; + + $lhs = '1' . str_repeat('0', $m_length + ($m_length >> 1)); + $u = bcdiv($lhs, $m, 0); + $m1 = bcsub($lhs, bcmul($u, $m)); + + $cache[self::DATA][] = [ + 'u' => $u, // m.length >> 1 (technically (m.length >> 1) + 1) + 'm1' => $m1 // m.length + ]; + } else { + extract($cache[self::DATA][$key]); + } + + $cutoff = $m_length + ($m_length >> 1); + + $lsd = substr($n, -$cutoff); + $msd = substr($n, 0, -$cutoff); + + $temp = bcmul($msd, $m1); // m.length + (m.length >> 1) + $n = bcadd($lsd, $temp); // m.length + (m.length >> 1) + 1 (so basically we're adding two same length numbers) + //if ($m_length & 1) { + // return self::regularBarrett($n, $m); + //} + + // (m.length + (m.length >> 1) + 1) - (m.length - 1) == (m.length >> 1) + 2 + $temp = substr($n, 0, -$m_length + 1); + // if even: ((m.length >> 1) + 2) + (m.length >> 1) == m.length + 2 + // if odd: ((m.length >> 1) + 2) + (m.length >> 1) == (m.length - 1) + 2 == m.length + 1 + $temp = bcmul($temp, $u); + // if even: (m.length + 2) - ((m.length >> 1) + 1) = m.length - (m.length >> 1) + 1 + // if odd: (m.length + 1) - ((m.length >> 1) + 1) = m.length - (m.length >> 1) + $temp = substr($temp, 0, -($m_length >> 1) - 1); + // if even: (m.length - (m.length >> 1) + 1) + m.length = 2 * m.length - (m.length >> 1) + 1 + // if odd: (m.length - (m.length >> 1)) + m.length = 2 * m.length - (m.length >> 1) + $temp = bcmul($temp, $m); + + // at this point, if m had an odd number of digits, we'd be subtracting a 2 * m.length - (m.length >> 1) digit + // number from a m.length + (m.length >> 1) + 1 digit number. ie. there'd be an extra digit and the while loop + // following this comment would loop a lot (hence our calling _regularBarrett() in that situation). + + $result = bcsub($n, $temp); + + //if (bccomp($result, '0') < 0) { + if ($result[0] == '-') { + $temp = '1' . str_repeat('0', $m_length + 1); + $result = bcadd($result, $temp); + } + + while (bccomp($result, $m) >= 0) { + $result = bcsub($result, $m); + } + + return $result; + } + + /** + * (Regular) Barrett Modular Reduction + * + * For numbers with more than four digits BigInteger::_barrett() is faster. The difference between that and this + * is that this function does not fold the denominator into a smaller form. + * + * @param string $x + * @param string $n + * @return string + */ + private static function regularBarrett($x, $n) + { + static $cache = [ + self::VARIABLE => [], + self::DATA => [] + ]; + + $n_length = strlen($n); + + if (strlen($x) > 2 * $n_length) { + return bcmod($x, $n); + } + + if (($key = array_search($n, $cache[self::VARIABLE])) === false) { + $key = count($cache[self::VARIABLE]); + $cache[self::VARIABLE][] = $n; + $lhs = '1' . str_repeat('0', 2 * $n_length); + $cache[self::DATA][] = bcdiv($lhs, $n, 0); + } + + $temp = substr($x, 0, -$n_length + 1); + $temp = bcmul($temp, $cache[self::DATA][$key]); + $temp = substr($temp, 0, -$n_length - 1); + + $r1 = substr($x, -$n_length - 1); + $r2 = substr(bcmul($temp, $n), -$n_length - 1); + $result = bcsub($r1, $r2); + + //if (bccomp($result, '0') < 0) { + if ($result[0] == '-') { + $q = '1' . str_repeat('0', $n_length + 1); + $result = bcadd($result, $q); + } + + while (bccomp($result, $n) >= 0) { + $result = bcsub($result, $n); + } + + return $result; + } +} |