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qa-tool/htdocs/oidc/phpseclib/Math/BigInteger/Engines/PHP/Montgomery.php

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+<?php
+
+/**
+ * PHP Montgomery Modular Exponentiation Engine
+ *
+ * PHP version 5 and 7
+ *
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+declare(strict_types=1);
+
+namespace phpseclib3\Math\BigInteger\Engines\PHP;
+
+use phpseclib3\Math\BigInteger\Engines\Engine;
+use phpseclib3\Math\BigInteger\Engines\PHP;
+use phpseclib3\Math\BigInteger\Engines\PHP\Reductions\PowerOfTwo;
+
+/**
+ * PHP Montgomery Modular Exponentiation Engine
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class Montgomery extends Base
+{
+    /**
+     * Test for engine validity
+     */
+    public static function isValidEngine(): bool
+    {
+        return static::class != __CLASS__;
+    }
+
+    /**
+     * Performs modular exponentiation.
+     *
+     * @template T of Engine
+     * @param class-string<T> $class
+     * @return T
+     */
+    protected static function slidingWindow(Engine $x, Engine $e, Engine $n, string $class)
+    {
+        // is the modulo odd?
+        if ($n->value[0] & 1) {
+            return parent::slidingWindow($x, $e, $n, $class);
+        }
+        // if it's not, it's even
+
+        // find the lowest set bit (eg. the max pow of 2 that divides $n)
+        for ($i = 0; $i < count($n->value); ++$i) {
+            if ($n->value[$i]) {
+                $temp = decbin($n->value[$i]);
+                $j = strlen($temp) - strrpos($temp, '1') - 1;
+                $j += $class::BASE * $i;
+                break;
+            }
+        }
+        // at this point, 2^$j * $n/(2^$j) == $n
+
+        $mod1 = clone $n;
+        $mod1->rshift($j);
+        $mod2 = new $class();
+        $mod2->value = [1];
+        $mod2->lshift($j);
+
+        $part1 = $mod1->value != [1] ? parent::slidingWindow($x, $e, $mod1, $class) : new $class();
+        $part2 = PowerOfTwo::slidingWindow($x, $e, $mod2, $class);
+
+        $y1 = $mod2->modInverse($mod1);
+        $y2 = $mod1->modInverse($mod2);
+
+        $result = $part1->multiply($mod2);
+        $result = $result->multiply($y1);
+
+        $temp = $part2->multiply($mod1);
+        $temp = $temp->multiply($y2);
+
+        $result = $result->add($temp);
+        [, $result] = $result->divide($n);
+
+        return $result;
+    }
+}