Add AES from phpseclib and use it for cookie encryption

This replaces the deprecated and broken Blowfish implementation that has
previously been used and should provide a lot more security.

9 files changed, 8095 insertions, 3 deletions

diff --git a/inc/auth.php b/inc/auth.php
index a1da971ae..f02bfebca 100644
--- a/inc/auth.php
+++ b/inc/auth.php
@@ -220,7 +220,7 @@ function auth_login($user, $pass, $sticky = false, $silent = false) {
             // make logininfo globally available
             $_SERVER['REMOTE_USER'] = $user;
             $secret                 = auth_cookiesalt(!$sticky, true); //bind non-sticky to session
-            auth_setCookie($user, PMA_blowfish_encrypt($pass, $secret), $sticky);
+            auth_setCookie($user, auth_encrypt($pass, $secret), $sticky);
             return true;
         } else {
             //invalid credentials - log off
@@ -251,7 +251,7 @@ function auth_login($user, $pass, $sticky = false, $silent = false) {
             }
             // no we don't trust it yet - recheck pass but silent
             $secret = auth_cookiesalt(!$sticky, true); //bind non-sticky to session
-            $pass   = PMA_blowfish_decrypt($pass, $secret);
+            $pass   = auth_decrypt($pass, $secret);
             return auth_login($user, $pass, $sticky, true);
         }
     }
@@ -450,6 +450,40 @@ function auth_random($min, $max) {
 }
 
 /**
+ * Encrypt data using the given secret using AES
+ *
+ * The mode is CBC with a random initialization vector, the key is derived
+ * using pbkdf2.
+ *
+ * @param string $data   The data that shall be encrypted
+ * @param string $secret The secret/password that shall be used
+ * @return string The ciphertext
+ */
+function auth_encrypt($data, $secret) {
+    $iv = auth_randombytes(16);
+    $cipher = new Crypt_AES();
+    $cipher->setPassword($secret);
+
+    return $cipher->encrypt($iv.$data);
+}
+
+/**
+ * Decrypt the given AES ciphertext
+ *
+ * The mode is CBC, the key is derived using pbkdf2
+ *
+ * @param string $ciphertext The encrypted data
+ * @param string $secret     The secret/password that shall be used
+ * @return string The decrypted data
+ */
+function auth_decrypt($ciphertext, $secret) {
+    $cipher = new Crypt_AES();
+    $cipher->setPassword($secret);
+
+    return substr($cipher->decrypt($ciphertext), 16);
+}
+
+/**
  * Log out the current user
  *
  * This clears all authentication data and thus log the user
@@ -992,7 +1026,7 @@ function updateprofile() {
         // update cookie and session with the changed data
         if($changes['pass']) {
             list( /*user*/, $sticky, /*pass*/) = auth_getCookie();
-            $pass = PMA_blowfish_encrypt($changes['pass'], auth_cookiesalt(!$sticky, true));
+            $pass = auth_encrypt($changes['pass'], auth_cookiesalt(!$sticky, true));
             auth_setCookie($_SERVER['REMOTE_USER'], $pass, (bool) $sticky);
         }
         return true;
diff --git a/inc/load.php b/inc/load.php
index 5ca9b4cd8..7fb328215 100644
--- a/inc/load.php
+++ b/inc/load.php
@@ -82,6 +82,10 @@ function load_autoload($name){
         'RemoteAPI'             => DOKU_INC.'inc/remote.php',
         'RemoteAPICore'         => DOKU_INC.'inc/RemoteAPICore.php',
         'Subscription'          => DOKU_INC.'inc/subscription.php',
+        'Crypt_Base'            => DOKU_INC.'inc/phpseclib/Crypt_Base.php',
+        'Crypt_Rijndael'        => DOKU_INC.'inc/phpseclib/Crypt_Rijndael.php',
+        'Crypt_AES'             => DOKU_INC.'inc/phpseclib/Crypt_AES.php',
+        'Crypt_Hash'            => DOKU_INC.'inc/phpseclib/Crypt_Hash.php',
 
         'DokuWiki_Action_Plugin' => DOKU_PLUGIN.'action.php',
         'DokuWiki_Admin_Plugin'  => DOKU_PLUGIN.'admin.php',
diff --git a/inc/phpseclib/Crypt_AES.php b/inc/phpseclib/Crypt_AES.php
new file mode 100644
index 000000000..81fa2feab
--- /dev/null
+++ b/inc/phpseclib/Crypt_AES.php
@@ -0,0 +1,188 @@
+<?php
+/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
+
+/**
+ * Pure-PHP implementation of AES.
+ *
+ * Uses mcrypt, if available/possible, and an internal implementation, otherwise.
+ *
+ * PHP versions 4 and 5
+ *
+ * If {@link Crypt_AES::setKeyLength() setKeyLength()} isn't called, it'll be calculated from
+ * {@link Crypt_AES::setKey() setKey()}.  ie. if the key is 128-bits, the key length will be 128-bits.  If it's 136-bits
+ * it'll be null-padded to 192-bits and 192 bits will be the key length until {@link Crypt_AES::setKey() setKey()}
+ * is called, again, at which point, it'll be recalculated.
+ *
+ * Since Crypt_AES extends Crypt_Rijndael, some functions are available to be called that, in the context of AES, don't
+ * make a whole lot of sense.  {@link Crypt_AES::setBlockLength() setBlockLength()}, for instance.  Calling that function,
+ * however possible, won't do anything (AES has a fixed block length whereas Rijndael has a variable one).
+ *
+ * Here's a short example of how to use this library:
+ * <code>
+ * <?php
+ *    include('Crypt/AES.php');
+ *
+ *    $aes = new Crypt_AES();
+ *
+ *    $aes->setKey('abcdefghijklmnop');
+ *
+ *    $size = 10 * 1024;
+ *    $plaintext = '';
+ *    for ($i = 0; $i < $size; $i++) {
+ *        $plaintext.= 'a';
+ *    }
+ *
+ *    echo $aes->decrypt($aes->encrypt($plaintext));
+ * ?>
+ * </code>
+ *
+ * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *
+ * @category   Crypt
+ * @package    Crypt_AES
+ * @author     Jim Wigginton <terrafrost@php.net>
+ * @copyright  MMVIII Jim Wigginton
+ * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link       http://phpseclib.sourceforge.net
+ */
+
+/**
+ * Include Crypt_Rijndael
+ */
+if (!class_exists('Crypt_Rijndael')) {
+    require_once('Rijndael.php');
+}
+
+/**#@+
+ * @access public
+ * @see Crypt_AES::encrypt()
+ * @see Crypt_AES::decrypt()
+ */
+/**
+ * Encrypt / decrypt using the Counter mode.
+ *
+ * Set to -1 since that's what Crypt/Random.php uses to index the CTR mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Counter_.28CTR.29
+ */
+define('CRYPT_AES_MODE_CTR', CRYPT_MODE_CTR);
+/**
+ * Encrypt / decrypt using the Electronic Code Book mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Electronic_codebook_.28ECB.29
+ */
+define('CRYPT_AES_MODE_ECB', CRYPT_MODE_ECB);
+/**
+ * Encrypt / decrypt using the Code Book Chaining mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher-block_chaining_.28CBC.29
+ */
+define('CRYPT_AES_MODE_CBC', CRYPT_MODE_CBC);
+/**
+ * Encrypt / decrypt using the Cipher Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher_feedback_.28CFB.29
+ */
+define('CRYPT_AES_MODE_CFB', CRYPT_MODE_CFB);
+/**
+ * Encrypt / decrypt using the Cipher Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Output_feedback_.28OFB.29
+ */
+define('CRYPT_AES_MODE_OFB', CRYPT_MODE_OFB);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Crypt_AES::Crypt_AES()
+ */
+/**
+ * Toggles the internal implementation
+ */
+define('CRYPT_AES_MODE_INTERNAL', CRYPT_MODE_INTERNAL);
+/**
+ * Toggles the mcrypt implementation
+ */
+define('CRYPT_AES_MODE_MCRYPT', CRYPT_MODE_MCRYPT);
+/**#@-*/
+
+/**
+ * Pure-PHP implementation of AES.
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @version 0.1.0
+ * @access  public
+ * @package Crypt_AES
+ */
+class Crypt_AES extends Crypt_Rijndael {
+    /**
+     * The namespace used by the cipher for its constants.
+     *
+     * @see Crypt_Base::const_namespace
+     * @var String
+     * @access private
+     */
+    var $const_namespace = 'AES';
+
+    /**
+     * Default Constructor.
+     *
+     * Determines whether or not the mcrypt extension should be used.
+     *
+     * $mode could be:
+     *
+     * - CRYPT_AES_MODE_ECB
+     *
+     * - CRYPT_AES_MODE_CBC
+     *
+     * - CRYPT_AES_MODE_CTR
+     *
+     * - CRYPT_AES_MODE_CFB
+     *
+     * - CRYPT_AES_MODE_OFB
+     *
+     * If not explictly set, CRYPT_AES_MODE_CBC will be used.
+     *
+     * @see Crypt_Rijndael::Crypt_Rijndael()
+     * @see Crypt_Base::Crypt_Base()
+     * @param optional Integer $mode
+     * @access public
+     */
+    function Crypt_AES($mode = CRYPT_AES_MODE_CBC)
+    {
+        parent::Crypt_Rijndael($mode);
+    }
+
+    /**
+     * Dummy function
+     *
+     * Since Crypt_AES extends Crypt_Rijndael, this function is, technically, available, but it doesn't do anything.
+     *
+     * @see Crypt_Rijndael::setBlockLength()
+     * @access public
+     * @param Integer $length
+     */
+    function setBlockLength($length)
+    {
+        return;
+    }
+}
+
+// vim: ts=4:sw=4:et:
+// vim6: fdl=1:
diff --git a/inc/phpseclib/Crypt_Base.php b/inc/phpseclib/Crypt_Base.php
new file mode 100644
index 000000000..7c650ca72
--- /dev/null
+++ b/inc/phpseclib/Crypt_Base.php
@@ -0,0 +1,1989 @@
+<?php
+/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
+
+/**
+ * Base Class for all Crypt_* cipher classes
+ *
+ * PHP versions 4 and 5
+ *
+ * Internally for phpseclib developers:
+ *  If you plan to add a new cipher class, please note following rules:
+ *
+ *  - The new Crypt_* cipher class should extend Crypt_Base
+ *
+ *  - Following methods are then required to be overridden/overloaded:
+ *
+ *    - _encryptBlock()
+ *
+ *    - _decryptBlock()
+ *
+ *    - _setupKey()
+ *
+ *  - All other methods are optional to be overridden/overloaded
+ *
+ *  - Look at the source code of the current ciphers how they extend Crypt_Base
+ *    and take one of them as a start up for the new cipher class.
+ *
+ *  - Please read all the other comments/notes/hints here also for each class var/method
+ *
+ * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *
+ * @category   Crypt
+ * @package    Crypt_Base
+ * @author     Jim Wigginton <terrafrost@php.net>
+ * @author     Hans-Juergen Petrich <petrich@tronic-media.com>
+ * @copyright  MMVII Jim Wigginton
+ * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @version    1.0.1
+ * @link       http://phpseclib.sourceforge.net
+ */
+
+/**#@+
+ * @access public
+ * @see Crypt_Base::encrypt()
+ * @see Crypt_Base::decrypt()
+ */
+/**
+ * Encrypt / decrypt using the Counter mode.
+ *
+ * Set to -1 since that's what Crypt/Random.php uses to index the CTR mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Counter_.28CTR.29
+ */
+define('CRYPT_MODE_CTR', -1);
+/**
+ * Encrypt / decrypt using the Electronic Code Book mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Electronic_codebook_.28ECB.29
+ */
+define('CRYPT_MODE_ECB', 1);
+/**
+ * Encrypt / decrypt using the Code Book Chaining mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher-block_chaining_.28CBC.29
+ */
+define('CRYPT_MODE_CBC', 2);
+/**
+ * Encrypt / decrypt using the Cipher Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher_feedback_.28CFB.29
+ */
+define('CRYPT_MODE_CFB', 3);
+/**
+ * Encrypt / decrypt using the Output Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Output_feedback_.28OFB.29
+ */
+define('CRYPT_MODE_OFB', 4);
+/**
+ * Encrypt / decrypt using streaming mode.
+ *
+ */
+define('CRYPT_MODE_STREAM', 5);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Crypt_Base::Crypt_Base()
+ */
+/**
+ * Base value for the internal implementation $engine switch
+ */
+define('CRYPT_MODE_INTERNAL', 1);
+/**
+ * Base value for the mcrypt implementation $engine switch
+ */
+define('CRYPT_MODE_MCRYPT', 2);
+/**#@-*/
+
+/**
+ * Base Class for all Crypt_* cipher classes
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @author  Hans-Juergen Petrich <petrich@tronic-media.com>
+ * @version 1.0.0
+ * @access  public
+ * @package Crypt_Base
+ */
+class Crypt_Base {
+    /**
+     * The Encryption Mode
+     *
+     * @see Crypt_Base::Crypt_Base()
+     * @var Integer
+     * @access private
+     */
+    var $mode;
+
+    /**
+     * The Block Length of the block cipher
+     *
+     * @var Integer
+     * @access private
+     */
+    var $block_size = 16;
+
+    /**
+     * The Key
+     *
+     * @see Crypt_Base::setKey()
+     * @var String
+     * @access private
+     */
+    var $key = "\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0";
+
+    /**
+     * The Initialization Vector
+     *
+     * @see Crypt_Base::setIV()
+     * @var String
+     * @access private
+     */
+    var $iv;
+
+    /**
+     * A "sliding" Initialization Vector
+     *
+     * @see Crypt_Base::enableContinuousBuffer()
+     * @see Crypt_Base::_clearBuffers()
+     * @var String
+     * @access private
+     */
+    var $encryptIV;
+
+    /**
+     * A "sliding" Initialization Vector
+     *
+     * @see Crypt_Base::enableContinuousBuffer()
+     * @see Crypt_Base::_clearBuffers()
+     * @var String
+     * @access private
+     */
+    var $decryptIV;
+
+    /**
+     * Continuous Buffer status
+     *
+     * @see Crypt_Base::enableContinuousBuffer()
+     * @var Boolean
+     * @access private
+     */
+    var $continuousBuffer = false;
+
+    /**
+     * Encryption buffer for CTR, OFB and CFB modes
+     *
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::_clearBuffers()
+     * @var Array
+     * @access private
+     */
+    var $enbuffer;
+
+    /**
+     * Decryption buffer for CTR, OFB and CFB modes
+     *
+     * @see Crypt_Base::decrypt()
+     * @see Crypt_Base::_clearBuffers()
+     * @var Array
+     * @access private
+     */
+    var $debuffer;
+
+    /**
+     * mcrypt resource for encryption
+     *
+     * The mcrypt resource can be recreated every time something needs to be created or it can be created just once.
+     * Since mcrypt operates in continuous mode, by default, it'll need to be recreated when in non-continuous mode.
+     *
+     * @see Crypt_Base::encrypt()
+     * @var Resource
+     * @access private
+     */
+    var $enmcrypt;
+
+    /**
+     * mcrypt resource for decryption
+     *
+     * The mcrypt resource can be recreated every time something needs to be created or it can be created just once.
+     * Since mcrypt operates in continuous mode, by default, it'll need to be recreated when in non-continuous mode.
+     *
+     * @see Crypt_Base::decrypt()
+     * @var Resource
+     * @access private
+     */
+    var $demcrypt;
+
+    /**
+     * Does the enmcrypt resource need to be (re)initialized?
+     *
+     * @see Crypt_Twofish::setKey()
+     * @see Crypt_Twofish::setIV()
+     * @var Boolean
+     * @access private
+     */
+    var $enchanged = true;
+
+    /**
+     * Does the demcrypt resource need to be (re)initialized?
+     *
+     * @see Crypt_Twofish::setKey()
+     * @see Crypt_Twofish::setIV()
+     * @var Boolean
+     * @access private
+     */
+    var $dechanged = true;
+
+    /**
+     * mcrypt resource for CFB mode
+     *
+     * mcrypt's CFB mode, in (and only in) buffered context,
+     * is broken, so phpseclib implements the CFB mode by it self,
+     * even when the mcrypt php extension is available.
+     *
+     * In order to do the CFB-mode work (fast) phpseclib
+     * use a separate ECB-mode mcrypt resource.
+     *
+     * @link http://phpseclib.sourceforge.net/cfb-demo.phps
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @see Crypt_Base::_setupMcrypt()
+     * @var Resource
+     * @access private
+     */
+    var $ecb;
+
+    /**
+     * Optimizing value while CFB-encrypting
+     *
+     * Only relevant if $continuousBuffer enabled
+     * and $engine == CRYPT_MODE_MCRYPT
+     *
+     * It's faster to re-init $enmcrypt if
+     * $buffer bytes > $cfb_init_len than
+     * using the $ecb resource furthermore.
+     *
+     * This value depends of the choosen cipher
+     * and the time it would be needed for it's
+     * initialization [by mcrypt_generic_init()]
+     * which, typically, depends on the complexity
+     * on its internaly Key-expanding algorithm.
+     *
+     * @see Crypt_Base::encrypt()
+     * @var Integer
+     * @access private
+     */
+    var $cfb_init_len = 600;
+
+    /**
+     * Does internal cipher state need to be (re)initialized?
+     *
+     * @see setKey()
+     * @see setIV()
+     * @see disableContinuousBuffer()
+     * @var Boolean
+     * @access private
+     */
+    var $changed = true;
+
+    /**
+     * Padding status
+     *
+     * @see Crypt_Base::enablePadding()
+     * @var Boolean
+     * @access private
+     */
+    var $padding = true;
+
+    /**
+     * Is the mode one that is paddable?
+     *
+     * @see Crypt_Base::Crypt_Base()
+     * @var Boolean
+     * @access private
+     */
+    var $paddable = false;
+
+    /**
+     * Holds which crypt engine internaly should be use,
+     * which will be determined automatically on __construct()
+     *
+     * Currently available $engines are:
+     * - CRYPT_MODE_MCRYPT   (fast, php-extension: mcrypt, extension_loaded('mcrypt') required)
+     * - CRYPT_MODE_INTERNAL (slower, pure php-engine, no php-extension required)
+     *
+     * In the pipeline... maybe. But currently not available:
+     * - CRYPT_MODE_OPENSSL  (very fast, php-extension: openssl, extension_loaded('openssl') required)
+     *
+     * If possible, CRYPT_MODE_MCRYPT will be used for each cipher.
+     * Otherwise CRYPT_MODE_INTERNAL
+     *
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @var Integer
+     * @access private
+     */
+    var $engine;
+
+    /**
+     * The mcrypt specific name of the cipher
+     *
+     * Only used if $engine == CRYPT_MODE_MCRYPT
+     *
+     * @link http://www.php.net/mcrypt_module_open
+     * @link http://www.php.net/mcrypt_list_algorithms
+     * @see Crypt_Base::_setupMcrypt()
+     * @var String
+     * @access private
+     */
+    var $cipher_name_mcrypt;
+
+    /**
+     * The default password key_size used by setPassword()
+     *
+     * @see Crypt_Base::setPassword()
+     * @var Integer
+     * @access private
+     */
+    var $password_key_size = 32;
+
+    /**
+     * The default salt used by setPassword()
+     *
+     * @see Crypt_Base::setPassword()
+     * @var String
+     * @access private
+     */
+    var $password_default_salt = 'phpseclib/salt';
+
+    /**
+     * The namespace used by the cipher for its constants.
+     *
+     * ie: AES.php is using CRYPT_AES_MODE_* for its constants
+     *     so $const_namespace is AES
+     *
+     *     DES.php is using CRYPT_DES_MODE_* for its constants
+     *     so $const_namespace is DES... and so on
+     *
+     * All CRYPT_<$const_namespace>_MODE_* are aliases of
+     * the generic CRYPT_MODE_* constants, so both could be used
+     * for each cipher.
+     *
+     * Example:
+     * $aes = new Crypt_AES(CRYPT_AES_MODE_CFB); // $aes will operate in cfb mode
+     * $aes = new Crypt_AES(CRYPT_MODE_CFB);     // identical
+     *
+     * @see Crypt_Base::Crypt_Base()
+     * @var String
+     * @access private
+     */
+    var $const_namespace;
+
+    /**
+     * The name of the performance-optimized callback function
+     *
+     * Used by encrypt() / decrypt()
+     * only if $engine == CRYPT_MODE_INTERNAL
+     *
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @see Crypt_Base::_setupInlineCrypt()
+     * @see Crypt_Base::$use_inline_crypt
+     * @var Callback
+     * @access private
+     */
+    var $inline_crypt;
+
+    /**
+     * Holds whether performance-optimized $inline_crypt() can/should be used.
+     *
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @see Crypt_Base::inline_crypt
+     * @var mixed
+     * @access private
+     */
+    var $use_inline_crypt;
+
+    /**
+     * Default Constructor.
+     *
+     * Determines whether or not the mcrypt extension should be used.
+     *
+     * $mode could be:
+     *
+     * - CRYPT_MODE_ECB
+     *
+     * - CRYPT_MODE_CBC
+     *
+     * - CRYPT_MODE_CTR
+     *
+     * - CRYPT_MODE_CFB
+     *
+     * - CRYPT_MODE_OFB
+     *
+     * (or the alias constants of the choosen cipher, for example for AES: CRYPT_AES_MODE_ECB or CRYPT_AES_MODE_CBC ...)
+     *
+     * If not explictly set, CRYPT_MODE_CBC will be used.
+     *
+     * @param optional Integer $mode
+     * @access public
+     */
+    function Crypt_Base($mode = CRYPT_MODE_CBC)
+    {
+        $const_crypt_mode = 'CRYPT_' . $this->const_namespace . '_MODE';
+
+        // Determining the availibility of mcrypt support for the cipher
+        if (!defined($const_crypt_mode)) {
+            switch (true) {
+                case extension_loaded('mcrypt') && in_array($this->cipher_name_mcrypt, mcrypt_list_algorithms()):
+                    define($const_crypt_mode, CRYPT_MODE_MCRYPT);
+                    break;
+                default:
+                    define($const_crypt_mode, CRYPT_MODE_INTERNAL);
+            }
+        }
+
+        // Determining which internal $engine should be used.
+        // The fastes possible first.
+        switch (true) {
+            case empty($this->cipher_name_mcrypt): // The cipher module has no mcrypt-engine support at all so we force CRYPT_MODE_INTERNAL
+                $this->engine = CRYPT_MODE_INTERNAL;
+                break;
+            case constant($const_crypt_mode) == CRYPT_MODE_MCRYPT:
+                $this->engine = CRYPT_MODE_MCRYPT;
+                break;
+            default:
+                $this->engine = CRYPT_MODE_INTERNAL;
+        }
+
+        // $mode dependent settings
+        switch ($mode) {
+            case CRYPT_MODE_ECB:
+                $this->paddable = true;
+                $this->mode = $mode;
+                break;
+            case CRYPT_MODE_CTR:
+            case CRYPT_MODE_CFB:
+            case CRYPT_MODE_OFB:
+            case CRYPT_MODE_STREAM:
+                $this->mode = $mode;
+                break;
+            case CRYPT_MODE_CBC:
+            default:
+                $this->paddable = true;
+                $this->mode = CRYPT_MODE_CBC;
+        }
+
+        // Determining whether inline crypting can be used by the cipher
+        if ($this->use_inline_crypt !== false && function_exists('create_function')) {
+            $this->use_inline_crypt = true;
+        }
+    }
+
+    /**
+     * Sets the initialization vector. (optional)
+     *
+     * SetIV is not required when CRYPT_MODE_ECB (or ie for AES: CRYPT_AES_MODE_ECB) is being used.  If not explictly set, it'll be assumed
+     * to be all zero's.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @access public
+     * @param String $iv
+     */
+    function setIV($iv)
+    {
+        if ($this->mode == CRYPT_MODE_ECB) {
+            return;
+        }
+
+        $this->iv = $iv;
+        $this->changed = true;
+    }
+
+    /**
+     * Sets the key.
+     *
+     * The min/max length(s) of the key depends on the cipher which is used.
+     * If the key not fits the length(s) of the cipher it will paded with null bytes
+     * up to the closest valid key length.  If the key is more than max length,
+     * we trim the excess bits.
+     *
+     * If the key is not explicitly set, it'll be assumed to be all null bytes.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @access public
+     * @param String $key
+     */
+    function setKey($key)
+    {
+        $this->key = $key;
+        $this->changed = true;
+    }
+
+    /**
+     * Sets the password.
+     *
+     * Depending on what $method is set to, setPassword()'s (optional) parameters are as follows:
+     *     {@link http://en.wikipedia.org/wiki/PBKDF2 pbkdf2}:
+     *         $hash, $salt, $count, $dkLen
+     *
+     *         Where $hash (default = sha1) currently supports the following hashes: see: Crypt/Hash.php
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see Crypt/Hash.php
+     * @param String $password
+     * @param optional String $method
+     * @access public
+     */
+    function setPassword($password, $method = 'pbkdf2')
+    {
+        $key = '';
+
+        switch ($method) {
+            default: // 'pbkdf2'
+                $func_args = func_get_args();
+
+                // Hash function
+                $hash = isset($func_args[2]) ? $func_args[2] : 'sha1';
+
+                // WPA and WPA2 use the SSID as the salt
+                $salt = isset($func_args[3]) ? $func_args[3] : $this->password_default_salt;
+
+                // RFC2898#section-4.2 uses 1,000 iterations by default
+                // WPA and WPA2 use 4,096.
+                $count = isset($func_args[4]) ? $func_args[4] : 1000;
+
+                // Keylength
+                $dkLen = isset($func_args[5]) ? $func_args[5] : $this->password_key_size;
+
+                // Determining if php[>=5.5.0]'s hash_pbkdf2() function avail- and useable
+                switch (true) {
+                    case !function_exists('hash_pbkdf2'):
+                    case !function_exists('hash_algos'):
+                    case !in_array($hash, hash_algos()):
+                        if (!class_exists('Crypt_Hash')) {
+                            require_once('Crypt/Hash.php');
+                        }
+                        $i = 1;
+                        while (strlen($key) < $dkLen) {
+                            $hmac = new Crypt_Hash();
+                            $hmac->setHash($hash);
+                            $hmac->setKey($password);
+                            $f = $u = $hmac->hash($salt . pack('N', $i++));
+                            for ($j = 2; $j <= $count; ++$j) {
+                                $u = $hmac->hash($u);
+                                $f^= $u;
+                            }
+                            $key.= $f;
+                        }
+                        $key = substr($key, 0, $dkLen);
+                        break;
+                    default:
+                        $key = hash_pbkdf2($hash, $password, $salt, $count, $dkLen, true);
+                }
+        }
+
+        $this->setKey($key);
+    }
+
+    /**
+     * Encrypts a message.
+     *
+     * $plaintext will be padded with additional bytes such that it's length is a multiple of the block size. Other cipher
+     * implementations may or may not pad in the same manner.  Other common approaches to padding and the reasons why it's
+     * necessary are discussed in the following
+     * URL:
+     *
+     * {@link http://www.di-mgt.com.au/cryptopad.html http://www.di-mgt.com.au/cryptopad.html}
+     *
+     * An alternative to padding is to, separately, send the length of the file.  This is what SSH, in fact, does.
+     * strlen($plaintext) will still need to be a multiple of the block size, however, arbitrary values can be added to make it that
+     * length.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see Crypt_Base::decrypt()
+     * @access public
+     * @param String $plaintext
+     * @return String $cipertext
+     */
+    function encrypt($plaintext)
+    {
+        if ($this->engine == CRYPT_MODE_MCRYPT) {
+            if ($this->changed) {
+                $this->_setupMcrypt();
+                $this->changed = false;
+            }
+            if ($this->enchanged) {
+                mcrypt_generic_init($this->enmcrypt, $this->key, $this->encryptIV);
+                $this->enchanged = false;
+            }
+
+            // re: {@link http://phpseclib.sourceforge.net/cfb-demo.phps}
+            // using mcrypt's default handing of CFB the above would output two different things.  using phpseclib's
+            // rewritten CFB implementation the above outputs the same thing twice.
+            if ($this->mode == CRYPT_MODE_CFB && $this->continuousBuffer) {
+                $block_size = $this->block_size;
+                $iv = &$this->encryptIV;
+                $pos = &$this->enbuffer['pos'];
+                $len = strlen($plaintext);
+                $ciphertext = '';
+                $i = 0;
+                if ($pos) {
+                    $orig_pos = $pos;
+                    $max = $block_size - $pos;
+                    if ($len >= $max) {
+                        $i = $max;
+                        $len-= $max;
+                        $pos = 0;
+                    } else {
+                        $i = $len;
+                        $pos+= $len;
+                        $len = 0;
+                    }
+                    $ciphertext = substr($iv, $orig_pos) ^ $plaintext;
+                    $iv = substr_replace($iv, $ciphertext, $orig_pos, $i);
+                    $this->enbuffer['enmcrypt_init'] = true;
+                }
+                if ($len >= $block_size) {
+                    if ($this->enbuffer['enmcrypt_init'] === false || $len > $this->cfb_init_len) {
+                        if ($this->enbuffer['enmcrypt_init'] === true) {
+                            mcrypt_generic_init($this->enmcrypt, $this->key, $iv);
+                            $this->enbuffer['enmcrypt_init'] = false;
+                        }
+                        $ciphertext.= mcrypt_generic($this->enmcrypt, substr($plaintext, $i, $len - $len % $block_size));
+                        $iv = substr($ciphertext, -$block_size);
+                        $len%= $block_size;
+                    } else {
+                        while ($len >= $block_size) {
+                            $iv = mcrypt_generic($this->ecb, $iv) ^ substr($plaintext, $i, $block_size);
+                            $ciphertext.= $iv;
+                            $len-= $block_size;
+                            $i+= $block_size;
+                        }
+                    }
+                }
+
+                if ($len) {
+                    $iv = mcrypt_generic($this->ecb, $iv);
+                    $block = $iv ^ substr($plaintext, -$len);
+                    $iv = substr_replace($iv, $block, 0, $len);
+                    $ciphertext.= $block;
+                    $pos = $len;
+                }
+
+                return $ciphertext;
+            }
+
+            if ($this->paddable) {
+                $plaintext = $this->_pad($plaintext);
+            }
+
+            $ciphertext = mcrypt_generic($this->enmcrypt, $plaintext);
+
+            if (!$this->continuousBuffer) {
+                mcrypt_generic_init($this->enmcrypt, $this->key, $this->encryptIV);
+            }
+
+            return $ciphertext;
+        }
+
+        if ($this->changed) {
+            $this->_setup();
+            $this->changed = false;
+        }
+        if ($this->use_inline_crypt) {
+            $inline = $this->inline_crypt;
+            return $inline('encrypt', $this, $plaintext);
+        }
+        if ($this->paddable) {
+            $plaintext = $this->_pad($plaintext);
+        }
+
+        $buffer = &$this->enbuffer;
+        $block_size = $this->block_size;
+        $ciphertext = '';
+        switch ($this->mode) {
+            case CRYPT_MODE_ECB:
+                for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                    $ciphertext.= $this->_encryptBlock(substr($plaintext, $i, $block_size));
+                }
+                break;
+            case CRYPT_MODE_CBC:
+                $xor = $this->encryptIV;
+                for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                    $block = substr($plaintext, $i, $block_size);
+                    $block = $this->_encryptBlock($block ^ $xor);
+                    $xor = $block;
+                    $ciphertext.= $block;
+                }
+                if ($this->continuousBuffer) {
+                    $this->encryptIV = $xor;
+                }
+                break;
+            case CRYPT_MODE_CTR:
+                $xor = $this->encryptIV;
+                if (strlen($buffer['encrypted'])) {
+                    for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                        $block = substr($plaintext, $i, $block_size);
+                        if (strlen($block) > strlen($buffer['encrypted'])) {
+                            $buffer['encrypted'].= $this->_encryptBlock($this->_generateXor($xor, $block_size));
+                        }
+                        $key = $this->_stringShift($buffer['encrypted'], $block_size);
+                        $ciphertext.= $block ^ $key;
+                    }
+                } else {
+                    for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                        $block = substr($plaintext, $i, $block_size);
+                        $key = $this->_encryptBlock($this->_generateXor($xor, $block_size));
+                        $ciphertext.= $block ^ $key;
+                    }
+                }
+                if ($this->continuousBuffer) {
+                    $this->encryptIV = $xor;
+                    if ($start = strlen($plaintext) % $block_size) {
+                        $buffer['encrypted'] = substr($key, $start) . $buffer['encrypted'];
+                    }
+                }
+                break;
+            case CRYPT_MODE_CFB:
+                // cfb loosely routines inspired by openssl's:
+                // {@link http://cvs.openssl.org/fileview?f=openssl/crypto/modes/cfb128.c&v=1.3.2.2.2.1}
+                if ($this->continuousBuffer) {
+                    $iv = &$this->encryptIV;
+                    $pos = &$buffer['pos'];
+                } else {
+                    $iv = $this->encryptIV;
+                    $pos = 0;
+                }
+                $len = strlen($plaintext);
+                $i = 0;
+                if ($pos) {
+                    $orig_pos = $pos;
+                    $max = $block_size - $pos;
+                    if ($len >= $max) {
+                        $i = $max;
+                        $len-= $max;
+                        $pos = 0;
+                    } else {
+                        $i = $len;
+                        $pos+= $len;
+                        $len = 0;
+                    }
+                    // ie. $i = min($max, $len), $len-= $i, $pos+= $i, $pos%= $blocksize
+                    $ciphertext = substr($iv, $orig_pos) ^ $plaintext;
+                    $iv = substr_replace($iv, $ciphertext, $orig_pos, $i);
+                }
+                while ($len >= $block_size) {
+                    $iv = $this->_encryptBlock($iv) ^ substr($plaintext, $i, $block_size);
+                    $ciphertext.= $iv;
+                    $len-= $block_size;
+                    $i+= $block_size;
+                }
+                if ($len) {
+                    $iv = $this->_encryptBlock($iv);
+                    $block = $iv ^ substr($plaintext, $i);
+                    $iv = substr_replace($iv, $block, 0, $len);
+                    $ciphertext.= $block;
+                    $pos = $len;
+                }
+                break;
+            case CRYPT_MODE_OFB:
+                $xor = $this->encryptIV;
+                if (strlen($buffer['xor'])) {
+                    for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                        $block = substr($plaintext, $i, $block_size);
+                        if (strlen($block) > strlen($buffer['xor'])) {
+                            $xor = $this->_encryptBlock($xor);
+                            $buffer['xor'].= $xor;
+                        }
+                        $key = $this->_stringShift($buffer['xor'], $block_size);
+                        $ciphertext.= $block ^ $key;
+                    }
+                } else {
+                    for ($i = 0; $i < strlen($plaintext); $i+=$block_size) {
+                        $xor = $this->_encryptBlock($xor);
+                        $ciphertext.= substr($plaintext, $i, $block_size) ^ $xor;
+                    }
+                    $key = $xor;
+                }
+                if ($this->continuousBuffer) {
+                    $this->encryptIV = $xor;
+                    if ($start = strlen($plaintext) % $block_size) {
+                         $buffer['xor'] = substr($key, $start) . $buffer['xor'];
+                    }
+                }
+                break;
+            case CRYPT_MODE_STREAM:
+                $ciphertext = $this->_encryptBlock($plaintext);
+                break;
+        }
+
+        return $ciphertext;
+    }
+
+    /**
+     * Decrypts a message.
+     *
+     * If strlen($ciphertext) is not a multiple of the block size, null bytes will be added to the end of the string until
+     * it is.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see Crypt_Base::encrypt()
+     * @access public
+     * @param String $ciphertext
+     * @return String $plaintext
+     */
+    function decrypt($ciphertext)
+    {
+        if ($this->engine == CRYPT_MODE_MCRYPT) {
+            $block_size = $this->block_size;
+            if ($this->changed) {
+                $this->_setupMcrypt();
+                $this->changed = false;
+            }
+            if ($this->dechanged) {
+                mcrypt_generic_init($this->demcrypt, $this->key, $this->decryptIV);
+                $this->dechanged = false;
+            }
+
+            if ($this->mode == CRYPT_MODE_CFB && $this->continuousBuffer) {
+                $iv = &$this->decryptIV;
+                $pos = &$this->debuffer['pos'];
+                $len = strlen($ciphertext);
+                $plaintext = '';
+                $i = 0;
+                if ($pos) {
+                    $orig_pos = $pos;
+                    $max = $block_size - $pos;
+                    if ($len >= $max) {
+                        $i = $max;
+                        $len-= $max;
+                        $pos = 0;
+                    } else {
+                        $i = $len;
+                        $pos+= $len;
+                        $len = 0;
+                    }
+                    // ie. $i = min($max, $len), $len-= $i, $pos+= $i, $pos%= $blocksize
+                    $plaintext = substr($iv, $orig_pos) ^ $ciphertext;
+                    $iv = substr_replace($iv, substr($ciphertext, 0, $i), $orig_pos, $i);
+                }
+                if ($len >= $block_size) {
+                    $cb = substr($ciphertext, $i, $len - $len % $block_size);
+                    $plaintext.= mcrypt_generic($this->ecb, $iv . $cb) ^ $cb;
+                    $iv = substr($cb, -$block_size);
+                    $len%= $block_size;
+                }
+                if ($len) {
+                    $iv = mcrypt_generic($this->ecb, $iv);
+                    $plaintext.= $iv ^ substr($ciphertext, -$len);
+                    $iv = substr_replace($iv, substr($ciphertext, -$len), 0, $len);
+                    $pos = $len;
+                }
+
+                return $plaintext;
+            }
+
+            if ($this->paddable) {
+                // we pad with chr(0) since that's what mcrypt_generic does.  to quote from {@link http://www.php.net/function.mcrypt-generic}:
+                // "The data is padded with "\0" to make sure the length of the data is n * blocksize."
+                $ciphertext = str_pad($ciphertext, strlen($ciphertext) + ($block_size - strlen($ciphertext) % $block_size) % $block_size, chr(0));
+            }
+
+            $plaintext = mdecrypt_generic($this->demcrypt, $ciphertext);
+
+            if (!$this->continuousBuffer) {
+                mcrypt_generic_init($this->demcrypt, $this->key, $this->decryptIV);
+            }
+
+            return $this->paddable ? $this->_unpad($plaintext) : $plaintext;
+        }
+
+        if ($this->changed) {
+            $this->_setup();
+            $this->changed = false;
+        }
+        if ($this->use_inline_crypt) {
+            $inline = $this->inline_crypt;
+            return $inline('decrypt', $this, $ciphertext);
+        }
+
+        $block_size = $this->block_size;
+        if ($this->paddable) {
+            // we pad with chr(0) since that's what mcrypt_generic does [...]
+            $ciphertext = str_pad($ciphertext, strlen($ciphertext) + ($block_size - strlen($ciphertext) % $block_size) % $block_size, chr(0));
+        }
+
+        $buffer = &$this->debuffer;
+        $plaintext = '';
+        switch ($this->mode) {
+            case CRYPT_MODE_ECB:
+                for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                    $plaintext.= $this->_decryptBlock(substr($ciphertext, $i, $block_size));
+                }
+                break;
+            case CRYPT_MODE_CBC:
+                $xor = $this->decryptIV;
+                for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                    $block = substr($ciphertext, $i, $block_size);
+                    $plaintext.= $this->_decryptBlock($block) ^ $xor;
+                    $xor = $block;
+                }
+                if ($this->continuousBuffer) {
+                    $this->decryptIV = $xor;
+                }
+                break;
+            case CRYPT_MODE_CTR:
+                $xor = $this->decryptIV;
+                if (strlen($buffer['ciphertext'])) {
+                    for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                        $block = substr($ciphertext, $i, $block_size);
+                        if (strlen($block) > strlen($buffer['ciphertext'])) {
+                            $buffer['ciphertext'].= $this->_encryptBlock($this->_generateXor($xor, $block_size));
+                        }
+                        $key = $this->_stringShift($buffer['ciphertext'], $block_size);
+                        $plaintext.= $block ^ $key;
+                    }
+                } else {
+                    for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                        $block = substr($ciphertext, $i, $block_size);
+                        $key = $this->_encryptBlock($this->_generateXor($xor, $block_size));
+                        $plaintext.= $block ^ $key;
+                    }
+                }
+                if ($this->continuousBuffer) {
+                    $this->decryptIV = $xor;
+                    if ($start = strlen($ciphertext) % $block_size) {
+                        $buffer['ciphertext'] = substr($key, $start) . $buffer['ciphertext'];
+                    }
+                }
+                break;
+            case CRYPT_MODE_CFB:
+                if ($this->continuousBuffer) {
+                    $iv = &$this->decryptIV;
+                    $pos = &$buffer['pos'];
+                } else {
+                    $iv = $this->decryptIV;
+                    $pos = 0;
+                }
+                $len = strlen($ciphertext);
+                $i = 0;
+                if ($pos) {
+                    $orig_pos = $pos;
+                    $max = $block_size - $pos;
+                    if ($len >= $max) {
+                        $i = $max;
+                        $len-= $max;
+                        $pos = 0;
+                    } else {
+                        $i = $len;
+                        $pos+= $len;
+                        $len = 0;
+                    }
+                    // ie. $i = min($max, $len), $len-= $i, $pos+= $i, $pos%= $blocksize
+                    $plaintext = substr($iv, $orig_pos) ^ $ciphertext;
+                    $iv = substr_replace($iv, substr($ciphertext, 0, $i), $orig_pos, $i);
+                }
+                while ($len >= $block_size) {
+                    $iv = $this->_encryptBlock($iv);
+                    $cb = substr($ciphertext, $i, $block_size);
+                    $plaintext.= $iv ^ $cb;
+                    $iv = $cb;
+                    $len-= $block_size;
+                    $i+= $block_size;
+                }
+                if ($len) {
+                    $iv = $this->_encryptBlock($iv);
+                    $plaintext.= $iv ^ substr($ciphertext, $i);
+                    $iv = substr_replace($iv, substr($ciphertext, $i), 0, $len);
+                    $pos = $len;
+                }
+                break;
+            case CRYPT_MODE_OFB:
+                $xor = $this->decryptIV;
+                if (strlen($buffer['xor'])) {
+                    for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                        $block = substr($ciphertext, $i, $block_size);
+                        if (strlen($block) > strlen($buffer['xor'])) {
+                            $xor = $this->_encryptBlock($xor);
+                            $buffer['xor'].= $xor;
+                        }
+                        $key = $this->_stringShift($buffer['xor'], $block_size);
+                        $plaintext.= $block ^ $key;
+                    }
+                } else {
+                    for ($i = 0; $i < strlen($ciphertext); $i+=$block_size) {
+                        $xor = $this->_encryptBlock($xor);
+                        $plaintext.= substr($ciphertext, $i, $block_size) ^ $xor;
+                    }
+                    $key = $xor;
+                }
+                if ($this->continuousBuffer) {
+                    $this->decryptIV = $xor;
+                    if ($start = strlen($ciphertext) % $block_size) {
+                         $buffer['xor'] = substr($key, $start) . $buffer['xor'];
+                    }
+                }
+                break;
+            case CRYPT_MODE_STREAM:
+                $plaintext = $this->_decryptBlock($ciphertext);
+                break;
+        }
+        return $this->paddable ? $this->_unpad($plaintext) : $plaintext;
+    }
+
+    /**
+     * Pad "packets".
+     *
+     * Block ciphers working by encrypting between their specified [$this->]block_size at a time
+     * If you ever need to encrypt or decrypt something that isn't of the proper length, it becomes necessary to
+     * pad the input so that it is of the proper length.
+     *
+     * Padding is enabled by default.  Sometimes, however, it is undesirable to pad strings.  Such is the case in SSH,
+     * where "packets" are padded with random bytes before being encrypted.  Unpad these packets and you risk stripping
+     * away characters that shouldn't be stripped away. (SSH knows how many bytes are added because the length is
+     * transmitted separately)
+     *
+     * @see Crypt_Base::disablePadding()
+     * @access public
+     */
+    function enablePadding()
+    {
+        $this->padding = true;
+    }
+
+    /**
+     * Do not pad packets.
+     *
+     * @see Crypt_Base::enablePadding()
+     * @access public
+     */
+    function disablePadding()
+    {
+        $this->padding = false;
+    }
+
+    /**
+     * Treat consecutive "packets" as if they are a continuous buffer.
+     *
+     * Say you have a 32-byte plaintext $plaintext.  Using the default behavior, the two following code snippets
+     * will yield different outputs:
+     *
+     * <code>
+     *    echo $rijndael->encrypt(substr($plaintext,  0, 16));
+     *    echo $rijndael->encrypt(substr($plaintext, 16, 16));
+     * </code>
+     * <code>
+     *    echo $rijndael->encrypt($plaintext);
+     * </code>
+     *
+     * The solution is to enable the continuous buffer.  Although this will resolve the above discrepancy, it creates
+     * another, as demonstrated with the following:
+     *
+     * <code>
+     *    $rijndael->encrypt(substr($plaintext, 0, 16));
+     *    echo $rijndael->decrypt($rijndael->encrypt(substr($plaintext, 16, 16)));
+     * </code>
+     * <code>
+     *    echo $rijndael->decrypt($rijndael->encrypt(substr($plaintext, 16, 16)));
+     * </code>
+     *
+     * With the continuous buffer disabled, these would yield the same output.  With it enabled, they yield different
+     * outputs.  The reason is due to the fact that the initialization vector's change after every encryption /
+     * decryption round when the continuous buffer is enabled.  When it's disabled, they remain constant.
+     *
+     * Put another way, when the continuous buffer is enabled, the state of the Crypt_*() object changes after each
+     * encryption / decryption round, whereas otherwise, it'd remain constant.  For this reason, it's recommended that
+     * continuous buffers not be used.  They do offer better security and are, in fact, sometimes required (SSH uses them),
+     * however, they are also less intuitive and more likely to cause you problems.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see Crypt_Base::disableContinuousBuffer()
+     * @access public
+     */
+    function enableContinuousBuffer()
+    {
+        if ($this->mode == CRYPT_MODE_ECB) {
+            return;
+        }
+
+        $this->continuousBuffer = true;
+    }
+
+    /**
+     * Treat consecutive packets as if they are a discontinuous buffer.
+     *
+     * The default behavior.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see Crypt_Base::enableContinuousBuffer()
+     * @access public
+     */
+    function disableContinuousBuffer()
+    {
+        if ($this->mode == CRYPT_MODE_ECB) {
+            return;
+        }
+        if (!$this->continuousBuffer) {
+            return;
+        }
+
+        $this->continuousBuffer = false;
+        $this->changed = true;
+    }
+
+    /**
+     * Encrypts a block
+     *
+     * Note: Must extend by the child Crypt_* class
+     *
+     * @access private
+     * @param String $in
+     * @return String
+     */
+    function _encryptBlock($in)
+    {
+        user_error((version_compare(PHP_VERSION, '5.0.0', '>=')  ? __METHOD__ : __FUNCTION__)  . '() must extend by class ' . get_class($this), E_USER_ERROR);
+    }
+
+    /**
+     * Decrypts a block
+     *
+     * Note: Must extend by the child Crypt_* class
+     *
+     * @access private
+     * @param String $in
+     * @return String
+     */
+    function _decryptBlock($in)
+    {
+        user_error((version_compare(PHP_VERSION, '5.0.0', '>=')  ? __METHOD__ : __FUNCTION__)  . '() must extend by class ' . get_class($this), E_USER_ERROR);
+    }
+
+    /**
+     * Setup the key (expansion)
+     *
+     * Only used if $engine == CRYPT_MODE_INTERNAL
+     *
+     * Note: Must extend by the child Crypt_* class
+     *
+     * @see Crypt_Base::_setup()
+     * @access private
+     */
+    function _setupKey()
+    {
+        user_error((version_compare(PHP_VERSION, '5.0.0', '>=')  ? __METHOD__ : __FUNCTION__)  . '() must extend by class ' . get_class($this), E_USER_ERROR);
+    }
+
+    /**
+     * Setup the CRYPT_MODE_INTERNAL $engine
+     *
+     * (re)init, if necessary, the internal cipher $engine and flush all $buffers
+     * Used (only) if $engine == CRYPT_MODE_INTERNAL
+     *
+     * _setup() will be called each time if $changed === true
+     * typically this happens when using one or more of following public methods:
+     *
+     * - setKey()
+     *
+     * - setIV()
+     *
+     * - disableContinuousBuffer()
+     *
+     * - First run of encrypt() / decrypt() with no init-settings
+     *
+     * Internally: _setup() is called always before(!) en/decryption.
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see setKey()
+     * @see setIV()
+     * @see disableContinuousBuffer()
+     * @access private
+     */
+    function _setup()
+    {
+        $this->_clearBuffers();
+        $this->_setupKey();
+
+        if ($this->use_inline_crypt) {
+            $this->_setupInlineCrypt();
+        }
+    }
+
+    /**
+     * Setup the CRYPT_MODE_MCRYPT $engine
+     *
+     * (re)init, if necessary, the (ext)mcrypt resources and flush all $buffers
+     * Used (only) if $engine = CRYPT_MODE_MCRYPT
+     *
+     * _setupMcrypt() will be called each time if $changed === true
+     * typically this happens when using one or more of following public methods:
+     *
+     * - setKey()
+     *
+     * - setIV()
+     *
+     * - disableContinuousBuffer()
+     *
+     * - First run of encrypt() / decrypt()
+     *
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @see setKey()
+     * @see setIV()
+     * @see disableContinuousBuffer()
+     * @access private
+     */
+    function _setupMcrypt()
+    {
+        $this->_clearBuffers();
+        $this->enchanged = $this->dechanged = true;
+
+        if (!isset($this->enmcrypt)) {
+            static $mcrypt_modes = array(
+                CRYPT_MODE_CTR    => 'ctr',
+                CRYPT_MODE_ECB    => MCRYPT_MODE_ECB,
+                CRYPT_MODE_CBC    => MCRYPT_MODE_CBC,
+                CRYPT_MODE_CFB    => 'ncfb',
+                CRYPT_MODE_OFB    => MCRYPT_MODE_NOFB,
+                CRYPT_MODE_STREAM => MCRYPT_MODE_STREAM,
+            );
+
+            $this->demcrypt = mcrypt_module_open($this->cipher_name_mcrypt, '', $mcrypt_modes[$this->mode], '');
+            $this->enmcrypt = mcrypt_module_open($this->cipher_name_mcrypt, '', $mcrypt_modes[$this->mode], '');
+
+            // we need the $ecb mcrypt resource (only) in MODE_CFB with enableContinuousBuffer()
+            // to workaround mcrypt's broken ncfb implementation in buffered mode
+            // see: {@link http://phpseclib.sourceforge.net/cfb-demo.phps}
+            if ($this->mode == CRYPT_MODE_CFB) {
+                $this->ecb = mcrypt_module_open($this->cipher_name_mcrypt, '', MCRYPT_MODE_ECB, '');
+            }
+
+        } // else should mcrypt_generic_deinit be called?
+
+        if ($this->mode == CRYPT_MODE_CFB) {
+            mcrypt_generic_init($this->ecb, $this->key, str_repeat("\0", $this->block_size));
+        }
+    }
+
+    /**
+     * Pads a string
+     *
+     * Pads a string using the RSA PKCS padding standards so that its length is a multiple of the blocksize.
+     * $this->block_size - (strlen($text) % $this->block_size) bytes are added, each of which is equal to
+     * chr($this->block_size - (strlen($text) % $this->block_size)
+     *
+     * If padding is disabled and $text is not a multiple of the blocksize, the string will be padded regardless
+     * and padding will, hence forth, be enabled.
+     *
+     * @see Crypt_Base::_unpad()
+     * @param String $text
+     * @access private
+     * @return String
+     */
+    function _pad($text)
+    {
+        $length = strlen($text);
+
+        if (!$this->padding) {
+            if ($length % $this->block_size == 0) {
+                return $text;
+            } else {
+                user_error("The plaintext's length ($length) is not a multiple of the block size ({$this->block_size})");
+                $this->padding = true;
+            }
+        }
+
+        $pad = $this->block_size - ($length % $this->block_size);
+
+        return str_pad($text, $length + $pad, chr($pad));
+    }
+
+    /**
+     * Unpads a string.
+     *
+     * If padding is enabled and the reported padding length is invalid the encryption key will be assumed to be wrong
+     * and false will be returned.
+     *
+     * @see Crypt_Base::_pad()
+     * @param String $text
+     * @access private
+     * @return String
+     */
+    function _unpad($text)
+    {
+        if (!$this->padding) {
+            return $text;
+        }
+
+        $length = ord($text[strlen($text) - 1]);
+
+        if (!$length || $length > $this->block_size) {
+            return false;
+        }
+
+        return substr($text, 0, -$length);
+    }
+
+    /**
+     * Clears internal buffers
+     *
+     * Clearing/resetting the internal buffers is done everytime
+     * after disableContinuousBuffer() or on cipher $engine (re)init
+     * ie after setKey() or setIV()
+     *
+     * Note: Could, but not must, extend by the child Crypt_* class
+     *
+     * @access public
+     */
+    function _clearBuffers()
+    {
+        $this->enbuffer = array('encrypted'  => '', 'xor' => '', 'pos' => 0, 'enmcrypt_init' => true);
+        $this->debuffer = array('ciphertext' => '', 'xor' => '', 'pos' => 0, 'demcrypt_init' => true);
+
+        // mcrypt's handling of invalid's $iv:
+        // $this->encryptIV = $this->decryptIV = strlen($this->iv) == $this->block_size ? $this->iv : str_repeat("\0", $this->block_size);
+        $this->encryptIV = $this->decryptIV = str_pad(substr($this->iv, 0, $this->block_size), $this->block_size, "\0");
+    }
+
+    /**
+     * String Shift
+     *
+     * Inspired by array_shift
+     *
+     * @param String $string
+     * @param optional Integer $index
+     * @access private
+     * @return String
+     */
+    function _stringShift(&$string, $index = 1)
+    {
+        $substr = substr($string, 0, $index);
+        $string = substr($string, $index);
+        return $substr;
+    }
+
+    /**
+     * Generate CTR XOR encryption key
+     *
+     * Encrypt the output of this and XOR it against the ciphertext / plaintext to get the
+     * plaintext / ciphertext in CTR mode.
+     *
+     * @see Crypt_Base::decrypt()
+     * @see Crypt_Base::encrypt()
+     * @param String $iv
+     * @param Integer $length
+     * @access private
+     * @return String $xor
+     */
+    function _generateXor(&$iv, $length)
+    {
+        $xor = '';
+        $block_size = $this->block_size;
+        $num_blocks = floor(($length + ($block_size - 1)) / $block_size);
+        for ($i = 0; $i < $num_blocks; $i++) {
+            $xor.= $iv;
+            for ($j = 4; $j <= $block_size; $j+= 4) {
+                $temp = substr($iv, -$j, 4);
+                switch ($temp) {
+                    case "\xFF\xFF\xFF\xFF":
+                        $iv = substr_replace($iv, "\x00\x00\x00\x00", -$j, 4);
+                        break;
+                    case "\x7F\xFF\xFF\xFF":
+                        $iv = substr_replace($iv, "\x80\x00\x00\x00", -$j, 4);
+                        break 2;
+                    default:
+                        extract(unpack('Ncount', $temp));
+                        $iv = substr_replace($iv, pack('N', $count + 1), -$j, 4);
+                        break 2;
+                }
+            }
+        }
+
+        return $xor;
+    }
+
+    /**
+     * Setup the performance-optimized function for de/encrypt()
+     *
+     * Stores the created (or existing) callback function-name
+     * in $this->inline_crypt
+     *
+     * Internally for phpseclib developers:
+     *
+     *     _setupInlineCrypt() would be called only if:
+     *
+     *     - $engine == CRYPT_MODE_INTERNAL and
+     *
+     *     - $use_inline_crypt === true
+     *
+     *     - each time on _setup(), after(!) _setupKey()
+     *
+     *
+     *     This ensures that _setupInlineCrypt() has allways a
+     *     full ready2go initializated internal cipher $engine state
+     *     where, for example, the keys allready expanded,
+     *     keys/block_size calculated and such.
+     *
+     *     It is, each time if called, the responsibility of _setupInlineCrypt():
+     *
+     *     - to set $this->inline_crypt to a valid and fully working callback function
+     *       as a (faster) replacement for encrypt() / decrypt()
+     *
+     *     - NOT to create unlimited callback functions (for memory reasons!)
+     *       no matter how often _setupInlineCrypt() would be called. At some
+     *       point of amount they must be generic re-useable.
+     *
+     *     - the code of _setupInlineCrypt() it self,
+     *       and the generated callback code,
+     *       must be, in following order:
+     *       - 100% safe
+     *       - 100% compatible to encrypt()/decrypt()
+     *       - using only php5+ features/lang-constructs/php-extensions if
+     *         compatibility (down to php4) or fallback is provided
+     *       - readable/maintainable/understandable/commented and... not-cryptic-styled-code :-)
+     *       - >= 10% faster than encrypt()/decrypt() [which is, by the way,
+     *         the reason for the existence of _setupInlineCrypt() :-)]
+     *       - memory-nice
+     *       - short (as good as possible)
+     *
+     * Note: - _setupInlineCrypt() is using _createInlineCryptFunction() to create the full callback function code.
+     *       - In case of using inline crypting, _setupInlineCrypt() must extend by the child Crypt_* class.
+     *       - The following variable names are reserved:
+     *         - $_*  (all variable names prefixed with an underscore)
+     *         - $self (object reference to it self. Do not use $this, but $self instead)
+     *         - $in (the content of $in has to en/decrypt by the generated code)
+     *       - The callback function should not use the 'return' statement, but en/decrypt'ing the content of $in only
+     *
+     *
+     * @see Crypt_Base::_setup()
+     * @see Crypt_Base::_createInlineCryptFunction()
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @access private
+     */
+    function _setupInlineCrypt()
+    {
+        // If a Crypt_* class providing inline crypting it must extend _setupInlineCrypt()
+
+        // If, for any reason, an extending Crypt_Base() Crypt_* class
+        // not using inline crypting then it must be ensured that: $this->use_inline_crypt = false
+        // ie in the class var declaration of $use_inline_crypt in general for the Crypt_* class,
+        // in the constructor at object instance-time
+        // or, if it's runtime-specific, at runtime
+
+        $this->use_inline_crypt = false;
+    }
+
+    /**
+     * Creates the performance-optimized function for en/decrypt()
+     *
+     * Internally for phpseclib developers:
+     *
+     *    _createInlineCryptFunction():
+     *
+     *    - merge the $cipher_code [setup'ed by _setupInlineCrypt()]
+     *      with the current [$this->]mode of operation code
+     *
+     *    - create the $inline function, which called by encrypt() / decrypt()
+     *      as its replacement to speed up the en/decryption operations.
+     *
+     *    - return the name of the created $inline callback function
+     *
+     *    - used to speed up en/decryption
+     *
+     *
+     *
+     *    The main reason why can speed up things [up to 50%] this way are:
+     *
+     *    - using variables more effective then regular.
+     *      (ie no use of expensive arrays but integers $k_0, $k_1 ...
+     *      or even, for example, the pure $key[] values hardcoded)
+     *
+     *    - avoiding 1000's of function calls of ie _encryptBlock()
+     *      but inlining the crypt operations.
+     *      in the mode of operation for() loop.
+     *
+     *    - full loop unroll the (sometimes key-dependent) rounds
+     *      avoiding this way ++$i counters and runtime-if's etc...
+     *
+     *    The basic code architectur of the generated $inline en/decrypt()
+     *    lambda function, in pseudo php, is:
+     *
+     *    <code>
+     *    +----------------------------------------------------------------------------------------------+
+     *    | callback $inline = create_function:                                                          |
+     *    | lambda_function_0001_crypt_ECB($action, $text)                                               |
+     *    | {                                                                                            |
+     *    |     INSERT PHP CODE OF:                                                                      |
+     *    |     $cipher_code['init_crypt'];                  // general init code.                       |
+     *    |                                                  // ie: $sbox'es declarations used for       |
+     *    |                                                  //     encrypt and decrypt'ing.             |
+     *    |                                                                                              |
+     *    |     switch ($action) {                                                                       |
+     *    |         case 'encrypt':                                                                      |
+     *    |             INSERT PHP CODE OF:                                                              |
+     *    |             $cipher_code['init_encrypt'];       // encrypt sepcific init code.               |
+     *    |                                                    ie: specified $key or $box                |
+     *    |                                                        declarations for encrypt'ing.         |
+     *    |                                                                                              |
+     *    |             foreach ($ciphertext) {                                                          |
+     *    |                 $in = $block_size of $ciphertext;                                            |
+     *    |                                                                                              |
+     *    |                 INSERT PHP CODE OF:                                                          |
+     *    |                 $cipher_code['encrypt_block'];  // encrypt's (string) $in, which is always:  |
+     *    |                                                 // strlen($in) == $this->block_size          |
+     *    |                                                 // here comes the cipher algorithm in action |
+     *    |                                                 // for encryption.                           |
+     *    |                                                 // $cipher_code['encrypt_block'] has to      |
+     *    |                                                 // encrypt the content of the $in variable   |
+     *    |                                                                                              |
+     *    |                 $plaintext .= $in;                                                           |
+     *    |             }                                                                                |
+     *    |             return $plaintext;                                                               |
+     *    |                                                                                              |
+     *    |         case 'decrypt':                                                                      |
+     *    |             INSERT PHP CODE OF:                                                              |
+     *    |             $cipher_code['init_decrypt'];       // decrypt sepcific init code                |
+     *    |                                                    ie: specified $key or $box                |
+     *    |                                                        declarations for decrypt'ing.         |
+     *    |             foreach ($plaintext) {                                                           |
+     *    |                 $in = $block_size of $plaintext;                                             |
+     *    |                                                                                              |
+     *    |                 INSERT PHP CODE OF:                                                          |
+     *    |                 $cipher_code['decrypt_block'];  // decrypt's (string) $in, which is always   |
+     *    |                                                 // strlen($in) == $this->block_size          |
+     *    |                                                 // here comes the cipher algorithm in action |
+     *    |                                                 // for decryption.                           |
+     *    |                                                 // $cipher_code['decrypt_block'] has to      |
+     *    |                                                 // decrypt the content of the $in variable   |
+     *    |                 $ciphertext .= $in;                                                          |
+     *    |             }                                                                                |
+     *    |             return $ciphertext;                                                              |
+     *    |     }                                                                                        |
+     *    | }                                                                                            |
+     *    +----------------------------------------------------------------------------------------------+
+     *    </code>
+     *
+     *    See also the Crypt_*::_setupInlineCrypt()'s for
+     *    productive inline $cipher_code's how they works.
+     *
+     *    Structure of:
+     *    <code>
+     *    $cipher_code = array(
+     *        'init_crypt'    => (string) '', // optional
+     *        'init_encrypt'  => (string) '', // optional
+     *        'init_decrypt'  => (string) '', // optional
+     *        'encrypt_block' => (string) '', // required
+     *        'decrypt_block' => (string) ''  // required
+     *    );
+     *    </code>
+     *
+     * @see Crypt_Base::_setupInlineCrypt()
+     * @see Crypt_Base::encrypt()
+     * @see Crypt_Base::decrypt()
+     * @param Array $cipher_code
+     * @access private
+     * @return String (the name of the created callback function)
+     */
+    function _createInlineCryptFunction($cipher_code)
+    {
+        $block_size = $this->block_size;
+
+        // optional
+        $init_crypt    = isset($cipher_code['init_crypt'])    ? $cipher_code['init_crypt']    : '';
+        $init_encrypt  = isset($cipher_code['init_encrypt'])  ? $cipher_code['init_encrypt']  : '';
+        $init_decrypt  = isset($cipher_code['init_decrypt'])  ? $cipher_code['init_decrypt']  : '';
+        // required
+        $encrypt_block = $cipher_code['encrypt_block'];
+        $decrypt_block = $cipher_code['decrypt_block'];
+
+        // Generating mode of operation inline code,
+        // merged with the $cipher_code algorithm
+        // for encrypt- and decryption.
+        switch ($this->mode) {
+            case CRYPT_MODE_ECB:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    $_text = $self->_pad($_text);
+                    $_plaintext_len = strlen($_text);
+
+                    for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                        $in = substr($_text, $_i, '.$block_size.');
+                        '.$encrypt_block.'
+                        $_ciphertext.= $in;
+                    }
+
+                    return $_ciphertext;
+                    ';
+
+                $decrypt = $init_decrypt . '
+                    $_plaintext = "";
+                    $_text = str_pad($_text, strlen($_text) + ('.$block_size.' - strlen($_text) % '.$block_size.') % '.$block_size.', chr(0));
+                    $_ciphertext_len = strlen($_text);
+
+                    for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                        $in = substr($_text, $_i, '.$block_size.');
+                        '.$decrypt_block.'
+                        $_plaintext.= $in;
+                    }
+
+                    return $self->_unpad($_plaintext);
+                    ';
+                break;
+            case CRYPT_MODE_CTR:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    $_plaintext_len = strlen($_text);
+                    $_xor = $self->encryptIV;
+                    $_buffer = &$self->enbuffer;
+
+                    if (strlen($_buffer["encrypted"])) {
+                        for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            if (strlen($_block) > strlen($_buffer["encrypted"])) {
+                                $in = $self->_generateXor($_xor, '.$block_size.');
+                                '.$encrypt_block.'
+                                $_buffer["encrypted"].= $in;
+                            }
+                            $_key = $self->_stringShift($_buffer["encrypted"], '.$block_size.');
+                            $_ciphertext.= $_block ^ $_key;
+                        }
+                    } else {
+                        for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            $in = $self->_generateXor($_xor, '.$block_size.');
+                            '.$encrypt_block.'
+                            $_key = $in;
+                            $_ciphertext.= $_block ^ $_key;
+                        }
+                    }
+                    if ($self->continuousBuffer) {
+                        $self->encryptIV = $_xor;
+                        if ($_start = $_plaintext_len % '.$block_size.') {
+                            $_buffer["encrypted"] = substr($_key, $_start) . $_buffer["encrypted"];
+                        }
+                    }
+
+                    return $_ciphertext;
+                ';
+
+                $decrypt = $init_encrypt . '
+                    $_plaintext = "";
+                    $_ciphertext_len = strlen($_text);
+                    $_xor = $self->decryptIV;
+                    $_buffer = &$self->debuffer;
+
+                    if (strlen($_buffer["ciphertext"])) {
+                        for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            if (strlen($_block) > strlen($_buffer["ciphertext"])) {
+                                $in = $self->_generateXor($_xor, '.$block_size.');
+                                '.$encrypt_block.'
+                                $_buffer["ciphertext"].= $in;
+                            }
+                            $_key = $self->_stringShift($_buffer["ciphertext"], '.$block_size.');
+                            $_plaintext.= $_block ^ $_key;
+                        }
+                    } else {
+                        for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            $in = $self->_generateXor($_xor, '.$block_size.');
+                            '.$encrypt_block.'
+                            $_key = $in;
+                            $_plaintext.= $_block ^ $_key;
+                        }
+                    }
+                    if ($self->continuousBuffer) {
+                        $self->decryptIV = $_xor;
+                        if ($_start = $_ciphertext_len % '.$block_size.') {
+                            $_buffer["ciphertext"] = substr($_key, $_start) . $_buffer["ciphertext"];
+                        }
+                    }
+
+                    return $_plaintext;
+                    ';
+                break;
+            case CRYPT_MODE_CFB:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    $_buffer = &$self->enbuffer;
+
+                    if ($self->continuousBuffer) {
+                        $_iv = &$self->encryptIV;
+                        $_pos = &$_buffer["pos"];
+                    } else {
+                        $_iv = $self->encryptIV;
+                        $_pos = 0;
+                    }
+                    $_len = strlen($_text);
+                    $_i = 0;
+                    if ($_pos) {
+                        $_orig_pos = $_pos;
+                        $_max = '.$block_size.' - $_pos;
+                        if ($_len >= $_max) {
+                            $_i = $_max;
+                            $_len-= $_max;
+                            $_pos = 0;
+                        } else {
+                            $_i = $_len;
+                            $_pos+= $_len;
+                            $_len = 0;
+                        }
+                        $_ciphertext = substr($_iv, $_orig_pos) ^ $_text;
+                        $_iv = substr_replace($_iv, $_ciphertext, $_orig_pos, $_i);
+                    }
+                    while ($_len >= '.$block_size.') {
+                        $in = $_iv;
+                        '.$encrypt_block.';
+                        $_iv = $in ^ substr($_text, $_i, '.$block_size.');
+                        $_ciphertext.= $_iv;
+                        $_len-= '.$block_size.';
+                        $_i+= '.$block_size.';
+                    }
+                    if ($_len) {
+                        $in = $_iv;
+                        '.$encrypt_block.'
+                        $_iv = $in;
+                        $_block = $_iv ^ substr($_text, $_i);
+                        $_iv = substr_replace($_iv, $_block, 0, $_len);
+                        $_ciphertext.= $_block;
+                        $_pos = $_len;
+                    }
+                    return $_ciphertext;
+                ';
+
+                $decrypt = $init_encrypt . '
+                    $_plaintext = "";
+                    $_buffer = &$self->debuffer;
+
+                    if ($self->continuousBuffer) {
+                        $_iv = &$self->decryptIV;
+                        $_pos = &$_buffer["pos"];
+                    } else {
+                        $_iv = $self->decryptIV;
+                        $_pos = 0;
+                    }
+                    $_len = strlen($_text);
+                    $_i = 0;
+                    if ($_pos) {
+                        $_orig_pos = $_pos;
+                        $_max = '.$block_size.' - $_pos;
+                        if ($_len >= $_max) {
+                            $_i = $_max;
+                            $_len-= $_max;
+                            $_pos = 0;
+                        } else {
+                            $_i = $_len;
+                            $_pos+= $_len;
+                            $_len = 0;
+                        }
+                        $_plaintext = substr($_iv, $_orig_pos) ^ $_text;
+                        $_iv = substr_replace($_iv, substr($_text, 0, $_i), $_orig_pos, $_i);
+                    }
+                    while ($_len >= '.$block_size.') {
+                        $in = $_iv;
+                        '.$encrypt_block.'
+                        $_iv = $in;
+                        $cb = substr($_text, $_i, '.$block_size.');
+                        $_plaintext.= $_iv ^ $cb;
+                        $_iv = $cb;
+                        $_len-= '.$block_size.';
+                        $_i+= '.$block_size.';
+                    }
+                    if ($_len) {
+                        $in = $_iv;
+                        '.$encrypt_block.'
+                        $_iv = $in;
+                        $_plaintext.= $_iv ^ substr($_text, $_i);
+                        $_iv = substr_replace($_iv, substr($_text, $_i), 0, $_len);
+                        $_pos = $_len;
+                    }
+
+                    return $_plaintext;
+                    ';
+                break;
+            case CRYPT_MODE_OFB:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    $_plaintext_len = strlen($_text);
+                    $_xor = $self->encryptIV;
+                    $_buffer = &$self->enbuffer;
+
+                    if (strlen($_buffer["xor"])) {
+                        for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            if (strlen($_block) > strlen($_buffer["xor"])) {
+                                $in = $_xor;
+                                '.$encrypt_block.'
+                                $_xor = $in;
+                                $_buffer["xor"].= $_xor;
+                            }
+                            $_key = $self->_stringShift($_buffer["xor"], '.$block_size.');
+                            $_ciphertext.= $_block ^ $_key;
+                        }
+                    } else {
+                        for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                            $in = $_xor;
+                            '.$encrypt_block.'
+                            $_xor = $in;
+                            $_ciphertext.= substr($_text, $_i, '.$block_size.') ^ $_xor;
+                        }
+                        $_key = $_xor;
+                    }
+                    if ($self->continuousBuffer) {
+                        $self->encryptIV = $_xor;
+                        if ($_start = $_plaintext_len % '.$block_size.') {
+                             $_buffer["xor"] = substr($_key, $_start) . $_buffer["xor"];
+                        }
+                    }
+                    return $_ciphertext;
+                    ';
+
+                $decrypt = $init_encrypt . '
+                    $_plaintext = "";
+                    $_ciphertext_len = strlen($_text);
+                    $_xor = $self->decryptIV;
+                    $_buffer = &$self->debuffer;
+
+                    if (strlen($_buffer["xor"])) {
+                        for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                            $_block = substr($_text, $_i, '.$block_size.');
+                            if (strlen($_block) > strlen($_buffer["xor"])) {
+                                $in = $_xor;
+                                '.$encrypt_block.'
+                                $_xor = $in;
+                                $_buffer["xor"].= $_xor;
+                            }
+                            $_key = $self->_stringShift($_buffer["xor"], '.$block_size.');
+                            $_plaintext.= $_block ^ $_key;
+                        }
+                    } else {
+                        for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                            $in = $_xor;
+                            '.$encrypt_block.'
+                            $_xor = $in;
+                            $_plaintext.= substr($_text, $_i, '.$block_size.') ^ $_xor;
+                        }
+                        $_key = $_xor;
+                    }
+                    if ($self->continuousBuffer) {
+                        $self->decryptIV = $_xor;
+                        if ($_start = $_ciphertext_len % '.$block_size.') {
+                             $_buffer["xor"] = substr($_key, $_start) . $_buffer["xor"];
+                        }
+                    }
+                    return $_plaintext;
+                    ';
+                break;
+            case CRYPT_MODE_STREAM:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    '.$encrypt_block.'
+                    return $_ciphertext;
+                    ';
+                $decrypt = $init_decrypt . '
+                    $_plaintext = "";
+                    '.$decrypt_block.'
+                    return $_plaintext;
+                    ';
+                break;
+            // case CRYPT_MODE_CBC:
+            default:
+                $encrypt = $init_encrypt . '
+                    $_ciphertext = "";
+                    $_text = $self->_pad($_text);
+                    $_plaintext_len = strlen($_text);
+
+                    $in = $self->encryptIV;
+
+                    for ($_i = 0; $_i < $_plaintext_len; $_i+= '.$block_size.') {
+                        $in = substr($_text, $_i, '.$block_size.') ^ $in;
+                        '.$encrypt_block.'
+                        $_ciphertext.= $in;
+                    }
+
+                    if ($self->continuousBuffer) {
+                        $self->encryptIV = $in;
+                    }
+
+                    return $_ciphertext;
+                    ';
+
+                $decrypt = $init_decrypt . '
+                    $_plaintext = "";
+                    $_text = str_pad($_text, strlen($_text) + ('.$block_size.' - strlen($_text) % '.$block_size.') % '.$block_size.', chr(0));
+                    $_ciphertext_len = strlen($_text);
+
+                    $_iv = $self->decryptIV;
+
+                    for ($_i = 0; $_i < $_ciphertext_len; $_i+= '.$block_size.') {
+                        $in = $_block = substr($_text, $_i, '.$block_size.');
+                        '.$decrypt_block.'
+                        $_plaintext.= $in ^ $_iv;
+                        $_iv = $_block;
+                    }
+
+                    if ($self->continuousBuffer) {
+                        $self->decryptIV = $_iv;
+                    }
+
+                    return $self->_unpad($_plaintext);
+                    ';
+                break;
+        }
+
+        // Create the $inline function and return its name as string. Ready to run!
+        return create_function('$_action, &$self, $_text', $init_crypt . 'if ($_action == "encrypt") { ' . $encrypt . ' } else { ' . $decrypt . ' }');
+    }
+
+    /**
+     * Holds the lambda_functions table (classwide)
+     *
+     * Each name of the lambda function, created from
+     * _setupInlineCrypt() && _createInlineCryptFunction()
+     * is stored, classwide (!), here for reusing.
+     *
+     * The string-based index of $function is a classwide
+     * uniqe value representing, at least, the $mode of
+     * operation (or more... depends of the optimizing level)
+     * for which $mode the lambda function was created.
+     *
+     * @access private
+     * @return &Array
+     */
+    function &_getLambdaFunctions()
+    {
+        static $functions = array();
+        return $functions;
+    }
+}
+
+// vim: ts=4:sw=4:et:
+// vim6: fdl=1:
diff --git a/inc/phpseclib/Crypt_Hash.php b/inc/phpseclib/Crypt_Hash.php
new file mode 100644
index 000000000..840fcd508
--- /dev/null
+++ b/inc/phpseclib/Crypt_Hash.php
@@ -0,0 +1,823 @@
+<?php
+/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
+
+/**
+ * Pure-PHP implementations of keyed-hash message authentication codes (HMACs) and various cryptographic hashing functions.
+ *
+ * Uses hash() or mhash() if available and an internal implementation, otherwise.  Currently supports the following:
+ *
+ * md2, md5, md5-96, sha1, sha1-96, sha256, sha384, and sha512
+ *
+ * If {@link Crypt_Hash::setKey() setKey()} is called, {@link Crypt_Hash::hash() hash()} will return the HMAC as opposed to
+ * the hash.  If no valid algorithm is provided, sha1 will be used.
+ *
+ * PHP versions 4 and 5
+ *
+ * {@internal The variable names are the same as those in 
+ * {@link http://tools.ietf.org/html/rfc2104#section-2 RFC2104}.}}
+ *
+ * Here's a short example of how to use this library:
+ * <code>
+ * <?php
+ *    include('Crypt/Hash.php');
+ *
+ *    $hash = new Crypt_Hash('sha1');
+ *
+ *    $hash->setKey('abcdefg');
+ *
+ *    echo base64_encode($hash->hash('abcdefg'));
+ * ?>
+ * </code>
+ *
+ * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ * 
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *
+ * @category   Crypt
+ * @package    Crypt_Hash
+ * @author     Jim Wigginton <terrafrost@php.net>
+ * @copyright  MMVII Jim Wigginton
+ * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link       http://phpseclib.sourceforge.net
+ */
+
+/**#@+
+ * @access private
+ * @see Crypt_Hash::Crypt_Hash()
+ */
+/**
+ * Toggles the internal implementation
+ */
+define('CRYPT_HASH_MODE_INTERNAL', 1);
+/**
+ * Toggles the mhash() implementation, which has been deprecated on PHP 5.3.0+.
+ */
+define('CRYPT_HASH_MODE_MHASH',    2);
+/**
+ * Toggles the hash() implementation, which works on PHP 5.1.2+.
+ */
+define('CRYPT_HASH_MODE_HASH',     3);
+/**#@-*/
+
+/**
+ * Pure-PHP implementations of keyed-hash message authentication codes (HMACs) and various cryptographic hashing functions.
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @version 0.1.0
+ * @access  public
+ * @package Crypt_Hash
+ */
+class Crypt_Hash {
+    /**
+     * Byte-length of compression blocks / key (Internal HMAC)
+     *
+     * @see Crypt_Hash::setAlgorithm()
+     * @var Integer
+     * @access private
+     */
+    var $b;
+
+    /**
+     * Byte-length of hash output (Internal HMAC)
+     *
+     * @see Crypt_Hash::setHash()
+     * @var Integer
+     * @access private
+     */
+    var $l = false;
+
+    /**
+     * Hash Algorithm
+     *
+     * @see Crypt_Hash::setHash()
+     * @var String
+     * @access private
+     */
+    var $hash;
+
+    /**
+     * Key
+     *
+     * @see Crypt_Hash::setKey()
+     * @var String
+     * @access private
+     */
+    var $key = false;
+
+    /**
+     * Outer XOR (Internal HMAC)
+     *
+     * @see Crypt_Hash::setKey()
+     * @var String
+     * @access private
+     */
+    var $opad;
+
+    /**
+     * Inner XOR (Internal HMAC)
+     *
+     * @see Crypt_Hash::setKey()
+     * @var String
+     * @access private
+     */
+    var $ipad;
+
+    /**
+     * Default Constructor.
+     *
+     * @param optional String $hash
+     * @return Crypt_Hash
+     * @access public
+     */
+    function Crypt_Hash($hash = 'sha1')
+    {
+        if ( !defined('CRYPT_HASH_MODE') ) {
+            switch (true) {
+                case extension_loaded('hash'):
+                    define('CRYPT_HASH_MODE', CRYPT_HASH_MODE_HASH);
+                    break;
+                case extension_loaded('mhash'):
+                    define('CRYPT_HASH_MODE', CRYPT_HASH_MODE_MHASH);
+                    break;
+                default:
+                    define('CRYPT_HASH_MODE', CRYPT_HASH_MODE_INTERNAL);
+            }
+        }
+
+        $this->setHash($hash);
+    }
+
+    /**
+     * Sets the key for HMACs
+     *
+     * Keys can be of any length.
+     *
+     * @access public
+     * @param optional String $key
+     */
+    function setKey($key = false)
+    {
+        $this->key = $key;
+    }
+
+    /**
+     * Sets the hash function.
+     *
+     * @access public
+     * @param String $hash
+     */
+    function setHash($hash)
+    {
+        $hash = strtolower($hash);
+        switch ($hash) {
+            case 'md5-96':
+            case 'sha1-96':
+                $this->l = 12; // 96 / 8 = 12
+                break;
+            case 'md2':
+            case 'md5':
+                $this->l = 16;
+                break;
+            case 'sha1':
+                $this->l = 20;
+                break;
+            case 'sha256':
+                $this->l = 32;
+                break;
+            case 'sha384':
+                $this->l = 48;
+                break;
+            case 'sha512':
+                $this->l = 64;
+        }
+
+        switch ($hash) {
+            case 'md2':
+                $mode = CRYPT_HASH_MODE == CRYPT_HASH_MODE_HASH && in_array('md2', hash_algos()) ?
+                    CRYPT_HASH_MODE_HASH : CRYPT_HASH_MODE_INTERNAL;
+                break;
+            case 'sha384':
+            case 'sha512':
+                $mode = CRYPT_HASH_MODE == CRYPT_HASH_MODE_MHASH ? CRYPT_HASH_MODE_INTERNAL : CRYPT_HASH_MODE;
+                break;
+            default:
+                $mode = CRYPT_HASH_MODE;
+        }
+
+        switch ( $mode ) {
+            case CRYPT_HASH_MODE_MHASH:
+                switch ($hash) {
+                    case 'md5':
+                    case 'md5-96':
+                        $this->hash = MHASH_MD5;
+                        break;
+                    case 'sha256':
+                        $this->hash = MHASH_SHA256;
+                        break;
+                    case 'sha1':
+                    case 'sha1-96':
+                    default:
+                        $this->hash = MHASH_SHA1;
+                }
+                return;
+            case CRYPT_HASH_MODE_HASH:
+                switch ($hash) {
+                    case 'md5':
+                    case 'md5-96':
+                        $this->hash = 'md5';
+                        return;
+                    case 'md2':
+                    case 'sha256':
+                    case 'sha384':
+                    case 'sha512':
+                        $this->hash = $hash;
+                        return;
+                    case 'sha1':
+                    case 'sha1-96':
+                    default:
+                        $this->hash = 'sha1';
+                }
+                return;
+        }
+
+        switch ($hash) {
+            case 'md2':
+                 $this->b = 16;
+                 $this->hash = array($this, '_md2');
+                 break;
+            case 'md5':
+            case 'md5-96':
+                 $this->b = 64;
+                 $this->hash = array($this, '_md5');
+                 break;
+            case 'sha256':
+                 $this->b = 64;
+                 $this->hash = array($this, '_sha256');
+                 break;
+            case 'sha384':
+            case 'sha512':
+                 $this->b = 128;
+                 $this->hash = array($this, '_sha512');
+                 break;
+            case 'sha1':
+            case 'sha1-96':
+            default:
+                 $this->b = 64;
+                 $this->hash = array($this, '_sha1');
+        }
+
+        $this->ipad = str_repeat(chr(0x36), $this->b);
+        $this->opad = str_repeat(chr(0x5C), $this->b);
+    }
+
+    /**
+     * Compute the HMAC.
+     *
+     * @access public
+     * @param String $text
+     * @return String
+     */
+    function hash($text)
+    {
+        $mode = is_array($this->hash) ? CRYPT_HASH_MODE_INTERNAL : CRYPT_HASH_MODE;
+
+        if (!empty($this->key) || is_string($this->key)) {
+            switch ( $mode ) {
+                case CRYPT_HASH_MODE_MHASH:
+                    $output = mhash($this->hash, $text, $this->key);
+                    break;
+                case CRYPT_HASH_MODE_HASH:
+                    $output = hash_hmac($this->hash, $text, $this->key, true);
+                    break;
+                case CRYPT_HASH_MODE_INTERNAL:
+                    /* "Applications that use keys longer than B bytes will first hash the key using H and then use the
+                        resultant L byte string as the actual key to HMAC."
+
+                        -- http://tools.ietf.org/html/rfc2104#section-2 */
+                    $key = strlen($this->key) > $this->b ? call_user_func($this->hash, $this->key) : $this->key;
+
+                    $key    = str_pad($key, $this->b, chr(0));      // step 1
+                    $temp   = $this->ipad ^ $key;                   // step 2
+                    $temp  .= $text;                                // step 3
+                    $temp   = call_user_func($this->hash, $temp);   // step 4
+                    $output = $this->opad ^ $key;                   // step 5
+                    $output.= $temp;                                // step 6
+                    $output = call_user_func($this->hash, $output); // step 7
+            }
+        } else {
+            switch ( $mode ) {
+                case CRYPT_HASH_MODE_MHASH:
+                    $output = mhash($this->hash, $text);
+                    break;
+                case CRYPT_HASH_MODE_HASH:
+                    $output = hash($this->hash, $text, true);
+                    break;
+                case CRYPT_HASH_MODE_INTERNAL:
+                    $output = call_user_func($this->hash, $text);
+            }
+        }
+
+        return substr($output, 0, $this->l);
+    }
+
+    /**
+     * Returns the hash length (in bytes)
+     *
+     * @access public
+     * @return Integer
+     */
+    function getLength()
+    {
+        return $this->l;
+    }
+
+    /**
+     * Wrapper for MD5
+     *
+     * @access private
+     * @param String $m
+     */
+    function _md5($m)
+    {
+        return pack('H*', md5($m));
+    }
+
+    /**
+     * Wrapper for SHA1
+     *
+     * @access private
+     * @param String $m
+     */
+    function _sha1($m)
+    {
+        return pack('H*', sha1($m));
+    }
+
+    /**
+     * Pure-PHP implementation of MD2
+     *
+     * See {@link http://tools.ietf.org/html/rfc1319 RFC1319}.
+     *
+     * @access private
+     * @param String $m
+     */
+    function _md2($m)
+    {
+        static $s = array(
+             41,  46,  67, 201, 162, 216, 124,   1,  61,  54,  84, 161, 236, 240, 6,
+             19,  98, 167,   5, 243, 192, 199, 115, 140, 152, 147,  43, 217, 188,
+             76, 130, 202,  30, 155,  87,  60, 253, 212, 224,  22, 103,  66, 111, 24,
+            138,  23, 229,  18, 190,  78, 196, 214, 218, 158, 222,  73, 160, 251,
+            245, 142, 187,  47, 238, 122, 169, 104, 121, 145,  21, 178,   7,  63,
+            148, 194,  16, 137,  11,  34,  95,  33, 128, 127,  93, 154,  90, 144, 50,
+             39,  53,  62, 204, 231, 191, 247, 151,   3, 255,  25,  48, 179,  72, 165,
+            181, 209, 215,  94, 146,  42, 172,  86, 170, 198,  79, 184,  56, 210,
+            150, 164, 125, 182, 118, 252, 107, 226, 156, 116,   4, 241,  69, 157,
+            112,  89, 100, 113, 135,  32, 134,  91, 207, 101, 230,  45, 168,   2, 27,
+             96,  37, 173, 174, 176, 185, 246,  28,  70,  97, 105,  52,  64, 126, 15,
+             85,  71, 163,  35, 221,  81, 175,  58, 195,  92, 249, 206, 186, 197,
+            234,  38,  44,  83,  13, 110, 133,  40, 132,   9, 211, 223, 205, 244, 65,
+            129,  77,  82, 106, 220,  55, 200, 108, 193, 171, 250,  36, 225, 123,
+              8,  12, 189, 177,  74, 120, 136, 149, 139, 227,  99, 232, 109, 233,
+            203, 213, 254,  59,   0,  29,  57, 242, 239, 183,  14, 102,  88, 208, 228,
+            166, 119, 114, 248, 235, 117,  75,  10,  49,  68,  80, 180, 143, 237,
+             31,  26, 219, 153, 141,  51, 159,  17, 131, 20
+        );
+
+        // Step 1. Append Padding Bytes
+        $pad = 16 - (strlen($m) & 0xF);
+        $m.= str_repeat(chr($pad), $pad);
+
+        $length = strlen($m);
+
+        // Step 2. Append Checksum
+        $c = str_repeat(chr(0), 16);
+        $l = chr(0);
+        for ($i = 0; $i < $length; $i+= 16) {
+            for ($j = 0; $j < 16; $j++) {
+                // RFC1319 incorrectly states that C[j] should be set to S[c xor L]
+                //$c[$j] = chr($s[ord($m[$i + $j] ^ $l)]);
+                // per <http://www.rfc-editor.org/errata_search.php?rfc=1319>, however, C[j] should be set to S[c xor L] xor C[j]
+                $c[$j] = chr($s[ord($m[$i + $j] ^ $l)] ^ ord($c[$j]));
+                $l = $c[$j];
+            }
+        }
+        $m.= $c;
+
+        $length+= 16;
+
+        // Step 3. Initialize MD Buffer
+        $x = str_repeat(chr(0), 48);
+
+        // Step 4. Process Message in 16-Byte Blocks
+        for ($i = 0; $i < $length; $i+= 16) {
+            for ($j = 0; $j < 16; $j++) {
+                $x[$j + 16] = $m[$i + $j];
+                $x[$j + 32] = $x[$j + 16] ^ $x[$j];
+            }
+            $t = chr(0);
+            for ($j = 0; $j < 18; $j++) {
+                for ($k = 0; $k < 48; $k++) {
+                    $x[$k] = $t = $x[$k] ^ chr($s[ord($t)]);
+                    //$t = $x[$k] = $x[$k] ^ chr($s[ord($t)]);
+                }
+                $t = chr(ord($t) + $j);
+            }
+        }
+
+        // Step 5. Output
+        return substr($x, 0, 16);
+    }
+
+    /**
+     * Pure-PHP implementation of SHA256
+     *
+     * See {@link http://en.wikipedia.org/wiki/SHA_hash_functions#SHA-256_.28a_SHA-2_variant.29_pseudocode SHA-256 (a SHA-2 variant) pseudocode - Wikipedia}.
+     *
+     * @access private
+     * @param String $m
+     */
+    function _sha256($m)
+    {
+        if (extension_loaded('suhosin')) {
+            return pack('H*', sha256($m));
+        }
+
+        // Initialize variables
+        $hash = array(
+            0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19
+        );
+        // Initialize table of round constants
+        // (first 32 bits of the fractional parts of the cube roots of the first 64 primes 2..311)
+        static $k = array(
+            0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5,
+            0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174,
+            0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da,
+            0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967,
+            0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85,
+            0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070,
+            0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3,
+            0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2
+        );
+
+        // Pre-processing
+        $length = strlen($m);
+        // to round to nearest 56 mod 64, we'll add 64 - (length + (64 - 56)) % 64
+        $m.= str_repeat(chr(0), 64 - (($length + 8) & 0x3F));
+        $m[$length] = chr(0x80);
+        // we don't support hashing strings 512MB long
+        $m.= pack('N2', 0, $length << 3);
+
+        // Process the message in successive 512-bit chunks
+        $chunks = str_split($m, 64);
+        foreach ($chunks as $chunk) {
+            $w = array();
+            for ($i = 0; $i < 16; $i++) {
+                extract(unpack('Ntemp', $this->_string_shift($chunk, 4)));
+                $w[] = $temp;
+            }
+
+            // Extend the sixteen 32-bit words into sixty-four 32-bit words
+            for ($i = 16; $i < 64; $i++) {
+                $s0 = $this->_rightRotate($w[$i - 15],  7) ^
+                      $this->_rightRotate($w[$i - 15], 18) ^
+                      $this->_rightShift( $w[$i - 15],  3);
+                $s1 = $this->_rightRotate($w[$i - 2], 17) ^
+                      $this->_rightRotate($w[$i - 2], 19) ^
+                      $this->_rightShift( $w[$i - 2], 10);
+                $w[$i] = $this->_add($w[$i - 16], $s0, $w[$i - 7], $s1);
+
+            }
+
+            // Initialize hash value for this chunk
+            list($a, $b, $c, $d, $e, $f, $g, $h) = $hash;
+
+            // Main loop
+            for ($i = 0; $i < 64; $i++) {
+                $s0 = $this->_rightRotate($a,  2) ^
+                      $this->_rightRotate($a, 13) ^
+                      $this->_rightRotate($a, 22);
+                $maj = ($a & $b) ^
+                       ($a & $c) ^
+                       ($b & $c);
+                $t2 = $this->_add($s0, $maj);
+
+                $s1 = $this->_rightRotate($e,  6) ^
+                      $this->_rightRotate($e, 11) ^
+                      $this->_rightRotate($e, 25);
+                $ch = ($e & $f) ^
+                      ($this->_not($e) & $g);
+                $t1 = $this->_add($h, $s1, $ch, $k[$i], $w[$i]);
+
+                $h = $g;
+                $g = $f;
+                $f = $e;
+                $e = $this->_add($d, $t1);
+                $d = $c;
+                $c = $b;
+                $b = $a;
+                $a = $this->_add($t1, $t2);
+            }
+
+            // Add this chunk's hash to result so far
+            $hash = array(
+                $this->_add($hash[0], $a),
+                $this->_add($hash[1], $b),
+                $this->_add($hash[2], $c),
+                $this->_add($hash[3], $d),
+                $this->_add($hash[4], $e),
+                $this->_add($hash[5], $f),
+                $this->_add($hash[6], $g),
+                $this->_add($hash[7], $h)
+            );
+        }
+
+        // Produce the final hash value (big-endian)
+        return pack('N8', $hash[0], $hash[1], $hash[2], $hash[3], $hash[4], $hash[5], $hash[6], $hash[7]);
+    }
+
+    /**
+     * Pure-PHP implementation of SHA384 and SHA512
+     *
+     * @access private
+     * @param String $m
+     */
+    function _sha512($m)
+    {
+        if (!class_exists('Math_BigInteger')) {
+            require_once('Math/BigInteger.php');
+        }
+
+        static $init384, $init512, $k;
+
+        if (!isset($k)) {
+            // Initialize variables
+            $init384 = array( // initial values for SHA384
+                'cbbb9d5dc1059ed8', '629a292a367cd507', '9159015a3070dd17', '152fecd8f70e5939', 
+                '67332667ffc00b31', '8eb44a8768581511', 'db0c2e0d64f98fa7', '47b5481dbefa4fa4'
+            );
+            $init512 = array( // initial values for SHA512
+                '6a09e667f3bcc908', 'bb67ae8584caa73b', '3c6ef372fe94f82b', 'a54ff53a5f1d36f1', 
+                '510e527fade682d1', '9b05688c2b3e6c1f', '1f83d9abfb41bd6b', '5be0cd19137e2179'
+            );
+
+            for ($i = 0; $i < 8; $i++) {
+                $init384[$i] = new Math_BigInteger($init384[$i], 16);
+                $init384[$i]->setPrecision(64);
+                $init512[$i] = new Math_BigInteger($init512[$i], 16);
+                $init512[$i]->setPrecision(64);
+            }
+
+            // Initialize table of round constants
+            // (first 64 bits of the fractional parts of the cube roots of the first 80 primes 2..409)
+            $k = array(
+                '428a2f98d728ae22', '7137449123ef65cd', 'b5c0fbcfec4d3b2f', 'e9b5dba58189dbbc',
+                '3956c25bf348b538', '59f111f1b605d019', '923f82a4af194f9b', 'ab1c5ed5da6d8118',
+                'd807aa98a3030242', '12835b0145706fbe', '243185be4ee4b28c', '550c7dc3d5ffb4e2',
+                '72be5d74f27b896f', '80deb1fe3b1696b1', '9bdc06a725c71235', 'c19bf174cf692694',
+                'e49b69c19ef14ad2', 'efbe4786384f25e3', '0fc19dc68b8cd5b5', '240ca1cc77ac9c65',
+                '2de92c6f592b0275', '4a7484aa6ea6e483', '5cb0a9dcbd41fbd4', '76f988da831153b5',
+                '983e5152ee66dfab', 'a831c66d2db43210', 'b00327c898fb213f', 'bf597fc7beef0ee4',
+                'c6e00bf33da88fc2', 'd5a79147930aa725', '06ca6351e003826f', '142929670a0e6e70',
+                '27b70a8546d22ffc', '2e1b21385c26c926', '4d2c6dfc5ac42aed', '53380d139d95b3df',
+                '650a73548baf63de', '766a0abb3c77b2a8', '81c2c92e47edaee6', '92722c851482353b',
+                'a2bfe8a14cf10364', 'a81a664bbc423001', 'c24b8b70d0f89791', 'c76c51a30654be30',
+                'd192e819d6ef5218', 'd69906245565a910', 'f40e35855771202a', '106aa07032bbd1b8',
+                '19a4c116b8d2d0c8', '1e376c085141ab53', '2748774cdf8eeb99', '34b0bcb5e19b48a8',
+                '391c0cb3c5c95a63', '4ed8aa4ae3418acb', '5b9cca4f7763e373', '682e6ff3d6b2b8a3',
+                '748f82ee5defb2fc', '78a5636f43172f60', '84c87814a1f0ab72', '8cc702081a6439ec',
+                '90befffa23631e28', 'a4506cebde82bde9', 'bef9a3f7b2c67915', 'c67178f2e372532b',
+                'ca273eceea26619c', 'd186b8c721c0c207', 'eada7dd6cde0eb1e', 'f57d4f7fee6ed178',
+                '06f067aa72176fba', '0a637dc5a2c898a6', '113f9804bef90dae', '1b710b35131c471b',
+                '28db77f523047d84', '32caab7b40c72493', '3c9ebe0a15c9bebc', '431d67c49c100d4c',
+                '4cc5d4becb3e42b6', '597f299cfc657e2a', '5fcb6fab3ad6faec', '6c44198c4a475817'
+            );
+
+            for ($i = 0; $i < 80; $i++) {
+                $k[$i] = new Math_BigInteger($k[$i], 16);
+            }
+        }
+
+        $hash = $this->l == 48 ? $init384 : $init512;
+
+        // Pre-processing
+        $length = strlen($m);
+        // to round to nearest 112 mod 128, we'll add 128 - (length + (128 - 112)) % 128
+        $m.= str_repeat(chr(0), 128 - (($length + 16) & 0x7F));
+        $m[$length] = chr(0x80);
+        // we don't support hashing strings 512MB long
+        $m.= pack('N4', 0, 0, 0, $length << 3);
+
+        // Process the message in successive 1024-bit chunks
+        $chunks = str_split($m, 128);
+        foreach ($chunks as $chunk) {
+            $w = array();
+            for ($i = 0; $i < 16; $i++) {
+                $temp = new Math_BigInteger($this->_string_shift($chunk, 8), 256);
+                $temp->setPrecision(64);
+                $w[] = $temp;
+            }
+
+            // Extend the sixteen 32-bit words into eighty 32-bit words
+            for ($i = 16; $i < 80; $i++) {
+                $temp = array(
+                          $w[$i - 15]->bitwise_rightRotate(1),
+                          $w[$i - 15]->bitwise_rightRotate(8),
+                          $w[$i - 15]->bitwise_rightShift(7)
+                );
+                $s0 = $temp[0]->bitwise_xor($temp[1]);
+                $s0 = $s0->bitwise_xor($temp[2]);
+                $temp = array(
+                          $w[$i - 2]->bitwise_rightRotate(19),
+                          $w[$i - 2]->bitwise_rightRotate(61),
+                          $w[$i - 2]->bitwise_rightShift(6)
+                );
+                $s1 = $temp[0]->bitwise_xor($temp[1]);
+                $s1 = $s1->bitwise_xor($temp[2]);
+                $w[$i] = $w[$i - 16]->copy();
+                $w[$i] = $w[$i]->add($s0);
+                $w[$i] = $w[$i]->add($w[$i - 7]);
+                $w[$i] = $w[$i]->add($s1);
+            }
+
+            // Initialize hash value for this chunk
+            $a = $hash[0]->copy();
+            $b = $hash[1]->copy();
+            $c = $hash[2]->copy();
+            $d = $hash[3]->copy();
+            $e = $hash[4]->copy();
+            $f = $hash[5]->copy();
+            $g = $hash[6]->copy();
+            $h = $hash[7]->copy();
+
+            // Main loop
+            for ($i = 0; $i < 80; $i++) {
+                $temp = array(
+                    $a->bitwise_rightRotate(28),
+                    $a->bitwise_rightRotate(34),
+                    $a->bitwise_rightRotate(39)
+                );
+                $s0 = $temp[0]->bitwise_xor($temp[1]);
+                $s0 = $s0->bitwise_xor($temp[2]);
+                $temp = array(
+                    $a->bitwise_and($b),
+                    $a->bitwise_and($c),
+                    $b->bitwise_and($c)
+                );
+                $maj = $temp[0]->bitwise_xor($temp[1]);
+                $maj = $maj->bitwise_xor($temp[2]);
+                $t2 = $s0->add($maj);
+
+                $temp = array(
+                    $e->bitwise_rightRotate(14),
+                    $e->bitwise_rightRotate(18),
+                    $e->bitwise_rightRotate(41)
+                );
+                $s1 = $temp[0]->bitwise_xor($temp[1]);
+                $s1 = $s1->bitwise_xor($temp[2]);
+                $temp = array(
+                    $e->bitwise_and($f),
+                    $g->bitwise_and($e->bitwise_not())
+                );
+                $ch = $temp[0]->bitwise_xor($temp[1]);
+                $t1 = $h->add($s1);
+                $t1 = $t1->add($ch);
+                $t1 = $t1->add($k[$i]);
+                $t1 = $t1->add($w[$i]);
+
+                $h = $g->copy();
+                $g = $f->copy();
+                $f = $e->copy();
+                $e = $d->add($t1);
+                $d = $c->copy();
+                $c = $b->copy();
+                $b = $a->copy();
+                $a = $t1->add($t2);
+            }
+
+            // Add this chunk's hash to result so far
+            $hash = array(
+                $hash[0]->add($a),
+                $hash[1]->add($b),
+                $hash[2]->add($c),
+                $hash[3]->add($d),
+                $hash[4]->add($e),
+                $hash[5]->add($f),
+                $hash[6]->add($g),
+                $hash[7]->add($h)
+            );
+        }
+
+        // Produce the final hash value (big-endian)
+        // (Crypt_Hash::hash() trims the output for hashes but not for HMACs.  as such, we trim the output here)
+        $temp = $hash[0]->toBytes() . $hash[1]->toBytes() . $hash[2]->toBytes() . $hash[3]->toBytes() .
+                $hash[4]->toBytes() . $hash[5]->toBytes();
+        if ($this->l != 48) {
+            $temp.= $hash[6]->toBytes() . $hash[7]->toBytes();
+        }
+
+        return $temp;
+    }
+
+    /**
+     * Right Rotate
+     *
+     * @access private
+     * @param Integer $int
+     * @param Integer $amt
+     * @see _sha256()
+     * @return Integer
+     */
+    function _rightRotate($int, $amt)
+    {
+        $invamt = 32 - $amt;
+        $mask = (1 << $invamt) - 1;
+        return (($int << $invamt) & 0xFFFFFFFF) | (($int >> $amt) & $mask);
+    }
+
+    /**
+     * Right Shift
+     *
+     * @access private
+     * @param Integer $int
+     * @param Integer $amt
+     * @see _sha256()
+     * @return Integer
+     */
+    function _rightShift($int, $amt)
+    {
+        $mask = (1 << (32 - $amt)) - 1;
+        return ($int >> $amt) & $mask;
+    }
+
+    /**
+     * Not
+     *
+     * @access private
+     * @param Integer $int
+     * @see _sha256()
+     * @return Integer
+     */
+    function _not($int)
+    {
+        return ~$int & 0xFFFFFFFF;
+    }
+
+    /**
+     * Add
+     *
+     * _sha256() adds multiple unsigned 32-bit integers.  Since PHP doesn't support unsigned integers and since the
+     * possibility of overflow exists, care has to be taken.  Math_BigInteger() could be used but this should be faster.
+     *
+     * @param Integer $...
+     * @return Integer
+     * @see _sha256()
+     * @access private
+     */
+    function _add()
+    {
+        static $mod;
+        if (!isset($mod)) {
+            $mod = pow(2, 32);
+        }
+
+        $result = 0;
+        $arguments = func_get_args();
+        foreach ($arguments as $argument) {
+            $result+= $argument < 0 ? ($argument & 0x7FFFFFFF) + 0x80000000 : $argument;
+        }
+
+        return fmod($result, $mod);
+    }
+
+    /**
+     * String Shift
+     *
+     * Inspired by array_shift
+     *
+     * @param String $string
+     * @param optional Integer $index
+     * @return String
+     * @access private
+     */
+    function _string_shift(&$string, $index = 1)
+    {
+        $substr = substr($string, 0, $index);
+        $string = substr($string, $index);
+        return $substr;
+    }
+}
diff --git a/inc/phpseclib/Crypt_Rijndael.php b/inc/phpseclib/Crypt_Rijndael.php
new file mode 100644
index 000000000..c63e0ff7e
--- /dev/null
+++ b/inc/phpseclib/Crypt_Rijndael.php
@@ -0,0 +1,1374 @@
+<?php
+/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
+
+/**
+ * Pure-PHP implementation of Rijndael.
+ *
+ * Uses mcrypt, if available/possible, and an internal implementation, otherwise.
+ *
+ * PHP versions 4 and 5
+ *
+ * If {@link Crypt_Rijndael::setBlockLength() setBlockLength()} isn't called, it'll be assumed to be 128 bits.  If
+ * {@link Crypt_Rijndael::setKeyLength() setKeyLength()} isn't called, it'll be calculated from
+ * {@link Crypt_Rijndael::setKey() setKey()}.  ie. if the key is 128-bits, the key length will be 128-bits.  If it's
+ * 136-bits it'll be null-padded to 192-bits and 192 bits will be the key length until
+ * {@link Crypt_Rijndael::setKey() setKey()} is called, again, at which point, it'll be recalculated.
+ *
+ * Not all Rijndael implementations may support 160-bits or 224-bits as the block length / key length.  mcrypt, for example,
+ * does not.  AES, itself, only supports block lengths of 128 and key lengths of 128, 192, and 256.
+ * {@link http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf#page=10 Rijndael-ammended.pdf#page=10} defines the
+ * algorithm for block lengths of 192 and 256 but not for block lengths / key lengths of 160 and 224.  Indeed, 160 and 224
+ * are first defined as valid key / block lengths in
+ * {@link http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf#page=44 Rijndael-ammended.pdf#page=44}:
+ * Extensions: Other block and Cipher Key lengths.
+ * Note: Use of 160/224-bit Keys must be explicitly set by setKeyLength(160) respectively setKeyLength(224).
+ *
+ * {@internal The variable names are the same as those in
+ * {@link http://www.csrc.nist.gov/publications/fips/fips197/fips-197.pdf#page=10 fips-197.pdf#page=10}.}}
+ *
+ * Here's a short example of how to use this library:
+ * <code>
+ * <?php
+ *    include('Crypt/Rijndael.php');
+ *
+ *    $rijndael = new Crypt_Rijndael();
+ *
+ *    $rijndael->setKey('abcdefghijklmnop');
+ *
+ *    $size = 10 * 1024;
+ *    $plaintext = '';
+ *    for ($i = 0; $i < $size; $i++) {
+ *        $plaintext.= 'a';
+ *    }
+ *
+ *    echo $rijndael->decrypt($rijndael->encrypt($plaintext));
+ * ?>
+ * </code>
+ *
+ * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *
+ * @category   Crypt
+ * @package    Crypt_Rijndael
+ * @author     Jim Wigginton <terrafrost@php.net>
+ * @copyright  MMVIII Jim Wigginton
+ * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link       http://phpseclib.sourceforge.net
+ */
+
+/**
+ * Include Crypt_Base
+ *
+ * Base cipher class
+ */
+if (!class_exists('Crypt_Base')) {
+    require_once('Base.php');
+}
+
+/**#@+
+ * @access public
+ * @see Crypt_Rijndael::encrypt()
+ * @see Crypt_Rijndael::decrypt()
+ */
+/**
+ * Encrypt / decrypt using the Counter mode.
+ *
+ * Set to -1 since that's what Crypt/Random.php uses to index the CTR mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Counter_.28CTR.29
+ */
+define('CRYPT_RIJNDAEL_MODE_CTR', CRYPT_MODE_CTR);
+/**
+ * Encrypt / decrypt using the Electronic Code Book mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Electronic_codebook_.28ECB.29
+ */
+define('CRYPT_RIJNDAEL_MODE_ECB', CRYPT_MODE_ECB);
+/**
+ * Encrypt / decrypt using the Code Book Chaining mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher-block_chaining_.28CBC.29
+ */
+define('CRYPT_RIJNDAEL_MODE_CBC', CRYPT_MODE_CBC);
+/**
+ * Encrypt / decrypt using the Cipher Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Cipher_feedback_.28CFB.29
+ */
+define('CRYPT_RIJNDAEL_MODE_CFB', CRYPT_MODE_CFB);
+/**
+ * Encrypt / decrypt using the Cipher Feedback mode.
+ *
+ * @link http://en.wikipedia.org/wiki/Block_cipher_modes_of_operation#Output_feedback_.28OFB.29
+ */
+define('CRYPT_RIJNDAEL_MODE_OFB', CRYPT_MODE_OFB);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Crypt_Rijndael::Crypt_Rijndael()
+ */
+/**
+ * Toggles the internal implementation
+ */
+define('CRYPT_RIJNDAEL_MODE_INTERNAL', CRYPT_MODE_INTERNAL);
+/**
+ * Toggles the mcrypt implementation
+ */
+define('CRYPT_RIJNDAEL_MODE_MCRYPT', CRYPT_MODE_MCRYPT);
+/**#@-*/
+
+/**
+ * Pure-PHP implementation of Rijndael.
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @version 0.1.0
+ * @access  public
+ * @package Crypt_Rijndael
+ */
+class Crypt_Rijndael extends Crypt_Base {
+    /**
+     * The default password key_size used by setPassword()
+     *
+     * @see Crypt_Base::password_key_size
+     * @see Crypt_Base::setPassword()
+     * @var Integer
+     * @access private
+     */
+    var $password_key_size = 16;
+
+    /**
+     * The namespace used by the cipher for its constants.
+     *
+     * @see Crypt_Base::const_namespace
+     * @var String
+     * @access private
+     */
+    var $const_namespace = 'RIJNDAEL';
+
+    /**
+     * The mcrypt specific name of the cipher
+     *
+     * Mcrypt is useable for 128/192/256-bit $block_size/$key_size. For 160/224 not.
+     * Crypt_Rijndael determines automatically whether mcrypt is useable
+     * or not for the current $block_size/$key_size.
+     * In case of, $cipher_name_mcrypt will be set dynamicaly at run time accordingly.
+     *
+     * @see Crypt_Base::cipher_name_mcrypt
+     * @see Crypt_Base::engine
+     * @see _setupEngine()
+     * @var String
+     * @access private
+     */
+    var $cipher_name_mcrypt = 'rijndael-128';
+
+    /**
+     * The default salt used by setPassword()
+     *
+     * @see Crypt_Base::password_default_salt
+     * @see Crypt_Base::setPassword()
+     * @var String
+     * @access private
+     */
+    var $password_default_salt = 'phpseclib';
+
+    /**
+     * Has the key length explicitly been set or should it be derived from the key, itself?
+     *
+     * @see setKeyLength()
+     * @var Boolean
+     * @access private
+     */
+    var $explicit_key_length = false;
+
+    /**
+     * The Key Schedule
+     *
+     * @see _setup()
+     * @var Array
+     * @access private
+     */
+    var $w;
+
+    /**
+     * The Inverse Key Schedule
+     *
+     * @see _setup()
+     * @var Array
+     * @access private
+     */
+    var $dw;
+
+    /**
+     * The Block Length divided by 32
+     *
+     * @see setBlockLength()
+     * @var Integer
+     * @access private
+     * @internal The max value is 256 / 32 = 8, the min value is 128 / 32 = 4.  Exists in conjunction with $block_size
+     *    because the encryption / decryption / key schedule creation requires this number and not $block_size.  We could
+     *    derive this from $block_size or vice versa, but that'd mean we'd have to do multiple shift operations, so in lieu
+     *    of that, we'll just precompute it once.
+     *
+     */
+    var $Nb = 4;
+
+    /**
+     * The Key Length
+     *
+     * @see setKeyLength()
+     * @var Integer
+     * @access private
+     * @internal The max value is 256 / 8 = 32, the min value is 128 / 8 = 16.  Exists in conjunction with $Nk
+     *    because the encryption / decryption / key schedule creation requires this number and not $key_size.  We could
+     *    derive this from $key_size or vice versa, but that'd mean we'd have to do multiple shift operations, so in lieu
+     *    of that, we'll just precompute it once.
+     */
+    var $key_size = 16;
+
+    /**
+     * The Key Length divided by 32
+     *
+     * @see setKeyLength()
+     * @var Integer
+     * @access private
+     * @internal The max value is 256 / 32 = 8, the min value is 128 / 32 = 4
+     */
+    var $Nk = 4;
+
+    /**
+     * The Number of Rounds
+     *
+     * @var Integer
+     * @access private
+     * @internal The max value is 14, the min value is 10.
+     */
+    var $Nr;
+
+    /**
+     * Shift offsets
+     *
+     * @var Array
+     * @access private
+     */
+    var $c;
+
+    /**
+     * Holds the last used key- and block_size information
+     *
+     * @var Array
+     * @access private
+     */
+    var $kl;
+
+    /**
+     * Precomputed mixColumns table
+     *
+     * According to <http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf#page=19> (section 5.2.1),
+     * precomputed tables can be used in the mixColumns phase.  in that example, they're assigned t0...t3, so
+     * those are the names we'll use.
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $t0 = array(
+        0xC66363A5, 0xF87C7C84, 0xEE777799, 0xF67B7B8D, 0xFFF2F20D, 0xD66B6BBD, 0xDE6F6FB1, 0x91C5C554,
+        0x60303050, 0x02010103, 0xCE6767A9, 0x562B2B7D, 0xE7FEFE19, 0xB5D7D762, 0x4DABABE6, 0xEC76769A,
+        0x8FCACA45, 0x1F82829D, 0x89C9C940, 0xFA7D7D87, 0xEFFAFA15, 0xB25959EB, 0x8E4747C9, 0xFBF0F00B,
+        0x41ADADEC, 0xB3D4D467, 0x5FA2A2FD, 0x45AFAFEA, 0x239C9CBF, 0x53A4A4F7, 0xE4727296, 0x9BC0C05B,
+        0x75B7B7C2, 0xE1FDFD1C, 0x3D9393AE, 0x4C26266A, 0x6C36365A, 0x7E3F3F41, 0xF5F7F702, 0x83CCCC4F,
+        0x6834345C, 0x51A5A5F4, 0xD1E5E534, 0xF9F1F108, 0xE2717193, 0xABD8D873, 0x62313153, 0x2A15153F,
+        0x0804040C, 0x95C7C752, 0x46232365, 0x9DC3C35E, 0x30181828, 0x379696A1, 0x0A05050F, 0x2F9A9AB5,
+        0x0E070709, 0x24121236, 0x1B80809B, 0xDFE2E23D, 0xCDEBEB26, 0x4E272769, 0x7FB2B2CD, 0xEA75759F,
+        0x1209091B, 0x1D83839E, 0x582C2C74, 0x341A1A2E, 0x361B1B2D, 0xDC6E6EB2, 0xB45A5AEE, 0x5BA0A0FB,
+        0xA45252F6, 0x763B3B4D, 0xB7D6D661, 0x7DB3B3CE, 0x5229297B, 0xDDE3E33E, 0x5E2F2F71, 0x13848497,
+        0xA65353F5, 0xB9D1D168, 0x00000000, 0xC1EDED2C, 0x40202060, 0xE3FCFC1F, 0x79B1B1C8, 0xB65B5BED,
+        0xD46A6ABE, 0x8DCBCB46, 0x67BEBED9, 0x7239394B, 0x944A4ADE, 0x984C4CD4, 0xB05858E8, 0x85CFCF4A,
+        0xBBD0D06B, 0xC5EFEF2A, 0x4FAAAAE5, 0xEDFBFB16, 0x864343C5, 0x9A4D4DD7, 0x66333355, 0x11858594,
+        0x8A4545CF, 0xE9F9F910, 0x04020206, 0xFE7F7F81, 0xA05050F0, 0x783C3C44, 0x259F9FBA, 0x4BA8A8E3,
+        0xA25151F3, 0x5DA3A3FE, 0x804040C0, 0x058F8F8A, 0x3F9292AD, 0x219D9DBC, 0x70383848, 0xF1F5F504,
+        0x63BCBCDF, 0x77B6B6C1, 0xAFDADA75, 0x42212163, 0x20101030, 0xE5FFFF1A, 0xFDF3F30E, 0xBFD2D26D,
+        0x81CDCD4C, 0x180C0C14, 0x26131335, 0xC3ECEC2F, 0xBE5F5FE1, 0x359797A2, 0x884444CC, 0x2E171739,
+        0x93C4C457, 0x55A7A7F2, 0xFC7E7E82, 0x7A3D3D47, 0xC86464AC, 0xBA5D5DE7, 0x3219192B, 0xE6737395,
+        0xC06060A0, 0x19818198, 0x9E4F4FD1, 0xA3DCDC7F, 0x44222266, 0x542A2A7E, 0x3B9090AB, 0x0B888883,
+        0x8C4646CA, 0xC7EEEE29, 0x6BB8B8D3, 0x2814143C, 0xA7DEDE79, 0xBC5E5EE2, 0x160B0B1D, 0xADDBDB76,
+        0xDBE0E03B, 0x64323256, 0x743A3A4E, 0x140A0A1E, 0x924949DB, 0x0C06060A, 0x4824246C, 0xB85C5CE4,
+        0x9FC2C25D, 0xBDD3D36E, 0x43ACACEF, 0xC46262A6, 0x399191A8, 0x319595A4, 0xD3E4E437, 0xF279798B,
+        0xD5E7E732, 0x8BC8C843, 0x6E373759, 0xDA6D6DB7, 0x018D8D8C, 0xB1D5D564, 0x9C4E4ED2, 0x49A9A9E0,
+        0xD86C6CB4, 0xAC5656FA, 0xF3F4F407, 0xCFEAEA25, 0xCA6565AF, 0xF47A7A8E, 0x47AEAEE9, 0x10080818,
+        0x6FBABAD5, 0xF0787888, 0x4A25256F, 0x5C2E2E72, 0x381C1C24, 0x57A6A6F1, 0x73B4B4C7, 0x97C6C651,
+        0xCBE8E823, 0xA1DDDD7C, 0xE874749C, 0x3E1F1F21, 0x964B4BDD, 0x61BDBDDC, 0x0D8B8B86, 0x0F8A8A85,
+        0xE0707090, 0x7C3E3E42, 0x71B5B5C4, 0xCC6666AA, 0x904848D8, 0x06030305, 0xF7F6F601, 0x1C0E0E12,
+        0xC26161A3, 0x6A35355F, 0xAE5757F9, 0x69B9B9D0, 0x17868691, 0x99C1C158, 0x3A1D1D27, 0x279E9EB9,
+        0xD9E1E138, 0xEBF8F813, 0x2B9898B3, 0x22111133, 0xD26969BB, 0xA9D9D970, 0x078E8E89, 0x339494A7,
+        0x2D9B9BB6, 0x3C1E1E22, 0x15878792, 0xC9E9E920, 0x87CECE49, 0xAA5555FF, 0x50282878, 0xA5DFDF7A,
+        0x038C8C8F, 0x59A1A1F8, 0x09898980, 0x1A0D0D17, 0x65BFBFDA, 0xD7E6E631, 0x844242C6, 0xD06868B8,
+        0x824141C3, 0x299999B0, 0x5A2D2D77, 0x1E0F0F11, 0x7BB0B0CB, 0xA85454FC, 0x6DBBBBD6, 0x2C16163A
+    );
+
+    /**
+     * Precomputed mixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $t1 = array(
+        0xA5C66363, 0x84F87C7C, 0x99EE7777, 0x8DF67B7B, 0x0DFFF2F2, 0xBDD66B6B, 0xB1DE6F6F, 0x5491C5C5,
+        0x50603030, 0x03020101, 0xA9CE6767, 0x7D562B2B, 0x19E7FEFE, 0x62B5D7D7, 0xE64DABAB, 0x9AEC7676,
+        0x458FCACA, 0x9D1F8282, 0x4089C9C9, 0x87FA7D7D, 0x15EFFAFA, 0xEBB25959, 0xC98E4747, 0x0BFBF0F0,
+        0xEC41ADAD, 0x67B3D4D4, 0xFD5FA2A2, 0xEA45AFAF, 0xBF239C9C, 0xF753A4A4, 0x96E47272, 0x5B9BC0C0,
+        0xC275B7B7, 0x1CE1FDFD, 0xAE3D9393, 0x6A4C2626, 0x5A6C3636, 0x417E3F3F, 0x02F5F7F7, 0x4F83CCCC,
+        0x5C683434, 0xF451A5A5, 0x34D1E5E5, 0x08F9F1F1, 0x93E27171, 0x73ABD8D8, 0x53623131, 0x3F2A1515,
+        0x0C080404, 0x5295C7C7, 0x65462323, 0x5E9DC3C3, 0x28301818, 0xA1379696, 0x0F0A0505, 0xB52F9A9A,
+        0x090E0707, 0x36241212, 0x9B1B8080, 0x3DDFE2E2, 0x26CDEBEB, 0x694E2727, 0xCD7FB2B2, 0x9FEA7575,
+        0x1B120909, 0x9E1D8383, 0x74582C2C, 0x2E341A1A, 0x2D361B1B, 0xB2DC6E6E, 0xEEB45A5A, 0xFB5BA0A0,
+        0xF6A45252, 0x4D763B3B, 0x61B7D6D6, 0xCE7DB3B3, 0x7B522929, 0x3EDDE3E3, 0x715E2F2F, 0x97138484,
+        0xF5A65353, 0x68B9D1D1, 0x00000000, 0x2CC1EDED, 0x60402020, 0x1FE3FCFC, 0xC879B1B1, 0xEDB65B5B,
+        0xBED46A6A, 0x468DCBCB, 0xD967BEBE, 0x4B723939, 0xDE944A4A, 0xD4984C4C, 0xE8B05858, 0x4A85CFCF,
+        0x6BBBD0D0, 0x2AC5EFEF, 0xE54FAAAA, 0x16EDFBFB, 0xC5864343, 0xD79A4D4D, 0x55663333, 0x94118585,
+        0xCF8A4545, 0x10E9F9F9, 0x06040202, 0x81FE7F7F, 0xF0A05050, 0x44783C3C, 0xBA259F9F, 0xE34BA8A8,
+        0xF3A25151, 0xFE5DA3A3, 0xC0804040, 0x8A058F8F, 0xAD3F9292, 0xBC219D9D, 0x48703838, 0x04F1F5F5,
+        0xDF63BCBC, 0xC177B6B6, 0x75AFDADA, 0x63422121, 0x30201010, 0x1AE5FFFF, 0x0EFDF3F3, 0x6DBFD2D2,
+        0x4C81CDCD, 0x14180C0C, 0x35261313, 0x2FC3ECEC, 0xE1BE5F5F, 0xA2359797, 0xCC884444, 0x392E1717,
+        0x5793C4C4, 0xF255A7A7, 0x82FC7E7E, 0x477A3D3D, 0xACC86464, 0xE7BA5D5D, 0x2B321919, 0x95E67373,
+        0xA0C06060, 0x98198181, 0xD19E4F4F, 0x7FA3DCDC, 0x66442222, 0x7E542A2A, 0xAB3B9090, 0x830B8888,
+        0xCA8C4646, 0x29C7EEEE, 0xD36BB8B8, 0x3C281414, 0x79A7DEDE, 0xE2BC5E5E, 0x1D160B0B, 0x76ADDBDB,
+        0x3BDBE0E0, 0x56643232, 0x4E743A3A, 0x1E140A0A, 0xDB924949, 0x0A0C0606, 0x6C482424, 0xE4B85C5C,
+        0x5D9FC2C2, 0x6EBDD3D3, 0xEF43ACAC, 0xA6C46262, 0xA8399191, 0xA4319595, 0x37D3E4E4, 0x8BF27979,
+        0x32D5E7E7, 0x438BC8C8, 0x596E3737, 0xB7DA6D6D, 0x8C018D8D, 0x64B1D5D5, 0xD29C4E4E, 0xE049A9A9,
+        0xB4D86C6C, 0xFAAC5656, 0x07F3F4F4, 0x25CFEAEA, 0xAFCA6565, 0x8EF47A7A, 0xE947AEAE, 0x18100808,
+        0xD56FBABA, 0x88F07878, 0x6F4A2525, 0x725C2E2E, 0x24381C1C, 0xF157A6A6, 0xC773B4B4, 0x5197C6C6,
+        0x23CBE8E8, 0x7CA1DDDD, 0x9CE87474, 0x213E1F1F, 0xDD964B4B, 0xDC61BDBD, 0x860D8B8B, 0x850F8A8A,
+        0x90E07070, 0x427C3E3E, 0xC471B5B5, 0xAACC6666, 0xD8904848, 0x05060303, 0x01F7F6F6, 0x121C0E0E,
+        0xA3C26161, 0x5F6A3535, 0xF9AE5757, 0xD069B9B9, 0x91178686, 0x5899C1C1, 0x273A1D1D, 0xB9279E9E,
+        0x38D9E1E1, 0x13EBF8F8, 0xB32B9898, 0x33221111, 0xBBD26969, 0x70A9D9D9, 0x89078E8E, 0xA7339494,
+        0xB62D9B9B, 0x223C1E1E, 0x92158787, 0x20C9E9E9, 0x4987CECE, 0xFFAA5555, 0x78502828, 0x7AA5DFDF,
+        0x8F038C8C, 0xF859A1A1, 0x80098989, 0x171A0D0D, 0xDA65BFBF, 0x31D7E6E6, 0xC6844242, 0xB8D06868,
+        0xC3824141, 0xB0299999, 0x775A2D2D, 0x111E0F0F, 0xCB7BB0B0, 0xFCA85454, 0xD66DBBBB, 0x3A2C1616
+    );
+
+    /**
+     * Precomputed mixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $t2 = array(
+        0x63A5C663, 0x7C84F87C, 0x7799EE77, 0x7B8DF67B, 0xF20DFFF2, 0x6BBDD66B, 0x6FB1DE6F, 0xC55491C5,
+        0x30506030, 0x01030201, 0x67A9CE67, 0x2B7D562B, 0xFE19E7FE, 0xD762B5D7, 0xABE64DAB, 0x769AEC76,
+        0xCA458FCA, 0x829D1F82, 0xC94089C9, 0x7D87FA7D, 0xFA15EFFA, 0x59EBB259, 0x47C98E47, 0xF00BFBF0,
+        0xADEC41AD, 0xD467B3D4, 0xA2FD5FA2, 0xAFEA45AF, 0x9CBF239C, 0xA4F753A4, 0x7296E472, 0xC05B9BC0,
+        0xB7C275B7, 0xFD1CE1FD, 0x93AE3D93, 0x266A4C26, 0x365A6C36, 0x3F417E3F, 0xF702F5F7, 0xCC4F83CC,
+        0x345C6834, 0xA5F451A5, 0xE534D1E5, 0xF108F9F1, 0x7193E271, 0xD873ABD8, 0x31536231, 0x153F2A15,
+        0x040C0804, 0xC75295C7, 0x23654623, 0xC35E9DC3, 0x18283018, 0x96A13796, 0x050F0A05, 0x9AB52F9A,
+        0x07090E07, 0x12362412, 0x809B1B80, 0xE23DDFE2, 0xEB26CDEB, 0x27694E27, 0xB2CD7FB2, 0x759FEA75,
+        0x091B1209, 0x839E1D83, 0x2C74582C, 0x1A2E341A, 0x1B2D361B, 0x6EB2DC6E, 0x5AEEB45A, 0xA0FB5BA0,
+        0x52F6A452, 0x3B4D763B, 0xD661B7D6, 0xB3CE7DB3, 0x297B5229, 0xE33EDDE3, 0x2F715E2F, 0x84971384,
+        0x53F5A653, 0xD168B9D1, 0x00000000, 0xED2CC1ED, 0x20604020, 0xFC1FE3FC, 0xB1C879B1, 0x5BEDB65B,
+        0x6ABED46A, 0xCB468DCB, 0xBED967BE, 0x394B7239, 0x4ADE944A, 0x4CD4984C, 0x58E8B058, 0xCF4A85CF,
+        0xD06BBBD0, 0xEF2AC5EF, 0xAAE54FAA, 0xFB16EDFB, 0x43C58643, 0x4DD79A4D, 0x33556633, 0x85941185,
+        0x45CF8A45, 0xF910E9F9, 0x02060402, 0x7F81FE7F, 0x50F0A050, 0x3C44783C, 0x9FBA259F, 0xA8E34BA8,
+        0x51F3A251, 0xA3FE5DA3, 0x40C08040, 0x8F8A058F, 0x92AD3F92, 0x9DBC219D, 0x38487038, 0xF504F1F5,
+        0xBCDF63BC, 0xB6C177B6, 0xDA75AFDA, 0x21634221, 0x10302010, 0xFF1AE5FF, 0xF30EFDF3, 0xD26DBFD2,
+        0xCD4C81CD, 0x0C14180C, 0x13352613, 0xEC2FC3EC, 0x5FE1BE5F, 0x97A23597, 0x44CC8844, 0x17392E17,
+        0xC45793C4, 0xA7F255A7, 0x7E82FC7E, 0x3D477A3D, 0x64ACC864, 0x5DE7BA5D, 0x192B3219, 0x7395E673,
+        0x60A0C060, 0x81981981, 0x4FD19E4F, 0xDC7FA3DC, 0x22664422, 0x2A7E542A, 0x90AB3B90, 0x88830B88,
+        0x46CA8C46, 0xEE29C7EE, 0xB8D36BB8, 0x143C2814, 0xDE79A7DE, 0x5EE2BC5E, 0x0B1D160B, 0xDB76ADDB,
+        0xE03BDBE0, 0x32566432, 0x3A4E743A, 0x0A1E140A, 0x49DB9249, 0x060A0C06, 0x246C4824, 0x5CE4B85C,
+        0xC25D9FC2, 0xD36EBDD3, 0xACEF43AC, 0x62A6C462, 0x91A83991, 0x95A43195, 0xE437D3E4, 0x798BF279,
+        0xE732D5E7, 0xC8438BC8, 0x37596E37, 0x6DB7DA6D, 0x8D8C018D, 0xD564B1D5, 0x4ED29C4E, 0xA9E049A9,
+        0x6CB4D86C, 0x56FAAC56, 0xF407F3F4, 0xEA25CFEA, 0x65AFCA65, 0x7A8EF47A, 0xAEE947AE, 0x08181008,
+        0xBAD56FBA, 0x7888F078, 0x256F4A25, 0x2E725C2E, 0x1C24381C, 0xA6F157A6, 0xB4C773B4, 0xC65197C6,
+        0xE823CBE8, 0xDD7CA1DD, 0x749CE874, 0x1F213E1F, 0x4BDD964B, 0xBDDC61BD, 0x8B860D8B, 0x8A850F8A,
+        0x7090E070, 0x3E427C3E, 0xB5C471B5, 0x66AACC66, 0x48D89048, 0x03050603, 0xF601F7F6, 0x0E121C0E,
+        0x61A3C261, 0x355F6A35, 0x57F9AE57, 0xB9D069B9, 0x86911786, 0xC15899C1, 0x1D273A1D, 0x9EB9279E,
+        0xE138D9E1, 0xF813EBF8, 0x98B32B98, 0x11332211, 0x69BBD269, 0xD970A9D9, 0x8E89078E, 0x94A73394,
+        0x9BB62D9B, 0x1E223C1E, 0x87921587, 0xE920C9E9, 0xCE4987CE, 0x55FFAA55, 0x28785028, 0xDF7AA5DF,
+        0x8C8F038C, 0xA1F859A1, 0x89800989, 0x0D171A0D, 0xBFDA65BF, 0xE631D7E6, 0x42C68442, 0x68B8D068,
+        0x41C38241, 0x99B02999, 0x2D775A2D, 0x0F111E0F, 0xB0CB7BB0, 0x54FCA854, 0xBBD66DBB, 0x163A2C16
+    );
+
+    /**
+     * Precomputed mixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $t3 = array(
+        0x6363A5C6, 0x7C7C84F8, 0x777799EE, 0x7B7B8DF6, 0xF2F20DFF, 0x6B6BBDD6, 0x6F6FB1DE, 0xC5C55491,
+        0x30305060, 0x01010302, 0x6767A9CE, 0x2B2B7D56, 0xFEFE19E7, 0xD7D762B5, 0xABABE64D, 0x76769AEC,
+        0xCACA458F, 0x82829D1F, 0xC9C94089, 0x7D7D87FA, 0xFAFA15EF, 0x5959EBB2, 0x4747C98E, 0xF0F00BFB,
+        0xADADEC41, 0xD4D467B3, 0xA2A2FD5F, 0xAFAFEA45, 0x9C9CBF23, 0xA4A4F753, 0x727296E4, 0xC0C05B9B,
+        0xB7B7C275, 0xFDFD1CE1, 0x9393AE3D, 0x26266A4C, 0x36365A6C, 0x3F3F417E, 0xF7F702F5, 0xCCCC4F83,
+        0x34345C68, 0xA5A5F451, 0xE5E534D1, 0xF1F108F9, 0x717193E2, 0xD8D873AB, 0x31315362, 0x15153F2A,
+        0x04040C08, 0xC7C75295, 0x23236546, 0xC3C35E9D, 0x18182830, 0x9696A137, 0x05050F0A, 0x9A9AB52F,
+        0x0707090E, 0x12123624, 0x80809B1B, 0xE2E23DDF, 0xEBEB26CD, 0x2727694E, 0xB2B2CD7F, 0x75759FEA,
+        0x09091B12, 0x83839E1D, 0x2C2C7458, 0x1A1A2E34, 0x1B1B2D36, 0x6E6EB2DC, 0x5A5AEEB4, 0xA0A0FB5B,
+        0x5252F6A4, 0x3B3B4D76, 0xD6D661B7, 0xB3B3CE7D, 0x29297B52, 0xE3E33EDD, 0x2F2F715E, 0x84849713,
+        0x5353F5A6, 0xD1D168B9, 0x00000000, 0xEDED2CC1, 0x20206040, 0xFCFC1FE3, 0xB1B1C879, 0x5B5BEDB6,
+        0x6A6ABED4, 0xCBCB468D, 0xBEBED967, 0x39394B72, 0x4A4ADE94, 0x4C4CD498, 0x5858E8B0, 0xCFCF4A85,
+        0xD0D06BBB, 0xEFEF2AC5, 0xAAAAE54F, 0xFBFB16ED, 0x4343C586, 0x4D4DD79A, 0x33335566, 0x85859411,
+        0x4545CF8A, 0xF9F910E9, 0x02020604, 0x7F7F81FE, 0x5050F0A0, 0x3C3C4478, 0x9F9FBA25, 0xA8A8E34B,
+        0x5151F3A2, 0xA3A3FE5D, 0x4040C080, 0x8F8F8A05, 0x9292AD3F, 0x9D9DBC21, 0x38384870, 0xF5F504F1,
+        0xBCBCDF63, 0xB6B6C177, 0xDADA75AF, 0x21216342, 0x10103020, 0xFFFF1AE5, 0xF3F30EFD, 0xD2D26DBF,
+        0xCDCD4C81, 0x0C0C1418, 0x13133526, 0xECEC2FC3, 0x5F5FE1BE, 0x9797A235, 0x4444CC88, 0x1717392E,
+        0xC4C45793, 0xA7A7F255, 0x7E7E82FC, 0x3D3D477A, 0x6464ACC8, 0x5D5DE7BA, 0x19192B32, 0x737395E6,
+        0x6060A0C0, 0x81819819, 0x4F4FD19E, 0xDCDC7FA3, 0x22226644, 0x2A2A7E54, 0x9090AB3B, 0x8888830B,
+        0x4646CA8C, 0xEEEE29C7, 0xB8B8D36B, 0x14143C28, 0xDEDE79A7, 0x5E5EE2BC, 0x0B0B1D16, 0xDBDB76AD,
+        0xE0E03BDB, 0x32325664, 0x3A3A4E74, 0x0A0A1E14, 0x4949DB92, 0x06060A0C, 0x24246C48, 0x5C5CE4B8,
+        0xC2C25D9F, 0xD3D36EBD, 0xACACEF43, 0x6262A6C4, 0x9191A839, 0x9595A431, 0xE4E437D3, 0x79798BF2,
+        0xE7E732D5, 0xC8C8438B, 0x3737596E, 0x6D6DB7DA, 0x8D8D8C01, 0xD5D564B1, 0x4E4ED29C, 0xA9A9E049,
+        0x6C6CB4D8, 0x5656FAAC, 0xF4F407F3, 0xEAEA25CF, 0x6565AFCA, 0x7A7A8EF4, 0xAEAEE947, 0x08081810,
+        0xBABAD56F, 0x787888F0, 0x25256F4A, 0x2E2E725C, 0x1C1C2438, 0xA6A6F157, 0xB4B4C773, 0xC6C65197,
+        0xE8E823CB, 0xDDDD7CA1, 0x74749CE8, 0x1F1F213E, 0x4B4BDD96, 0xBDBDDC61, 0x8B8B860D, 0x8A8A850F,
+        0x707090E0, 0x3E3E427C, 0xB5B5C471, 0x6666AACC, 0x4848D890, 0x03030506, 0xF6F601F7, 0x0E0E121C,
+        0x6161A3C2, 0x35355F6A, 0x5757F9AE, 0xB9B9D069, 0x86869117, 0xC1C15899, 0x1D1D273A, 0x9E9EB927,
+        0xE1E138D9, 0xF8F813EB, 0x9898B32B, 0x11113322, 0x6969BBD2, 0xD9D970A9, 0x8E8E8907, 0x9494A733,
+        0x9B9BB62D, 0x1E1E223C, 0x87879215, 0xE9E920C9, 0xCECE4987, 0x5555FFAA, 0x28287850, 0xDFDF7AA5,
+        0x8C8C8F03, 0xA1A1F859, 0x89898009, 0x0D0D171A, 0xBFBFDA65, 0xE6E631D7, 0x4242C684, 0x6868B8D0,
+        0x4141C382, 0x9999B029, 0x2D2D775A, 0x0F0F111E, 0xB0B0CB7B, 0x5454FCA8, 0xBBBBD66D, 0x16163A2C
+    );
+
+    /**
+     * Precomputed invMixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $dt0 = array(
+        0x51F4A750, 0x7E416553, 0x1A17A4C3, 0x3A275E96, 0x3BAB6BCB, 0x1F9D45F1, 0xACFA58AB, 0x4BE30393,
+        0x2030FA55, 0xAD766DF6, 0x88CC7691, 0xF5024C25, 0x4FE5D7FC, 0xC52ACBD7, 0x26354480, 0xB562A38F,
+        0xDEB15A49, 0x25BA1B67, 0x45EA0E98, 0x5DFEC0E1, 0xC32F7502, 0x814CF012, 0x8D4697A3, 0x6BD3F9C6,
+        0x038F5FE7, 0x15929C95, 0xBF6D7AEB, 0x955259DA, 0xD4BE832D, 0x587421D3, 0x49E06929, 0x8EC9C844,
+        0x75C2896A, 0xF48E7978, 0x99583E6B, 0x27B971DD, 0xBEE14FB6, 0xF088AD17, 0xC920AC66, 0x7DCE3AB4,
+        0x63DF4A18, 0xE51A3182, 0x97513360, 0x62537F45, 0xB16477E0, 0xBB6BAE84, 0xFE81A01C, 0xF9082B94,
+        0x70486858, 0x8F45FD19, 0x94DE6C87, 0x527BF8B7, 0xAB73D323, 0x724B02E2, 0xE31F8F57, 0x6655AB2A,
+        0xB2EB2807, 0x2FB5C203, 0x86C57B9A, 0xD33708A5, 0x302887F2, 0x23BFA5B2, 0x02036ABA, 0xED16825C,
+        0x8ACF1C2B, 0xA779B492, 0xF307F2F0, 0x4E69E2A1, 0x65DAF4CD, 0x0605BED5, 0xD134621F, 0xC4A6FE8A,
+        0x342E539D, 0xA2F355A0, 0x058AE132, 0xA4F6EB75, 0x0B83EC39, 0x4060EFAA, 0x5E719F06, 0xBD6E1051,
+        0x3E218AF9, 0x96DD063D, 0xDD3E05AE, 0x4DE6BD46, 0x91548DB5, 0x71C45D05, 0x0406D46F, 0x605015FF,
+        0x1998FB24, 0xD6BDE997, 0x894043CC, 0x67D99E77, 0xB0E842BD, 0x07898B88, 0xE7195B38, 0x79C8EEDB,
+        0xA17C0A47, 0x7C420FE9, 0xF8841EC9, 0x00000000, 0x09808683, 0x322BED48, 0x1E1170AC, 0x6C5A724E,
+        0xFD0EFFFB, 0x0F853856, 0x3DAED51E, 0x362D3927, 0x0A0FD964, 0x685CA621, 0x9B5B54D1, 0x24362E3A,
+        0x0C0A67B1, 0x9357E70F, 0xB4EE96D2, 0x1B9B919E, 0x80C0C54F, 0x61DC20A2, 0x5A774B69, 0x1C121A16,
+        0xE293BA0A, 0xC0A02AE5, 0x3C22E043, 0x121B171D, 0x0E090D0B, 0xF28BC7AD, 0x2DB6A8B9, 0x141EA9C8,
+        0x57F11985, 0xAF75074C, 0xEE99DDBB, 0xA37F60FD, 0xF701269F, 0x5C72F5BC, 0x44663BC5, 0x5BFB7E34,
+        0x8B432976, 0xCB23C6DC, 0xB6EDFC68, 0xB8E4F163, 0xD731DCCA, 0x42638510, 0x13972240, 0x84C61120,
+        0x854A247D, 0xD2BB3DF8, 0xAEF93211, 0xC729A16D, 0x1D9E2F4B, 0xDCB230F3, 0x0D8652EC, 0x77C1E3D0,
+        0x2BB3166C, 0xA970B999, 0x119448FA, 0x47E96422, 0xA8FC8CC4, 0xA0F03F1A, 0x567D2CD8, 0x223390EF,
+        0x87494EC7, 0xD938D1C1, 0x8CCAA2FE, 0x98D40B36, 0xA6F581CF, 0xA57ADE28, 0xDAB78E26, 0x3FADBFA4,
+        0x2C3A9DE4, 0x5078920D, 0x6A5FCC9B, 0x547E4662, 0xF68D13C2, 0x90D8B8E8, 0x2E39F75E, 0x82C3AFF5,
+        0x9F5D80BE, 0x69D0937C, 0x6FD52DA9, 0xCF2512B3, 0xC8AC993B, 0x10187DA7, 0xE89C636E, 0xDB3BBB7B,
+        0xCD267809, 0x6E5918F4, 0xEC9AB701, 0x834F9AA8, 0xE6956E65, 0xAAFFE67E, 0x21BCCF08, 0xEF15E8E6,
+        0xBAE79BD9, 0x4A6F36CE, 0xEA9F09D4, 0x29B07CD6, 0x31A4B2AF, 0x2A3F2331, 0xC6A59430, 0x35A266C0,
+        0x744EBC37, 0xFC82CAA6, 0xE090D0B0, 0x33A7D815, 0xF104984A, 0x41ECDAF7, 0x7FCD500E, 0x1791F62F,
+        0x764DD68D, 0x43EFB04D, 0xCCAA4D54, 0xE49604DF, 0x9ED1B5E3, 0x4C6A881B, 0xC12C1FB8, 0x4665517F,
+        0x9D5EEA04, 0x018C355D, 0xFA877473, 0xFB0B412E, 0xB3671D5A, 0x92DBD252, 0xE9105633, 0x6DD64713,
+        0x9AD7618C, 0x37A10C7A, 0x59F8148E, 0xEB133C89, 0xCEA927EE, 0xB761C935, 0xE11CE5ED, 0x7A47B13C,
+        0x9CD2DF59, 0x55F2733F, 0x1814CE79, 0x73C737BF, 0x53F7CDEA, 0x5FFDAA5B, 0xDF3D6F14, 0x7844DB86,
+        0xCAAFF381, 0xB968C43E, 0x3824342C, 0xC2A3405F, 0x161DC372, 0xBCE2250C, 0x283C498B, 0xFF0D9541,
+        0x39A80171, 0x080CB3DE, 0xD8B4E49C, 0x6456C190, 0x7BCB8461, 0xD532B670, 0x486C5C74, 0xD0B85742
+    );
+
+    /**
+     * Precomputed invMixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $dt1 = array(
+        0x5051F4A7, 0x537E4165, 0xC31A17A4, 0x963A275E, 0xCB3BAB6B, 0xF11F9D45, 0xABACFA58, 0x934BE303,
+        0x552030FA, 0xF6AD766D, 0x9188CC76, 0x25F5024C, 0xFC4FE5D7, 0xD7C52ACB, 0x80263544, 0x8FB562A3,
+        0x49DEB15A, 0x6725BA1B, 0x9845EA0E, 0xE15DFEC0, 0x02C32F75, 0x12814CF0, 0xA38D4697, 0xC66BD3F9,
+        0xE7038F5F, 0x9515929C, 0xEBBF6D7A, 0xDA955259, 0x2DD4BE83, 0xD3587421, 0x2949E069, 0x448EC9C8,
+        0x6A75C289, 0x78F48E79, 0x6B99583E, 0xDD27B971, 0xB6BEE14F, 0x17F088AD, 0x66C920AC, 0xB47DCE3A,
+        0x1863DF4A, 0x82E51A31, 0x60975133, 0x4562537F, 0xE0B16477, 0x84BB6BAE, 0x1CFE81A0, 0x94F9082B,
+        0x58704868, 0x198F45FD, 0x8794DE6C, 0xB7527BF8, 0x23AB73D3, 0xE2724B02, 0x57E31F8F, 0x2A6655AB,
+        0x07B2EB28, 0x032FB5C2, 0x9A86C57B, 0xA5D33708, 0xF2302887, 0xB223BFA5, 0xBA02036A, 0x5CED1682,
+        0x2B8ACF1C, 0x92A779B4, 0xF0F307F2, 0xA14E69E2, 0xCD65DAF4, 0xD50605BE, 0x1FD13462, 0x8AC4A6FE,
+        0x9D342E53, 0xA0A2F355, 0x32058AE1, 0x75A4F6EB, 0x390B83EC, 0xAA4060EF, 0x065E719F, 0x51BD6E10,
+        0xF93E218A, 0x3D96DD06, 0xAEDD3E05, 0x464DE6BD, 0xB591548D, 0x0571C45D, 0x6F0406D4, 0xFF605015,
+        0x241998FB, 0x97D6BDE9, 0xCC894043, 0x7767D99E, 0xBDB0E842, 0x8807898B, 0x38E7195B, 0xDB79C8EE,
+        0x47A17C0A, 0xE97C420F, 0xC9F8841E, 0x00000000, 0x83098086, 0x48322BED, 0xAC1E1170, 0x4E6C5A72,
+        0xFBFD0EFF, 0x560F8538, 0x1E3DAED5, 0x27362D39, 0x640A0FD9, 0x21685CA6, 0xD19B5B54, 0x3A24362E,
+        0xB10C0A67, 0x0F9357E7, 0xD2B4EE96, 0x9E1B9B91, 0x4F80C0C5, 0xA261DC20, 0x695A774B, 0x161C121A,
+        0x0AE293BA, 0xE5C0A02A, 0x433C22E0, 0x1D121B17, 0x0B0E090D, 0xADF28BC7, 0xB92DB6A8, 0xC8141EA9,
+        0x8557F119, 0x4CAF7507, 0xBBEE99DD, 0xFDA37F60, 0x9FF70126, 0xBC5C72F5, 0xC544663B, 0x345BFB7E,
+        0x768B4329, 0xDCCB23C6, 0x68B6EDFC, 0x63B8E4F1, 0xCAD731DC, 0x10426385, 0x40139722, 0x2084C611,
+        0x7D854A24, 0xF8D2BB3D, 0x11AEF932, 0x6DC729A1, 0x4B1D9E2F, 0xF3DCB230, 0xEC0D8652, 0xD077C1E3,
+        0x6C2BB316, 0x99A970B9, 0xFA119448, 0x2247E964, 0xC4A8FC8C, 0x1AA0F03F, 0xD8567D2C, 0xEF223390,
+        0xC787494E, 0xC1D938D1, 0xFE8CCAA2, 0x3698D40B, 0xCFA6F581, 0x28A57ADE, 0x26DAB78E, 0xA43FADBF,
+        0xE42C3A9D, 0x0D507892, 0x9B6A5FCC, 0x62547E46, 0xC2F68D13, 0xE890D8B8, 0x5E2E39F7, 0xF582C3AF,
+        0xBE9F5D80, 0x7C69D093, 0xA96FD52D, 0xB3CF2512, 0x3BC8AC99, 0xA710187D, 0x6EE89C63, 0x7BDB3BBB,
+        0x09CD2678, 0xF46E5918, 0x01EC9AB7, 0xA8834F9A, 0x65E6956E, 0x7EAAFFE6, 0x0821BCCF, 0xE6EF15E8,
+        0xD9BAE79B, 0xCE4A6F36, 0xD4EA9F09, 0xD629B07C, 0xAF31A4B2, 0x312A3F23, 0x30C6A594, 0xC035A266,
+        0x37744EBC, 0xA6FC82CA, 0xB0E090D0, 0x1533A7D8, 0x4AF10498, 0xF741ECDA, 0x0E7FCD50, 0x2F1791F6,
+        0x8D764DD6, 0x4D43EFB0, 0x54CCAA4D, 0xDFE49604, 0xE39ED1B5, 0x1B4C6A88, 0xB8C12C1F, 0x7F466551,
+        0x049D5EEA, 0x5D018C35, 0x73FA8774, 0x2EFB0B41, 0x5AB3671D, 0x5292DBD2, 0x33E91056, 0x136DD647,
+        0x8C9AD761, 0x7A37A10C, 0x8E59F814, 0x89EB133C, 0xEECEA927, 0x35B761C9, 0xEDE11CE5, 0x3C7A47B1,
+        0x599CD2DF, 0x3F55F273, 0x791814CE, 0xBF73C737, 0xEA53F7CD, 0x5B5FFDAA, 0x14DF3D6F, 0x867844DB,
+        0x81CAAFF3, 0x3EB968C4, 0x2C382434, 0x5FC2A340, 0x72161DC3, 0x0CBCE225, 0x8B283C49, 0x41FF0D95,
+        0x7139A801, 0xDE080CB3, 0x9CD8B4E4, 0x906456C1, 0x617BCB84, 0x70D532B6, 0x74486C5C, 0x42D0B857
+    );
+
+    /**
+     * Precomputed invMixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $dt2 = array(
+        0xA75051F4, 0x65537E41, 0xA4C31A17, 0x5E963A27, 0x6BCB3BAB, 0x45F11F9D, 0x58ABACFA, 0x03934BE3,
+        0xFA552030, 0x6DF6AD76, 0x769188CC, 0x4C25F502, 0xD7FC4FE5, 0xCBD7C52A, 0x44802635, 0xA38FB562,
+        0x5A49DEB1, 0x1B6725BA, 0x0E9845EA, 0xC0E15DFE, 0x7502C32F, 0xF012814C, 0x97A38D46, 0xF9C66BD3,
+        0x5FE7038F, 0x9C951592, 0x7AEBBF6D, 0x59DA9552, 0x832DD4BE, 0x21D35874, 0x692949E0, 0xC8448EC9,
+        0x896A75C2, 0x7978F48E, 0x3E6B9958, 0x71DD27B9, 0x4FB6BEE1, 0xAD17F088, 0xAC66C920, 0x3AB47DCE,
+        0x4A1863DF, 0x3182E51A, 0x33609751, 0x7F456253, 0x77E0B164, 0xAE84BB6B, 0xA01CFE81, 0x2B94F908,
+        0x68587048, 0xFD198F45, 0x6C8794DE, 0xF8B7527B, 0xD323AB73, 0x02E2724B, 0x8F57E31F, 0xAB2A6655,
+        0x2807B2EB, 0xC2032FB5, 0x7B9A86C5, 0x08A5D337, 0x87F23028, 0xA5B223BF, 0x6ABA0203, 0x825CED16,
+        0x1C2B8ACF, 0xB492A779, 0xF2F0F307, 0xE2A14E69, 0xF4CD65DA, 0xBED50605, 0x621FD134, 0xFE8AC4A6,
+        0x539D342E, 0x55A0A2F3, 0xE132058A, 0xEB75A4F6, 0xEC390B83, 0xEFAA4060, 0x9F065E71, 0x1051BD6E,
+        0x8AF93E21, 0x063D96DD, 0x05AEDD3E, 0xBD464DE6, 0x8DB59154, 0x5D0571C4, 0xD46F0406, 0x15FF6050,
+        0xFB241998, 0xE997D6BD, 0x43CC8940, 0x9E7767D9, 0x42BDB0E8, 0x8B880789, 0x5B38E719, 0xEEDB79C8,
+        0x0A47A17C, 0x0FE97C42, 0x1EC9F884, 0x00000000, 0x86830980, 0xED48322B, 0x70AC1E11, 0x724E6C5A,
+        0xFFFBFD0E, 0x38560F85, 0xD51E3DAE, 0x3927362D, 0xD9640A0F, 0xA621685C, 0x54D19B5B, 0x2E3A2436,
+        0x67B10C0A, 0xE70F9357, 0x96D2B4EE, 0x919E1B9B, 0xC54F80C0, 0x20A261DC, 0x4B695A77, 0x1A161C12,
+        0xBA0AE293, 0x2AE5C0A0, 0xE0433C22, 0x171D121B, 0x0D0B0E09, 0xC7ADF28B, 0xA8B92DB6, 0xA9C8141E,
+        0x198557F1, 0x074CAF75, 0xDDBBEE99, 0x60FDA37F, 0x269FF701, 0xF5BC5C72, 0x3BC54466, 0x7E345BFB,
+        0x29768B43, 0xC6DCCB23, 0xFC68B6ED, 0xF163B8E4, 0xDCCAD731, 0x85104263, 0x22401397, 0x112084C6,
+        0x247D854A, 0x3DF8D2BB, 0x3211AEF9, 0xA16DC729, 0x2F4B1D9E, 0x30F3DCB2, 0x52EC0D86, 0xE3D077C1,
+        0x166C2BB3, 0xB999A970, 0x48FA1194, 0x642247E9, 0x8CC4A8FC, 0x3F1AA0F0, 0x2CD8567D, 0x90EF2233,
+        0x4EC78749, 0xD1C1D938, 0xA2FE8CCA, 0x0B3698D4, 0x81CFA6F5, 0xDE28A57A, 0x8E26DAB7, 0xBFA43FAD,
+        0x9DE42C3A, 0x920D5078, 0xCC9B6A5F, 0x4662547E, 0x13C2F68D, 0xB8E890D8, 0xF75E2E39, 0xAFF582C3,
+        0x80BE9F5D, 0x937C69D0, 0x2DA96FD5, 0x12B3CF25, 0x993BC8AC, 0x7DA71018, 0x636EE89C, 0xBB7BDB3B,
+        0x7809CD26, 0x18F46E59, 0xB701EC9A, 0x9AA8834F, 0x6E65E695, 0xE67EAAFF, 0xCF0821BC, 0xE8E6EF15,
+        0x9BD9BAE7, 0x36CE4A6F, 0x09D4EA9F, 0x7CD629B0, 0xB2AF31A4, 0x23312A3F, 0x9430C6A5, 0x66C035A2,
+        0xBC37744E, 0xCAA6FC82, 0xD0B0E090, 0xD81533A7, 0x984AF104, 0xDAF741EC, 0x500E7FCD, 0xF62F1791,
+        0xD68D764D, 0xB04D43EF, 0x4D54CCAA, 0x04DFE496, 0xB5E39ED1, 0x881B4C6A, 0x1FB8C12C, 0x517F4665,
+        0xEA049D5E, 0x355D018C, 0x7473FA87, 0x412EFB0B, 0x1D5AB367, 0xD25292DB, 0x5633E910, 0x47136DD6,
+        0x618C9AD7, 0x0C7A37A1, 0x148E59F8, 0x3C89EB13, 0x27EECEA9, 0xC935B761, 0xE5EDE11C, 0xB13C7A47,
+        0xDF599CD2, 0x733F55F2, 0xCE791814, 0x37BF73C7, 0xCDEA53F7, 0xAA5B5FFD, 0x6F14DF3D, 0xDB867844,
+        0xF381CAAF, 0xC43EB968, 0x342C3824, 0x405FC2A3, 0xC372161D, 0x250CBCE2, 0x498B283C, 0x9541FF0D,
+        0x017139A8, 0xB3DE080C, 0xE49CD8B4, 0xC1906456, 0x84617BCB, 0xB670D532, 0x5C74486C, 0x5742D0B8
+    );
+
+    /**
+     * Precomputed invMixColumns table
+     *
+     * @see Crypt_Rijndael:_encryptBlock()
+     * @see Crypt_Rijndael:_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $dt3 = array(
+        0xF4A75051, 0x4165537E, 0x17A4C31A, 0x275E963A, 0xAB6BCB3B, 0x9D45F11F, 0xFA58ABAC, 0xE303934B,
+        0x30FA5520, 0x766DF6AD, 0xCC769188, 0x024C25F5, 0xE5D7FC4F, 0x2ACBD7C5, 0x35448026, 0x62A38FB5,
+        0xB15A49DE, 0xBA1B6725, 0xEA0E9845, 0xFEC0E15D, 0x2F7502C3, 0x4CF01281, 0x4697A38D, 0xD3F9C66B,
+        0x8F5FE703, 0x929C9515, 0x6D7AEBBF, 0x5259DA95, 0xBE832DD4, 0x7421D358, 0xE0692949, 0xC9C8448E,
+        0xC2896A75, 0x8E7978F4, 0x583E6B99, 0xB971DD27, 0xE14FB6BE, 0x88AD17F0, 0x20AC66C9, 0xCE3AB47D,
+        0xDF4A1863, 0x1A3182E5, 0x51336097, 0x537F4562, 0x6477E0B1, 0x6BAE84BB, 0x81A01CFE, 0x082B94F9,
+        0x48685870, 0x45FD198F, 0xDE6C8794, 0x7BF8B752, 0x73D323AB, 0x4B02E272, 0x1F8F57E3, 0x55AB2A66,
+        0xEB2807B2, 0xB5C2032F, 0xC57B9A86, 0x3708A5D3, 0x2887F230, 0xBFA5B223, 0x036ABA02, 0x16825CED,
+        0xCF1C2B8A, 0x79B492A7, 0x07F2F0F3, 0x69E2A14E, 0xDAF4CD65, 0x05BED506, 0x34621FD1, 0xA6FE8AC4,
+        0x2E539D34, 0xF355A0A2, 0x8AE13205, 0xF6EB75A4, 0x83EC390B, 0x60EFAA40, 0x719F065E, 0x6E1051BD,
+        0x218AF93E, 0xDD063D96, 0x3E05AEDD, 0xE6BD464D, 0x548DB591, 0xC45D0571, 0x06D46F04, 0x5015FF60,
+        0x98FB2419, 0xBDE997D6, 0x4043CC89, 0xD99E7767, 0xE842BDB0, 0x898B8807, 0x195B38E7, 0xC8EEDB79,
+        0x7C0A47A1, 0x420FE97C, 0x841EC9F8, 0x00000000, 0x80868309, 0x2BED4832, 0x1170AC1E, 0x5A724E6C,
+        0x0EFFFBFD, 0x8538560F, 0xAED51E3D, 0x2D392736, 0x0FD9640A, 0x5CA62168, 0x5B54D19B, 0x362E3A24,
+        0x0A67B10C, 0x57E70F93, 0xEE96D2B4, 0x9B919E1B, 0xC0C54F80, 0xDC20A261, 0x774B695A, 0x121A161C,
+        0x93BA0AE2, 0xA02AE5C0, 0x22E0433C, 0x1B171D12, 0x090D0B0E, 0x8BC7ADF2, 0xB6A8B92D, 0x1EA9C814,
+        0xF1198557, 0x75074CAF, 0x99DDBBEE, 0x7F60FDA3, 0x01269FF7, 0x72F5BC5C, 0x663BC544, 0xFB7E345B,
+        0x4329768B, 0x23C6DCCB, 0xEDFC68B6, 0xE4F163B8, 0x31DCCAD7, 0x63851042, 0x97224013, 0xC6112084,
+        0x4A247D85, 0xBB3DF8D2, 0xF93211AE, 0x29A16DC7, 0x9E2F4B1D, 0xB230F3DC, 0x8652EC0D, 0xC1E3D077,
+        0xB3166C2B, 0x70B999A9, 0x9448FA11, 0xE9642247, 0xFC8CC4A8, 0xF03F1AA0, 0x7D2CD856, 0x3390EF22,
+        0x494EC787, 0x38D1C1D9, 0xCAA2FE8C, 0xD40B3698, 0xF581CFA6, 0x7ADE28A5, 0xB78E26DA, 0xADBFA43F,
+        0x3A9DE42C, 0x78920D50, 0x5FCC9B6A, 0x7E466254, 0x8D13C2F6, 0xD8B8E890, 0x39F75E2E, 0xC3AFF582,
+        0x5D80BE9F, 0xD0937C69, 0xD52DA96F, 0x2512B3CF, 0xAC993BC8, 0x187DA710, 0x9C636EE8, 0x3BBB7BDB,
+        0x267809CD, 0x5918F46E, 0x9AB701EC, 0x4F9AA883, 0x956E65E6, 0xFFE67EAA, 0xBCCF0821, 0x15E8E6EF,
+        0xE79BD9BA, 0x6F36CE4A, 0x9F09D4EA, 0xB07CD629, 0xA4B2AF31, 0x3F23312A, 0xA59430C6, 0xA266C035,
+        0x4EBC3774, 0x82CAA6FC, 0x90D0B0E0, 0xA7D81533, 0x04984AF1, 0xECDAF741, 0xCD500E7F, 0x91F62F17,
+        0x4DD68D76, 0xEFB04D43, 0xAA4D54CC, 0x9604DFE4, 0xD1B5E39E, 0x6A881B4C, 0x2C1FB8C1, 0x65517F46,
+        0x5EEA049D, 0x8C355D01, 0x877473FA, 0x0B412EFB, 0x671D5AB3, 0xDBD25292, 0x105633E9, 0xD647136D,
+        0xD7618C9A, 0xA10C7A37, 0xF8148E59, 0x133C89EB, 0xA927EECE, 0x61C935B7, 0x1CE5EDE1, 0x47B13C7A,
+        0xD2DF599C, 0xF2733F55, 0x14CE7918, 0xC737BF73, 0xF7CDEA53, 0xFDAA5B5F, 0x3D6F14DF, 0x44DB8678,
+        0xAFF381CA, 0x68C43EB9, 0x24342C38, 0xA3405FC2, 0x1DC37216, 0xE2250CBC, 0x3C498B28, 0x0D9541FF,
+        0xA8017139, 0x0CB3DE08, 0xB4E49CD8, 0x56C19064, 0xCB84617B, 0x32B670D5, 0x6C5C7448, 0xB85742D0
+    );
+
+    /**
+     * The SubByte S-Box
+     *
+     * @see Crypt_Rijndael::_encryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $sbox = array(
+        0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76,
+        0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0,
+        0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15,
+        0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75,
+        0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84,
+        0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF,
+        0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8,
+        0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2,
+        0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73,
+        0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB,
+        0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79,
+        0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08,
+        0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A,
+        0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E,
+        0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF,
+        0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16
+    );
+
+    /**
+     * The inverse SubByte S-Box
+     *
+     * @see Crypt_Rijndael::_decryptBlock()
+     * @var Array
+     * @access private
+     */
+    var $isbox = array(
+        0x52, 0x09, 0x6A, 0xD5, 0x30, 0x36, 0xA5, 0x38, 0xBF, 0x40, 0xA3, 0x9E, 0x81, 0xF3, 0xD7, 0xFB,
+        0x7C, 0xE3, 0x39, 0x82, 0x9B, 0x2F, 0xFF, 0x87, 0x34, 0x8E, 0x43, 0x44, 0xC4, 0xDE, 0xE9, 0xCB,
+        0x54, 0x7B, 0x94, 0x32, 0xA6, 0xC2, 0x23, 0x3D, 0xEE, 0x4C, 0x95, 0x0B, 0x42, 0xFA, 0xC3, 0x4E,
+        0x08, 0x2E, 0xA1, 0x66, 0x28, 0xD9, 0x24, 0xB2, 0x76, 0x5B, 0xA2, 0x49, 0x6D, 0x8B, 0xD1, 0x25,
+        0x72, 0xF8, 0xF6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xD4, 0xA4, 0x5C, 0xCC, 0x5D, 0x65, 0xB6, 0x92,
+        0x6C, 0x70, 0x48, 0x50, 0xFD, 0xED, 0xB9, 0xDA, 0x5E, 0x15, 0x46, 0x57, 0xA7, 0x8D, 0x9D, 0x84,
+        0x90, 0xD8, 0xAB, 0x00, 0x8C, 0xBC, 0xD3, 0x0A, 0xF7, 0xE4, 0x58, 0x05, 0xB8, 0xB3, 0x45, 0x06,
+        0xD0, 0x2C, 0x1E, 0x8F, 0xCA, 0x3F, 0x0F, 0x02, 0xC1, 0xAF, 0xBD, 0x03, 0x01, 0x13, 0x8A, 0x6B,
+        0x3A, 0x91, 0x11, 0x41, 0x4F, 0x67, 0xDC, 0xEA, 0x97, 0xF2, 0xCF, 0xCE, 0xF0, 0xB4, 0xE6, 0x73,
+        0x96, 0xAC, 0x74, 0x22, 0xE7, 0xAD, 0x35, 0x85, 0xE2, 0xF9, 0x37, 0xE8, 0x1C, 0x75, 0xDF, 0x6E,
+        0x47, 0xF1, 0x1A, 0x71, 0x1D, 0x29, 0xC5, 0x89, 0x6F, 0xB7, 0x62, 0x0E, 0xAA, 0x18, 0xBE, 0x1B,
+        0xFC, 0x56, 0x3E, 0x4B, 0xC6, 0xD2, 0x79, 0x20, 0x9A, 0xDB, 0xC0, 0xFE, 0x78, 0xCD, 0x5A, 0xF4,
+        0x1F, 0xDD, 0xA8, 0x33, 0x88, 0x07, 0xC7, 0x31, 0xB1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xEC, 0x5F,
+        0x60, 0x51, 0x7F, 0xA9, 0x19, 0xB5, 0x4A, 0x0D, 0x2D, 0xE5, 0x7A, 0x9F, 0x93, 0xC9, 0x9C, 0xEF,
+        0xA0, 0xE0, 0x3B, 0x4D, 0xAE, 0x2A, 0xF5, 0xB0, 0xC8, 0xEB, 0xBB, 0x3C, 0x83, 0x53, 0x99, 0x61,
+        0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D
+    );
+
+    /**
+     * Default Constructor.
+     *
+     * Determines whether or not the mcrypt extension should be used.
+     *
+     * $mode could be:
+     *
+     * - CRYPT_RIJNDAEL_MODE_ECB
+     *
+     * - CRYPT_RIJNDAEL_MODE_CBC
+     *
+     * - CRYPT_RIJNDAEL_MODE_CTR
+     *
+     * - CRYPT_RIJNDAEL_MODE_CFB
+     *
+     * - CRYPT_RIJNDAEL_MODE_OFB
+     *
+     * If not explictly set, CRYPT_RIJNDAEL_MODE_CBC will be used.
+     *
+     * @see Crypt_Base::Crypt_Base()
+     * @param optional Integer $mode
+     * @access public
+     */
+    function Crypt_Rijndael($mode = CRYPT_RIJNDAEL_MODE_CBC)
+    {
+        parent::Crypt_Base($mode);
+    }
+
+    /**
+     * Sets the key.
+     *
+     * Keys can be of any length.  Rijndael, itself, requires the use of a key that's between 128-bits and 256-bits long and
+     * whose length is a multiple of 32.  If the key is less than 256-bits and the key length isn't set, we round the length
+     * up to the closest valid key length, padding $key with null bytes.  If the key is more than 256-bits, we trim the
+     * excess bits.
+     *
+     * If the key is not explicitly set, it'll be assumed to be all null bytes.
+     *
+     * Note: 160/224-bit keys must explicitly set by setKeyLength(), otherwise they will be round/pad up to 192/256 bits.
+     *
+     * @see Crypt_Base:setKey()
+     * @see setKeyLength()
+     * @access public
+     * @param String $key
+     */
+    function setKey($key)
+    {
+        parent::setKey($key);
+
+        if (!$this->explicit_key_length) {
+            $length = strlen($key);
+            switch (true) {
+                case $length <= 16:
+                    $this->key_size = 16;
+                    break;
+                case $length <= 24:
+                    $this->key_size = 24;
+                    break;
+                default:
+                    $this->key_size = 32;
+            }
+            $this->_setupEngine();
+        }
+    }
+
+    /**
+     * Sets the key length
+     *
+     * Valid key lengths are 128, 160, 192, 224, and 256.  If the length is less than 128, it will be rounded up to
+     * 128.  If the length is greater than 128 and invalid, it will be rounded down to the closest valid amount.
+     *
+     * Note: phpseclib extends Rijndael (and AES) for using 160- and 224-bit keys but they are officially not defined
+     *       and the most (if not all) implementations are not able using 160/224-bit keys but round/pad them up to
+     *       192/256 bits as, for example, mcrypt will do.
+     *
+     *       That said, if you want be compatible with other Rijndael and AES implementations,
+     *       you should not setKeyLength(160) or setKeyLength(224).
+     *
+     * Additional: In case of 160- and 224-bit keys, phpseclib will/can, for that reason, not use
+     *             the mcrypt php extention, even if available.
+     *             This results then in slower encryption.
+     *
+     * @access public
+     * @param Integer $length
+     */
+    function setKeyLength($length)
+    {
+        switch (true) {
+            case $length == 160:
+                $this->key_size = 20;
+                break;
+            case $length == 224:
+                $this->key_size = 28;
+                break;
+            case $length <= 128:
+                $this->key_size = 16;
+                break;
+            case $length <= 192:
+                $this->key_size = 24;
+                break;
+            default:
+                $this->key_size = 32;
+        }
+
+        $this->explicit_key_length = true;
+        $this->changed = true;
+        $this->_setupEngine();
+    }
+
+    /**
+     * Sets the block length
+     *
+     * Valid block lengths are 128, 160, 192, 224, and 256.  If the length is less than 128, it will be rounded up to
+     * 128.  If the length is greater than 128 and invalid, it will be rounded down to the closest valid amount.
+     *
+     * @access public
+     * @param Integer $length
+     */
+    function setBlockLength($length)
+    {
+        $length >>= 5;
+        if ($length > 8) {
+            $length = 8;
+        } else if ($length < 4) {
+            $length = 4;
+        }
+        $this->Nb = $length;
+        $this->block_size = $length << 2;
+        $this->changed = true;
+        $this->_setupEngine();
+    }
+
+    /**
+     * Setup the fastest possible $engine
+     *
+     * Determines if the mcrypt (MODE_MCRYPT) $engine available
+     * and usable for the current $block_size and $key_size.
+     *
+     * If not, the slower MODE_INTERNAL $engine will be set.
+     *
+     * @see setKey()
+     * @see setKeyLength()
+     * @see setBlockLength()
+     * @access private
+     */
+    function _setupEngine()
+    {
+        if (constant('CRYPT_' . $this->const_namespace . '_MODE') == CRYPT_MODE_INTERNAL) {
+            // No mcrypt support at all for rijndael
+            return;
+        }
+
+        // The required mcrypt module name for the current $block_size of rijndael
+        $cipher_name_mcrypt = 'rijndael-' . ($this->block_size << 3);
+
+        // Determining the availibility/usability of $cipher_name_mcrypt
+        switch (true) {
+            case $this->key_size % 8: // mcrypt is not usable for 160/224-bit keys, only for 128/192/256-bit keys
+            case !in_array($cipher_name_mcrypt, mcrypt_list_algorithms()): // $cipher_name_mcrypt is not available for the current $block_size
+                $engine = CRYPT_MODE_INTERNAL;
+                break;
+            default:
+                $engine = CRYPT_MODE_MCRYPT;
+        }
+
+        if ($this->engine == $engine && $this->cipher_name_mcrypt == $cipher_name_mcrypt) {
+            // allready set, so we not unnecessary close $this->enmcrypt/demcrypt/ecb
+            return;
+        }
+
+        // Set the $engine
+        $this->engine = $engine;
+        $this->cipher_name_mcrypt = $cipher_name_mcrypt;
+
+        if ($this->enmcrypt) {
+            // Closing the current mcrypt resource(s). _mcryptSetup() will, if needed,
+            // (re)open them with the module named in $this->cipher_name_mcrypt
+            mcrypt_module_close($this->enmcrypt);
+            mcrypt_module_close($this->demcrypt);
+            $this->enmcrypt = null;
+            $this->demcrypt = null;
+
+            if ($this->ecb) {
+                mcrypt_module_close($this->ecb);
+                $this->ecb = null;
+            }
+        }
+    }
+
+    /**
+     * Setup the CRYPT_MODE_MCRYPT $engine
+     *
+     * @see Crypt_Base::_setupMcrypt()
+     * @access private
+     */
+    function _setupMcrypt()
+    {
+        $this->key = str_pad(substr($this->key, 0, $this->key_size), $this->key_size, "\0");
+        parent::_setupMcrypt();
+    }
+
+    /**
+     * Encrypts a block
+     *
+     * @access private
+     * @param String $in
+     * @return String
+     */
+    function _encryptBlock($in)
+    {
+        static $t0, $t1, $t2, $t3, $sbox;
+        if (!$t0) {
+            for ($i = 0; $i < 256; ++$i) {
+                $t0[] = (int)$this->t0[$i];
+                $t1[] = (int)$this->t1[$i];
+                $t2[] = (int)$this->t2[$i];
+                $t3[] = (int)$this->t3[$i];
+                $sbox[] = (int)$this->sbox[$i];
+            }
+        }
+
+        $state = array();
+        $words = unpack('N*', $in);
+
+        $c = $this->c;
+        $w = $this->w;
+        $Nb = $this->Nb;
+        $Nr = $this->Nr;
+
+        // addRoundKey
+        $i = -1;
+        foreach ($words as $word) {
+            $state[] = $word ^ $w[0][++$i];
+        }
+
+        // fips-197.pdf#page=19, "Figure 5. Pseudo Code for the Cipher", states that this loop has four components -
+        // subBytes, shiftRows, mixColumns, and addRoundKey. fips-197.pdf#page=30, "Implementation Suggestions Regarding
+        // Various Platforms" suggests that performs enhanced implementations are described in Rijndael-ammended.pdf.
+        // Rijndael-ammended.pdf#page=20, "Implementation aspects / 32-bit processor", discusses such an optimization.
+        // Unfortunately, the description given there is not quite correct.  Per aes.spec.v316.pdf#page=19 [1],
+        // equation (7.4.7) is supposed to use addition instead of subtraction, so we'll do that here, as well.
+
+        // [1] http://fp.gladman.plus.com/cryptography_technology/rijndael/aes.spec.v316.pdf
+        $temp = array();
+        for ($round = 1; $round < $Nr; ++$round) {
+            $i = 0; // $c[0] == 0
+            $j = $c[1];
+            $k = $c[2];
+            $l = $c[3];
+
+            while ($i < $Nb) {
+                $temp[$i] = $t0[$state[$i] >> 24 & 0x000000FF] ^
+                            $t1[$state[$j] >> 16 & 0x000000FF] ^
+                            $t2[$state[$k] >>  8 & 0x000000FF] ^
+                            $t3[$state[$l]       & 0x000000FF] ^
+                            $w[$round][$i];
+                ++$i;
+                $j = ($j + 1) % $Nb;
+                $k = ($k + 1) % $Nb;
+                $l = ($l + 1) % $Nb;
+            }
+            $state = $temp;
+        }
+
+        // subWord
+        for ($i = 0; $i < $Nb; ++$i) {
+            $state[$i] =   $sbox[$state[$i]       & 0x000000FF]        |
+                          ($sbox[$state[$i] >>  8 & 0x000000FF] <<  8) |
+                          ($sbox[$state[$i] >> 16 & 0x000000FF] << 16) |
+                          ($sbox[$state[$i] >> 24 & 0x000000FF] << 24);
+        }
+
+        // shiftRows + addRoundKey
+        $i = 0; // $c[0] == 0
+        $j = $c[1];
+        $k = $c[2];
+        $l = $c[3];
+        while ($i < $Nb) {
+            $temp[$i] = ($state[$i] & 0xFF000000) ^
+                        ($state[$j] & 0x00FF0000) ^
+                        ($state[$k] & 0x0000FF00) ^
+                        ($state[$l] & 0x000000FF) ^
+                         $w[$Nr][$i];
+            ++$i;
+            $j = ($j + 1) % $Nb;
+            $k = ($k + 1) % $Nb;
+            $l = ($l + 1) % $Nb;
+        }
+
+        switch ($Nb) {
+            case 8:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5], $temp[6], $temp[7]);
+            case 7:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5], $temp[6]);
+            case 6:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5]);
+            case 5:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4]);
+            default:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3]);
+        }
+    }
+
+    /**
+     * Decrypts a block
+     *
+     * @access private
+     * @param String $in
+     * @return String
+     */
+    function _decryptBlock($in)
+    {
+        static $dt0, $dt1, $dt2, $dt3, $isbox;
+        if (!$dt0) {
+            for ($i = 0; $i < 256; ++$i) {
+                $dt0[] = (int)$this->dt0[$i];
+                $dt1[] = (int)$this->dt1[$i];
+                $dt2[] = (int)$this->dt2[$i];
+                $dt3[] = (int)$this->dt3[$i];
+                $isbox[] = (int)$this->isbox[$i];
+            }
+        }
+
+        $state = array();
+        $words = unpack('N*', $in);
+
+        $c  = $this->c;
+        $dw = $this->dw;
+        $Nb = $this->Nb;
+        $Nr = $this->Nr;
+
+        // addRoundKey
+        $i = -1;
+        foreach ($words as $word) {
+            $state[] = $word ^ $dw[$Nr][++$i];
+        }
+
+        $temp = array();
+        for ($round = $Nr - 1; $round > 0; --$round) {
+            $i = 0; // $c[0] == 0
+            $j = $Nb - $c[1];
+            $k = $Nb - $c[2];
+            $l = $Nb - $c[3];
+
+            while ($i < $Nb) {
+                $temp[$i] = $dt0[$state[$i] >> 24 & 0x000000FF] ^
+                            $dt1[$state[$j] >> 16 & 0x000000FF] ^
+                            $dt2[$state[$k] >>  8 & 0x000000FF] ^
+                            $dt3[$state[$l]       & 0x000000FF] ^
+                            $dw[$round][$i];
+                ++$i;
+                $j = ($j + 1) % $Nb;
+                $k = ($k + 1) % $Nb;
+                $l = ($l + 1) % $Nb;
+            }
+            $state = $temp;
+        }
+
+        // invShiftRows + invSubWord + addRoundKey
+        $i = 0; // $c[0] == 0
+        $j = $Nb - $c[1];
+        $k = $Nb - $c[2];
+        $l = $Nb - $c[3];
+
+        while ($i < $Nb) {
+            $word = ($state[$i] & 0xFF000000) |
+                    ($state[$j] & 0x00FF0000) |
+                    ($state[$k] & 0x0000FF00) |
+                    ($state[$l] & 0x000000FF);
+
+            $temp[$i] = $dw[0][$i] ^ ($isbox[$word       & 0x000000FF]        |
+                                     ($isbox[$word >>  8 & 0x000000FF] <<  8) |
+                                     ($isbox[$word >> 16 & 0x000000FF] << 16) |
+                                     ($isbox[$word >> 24 & 0x000000FF] << 24));
+            ++$i;
+            $j = ($j + 1) % $Nb;
+            $k = ($k + 1) % $Nb;
+            $l = ($l + 1) % $Nb;
+        }
+
+        switch ($Nb) {
+            case 8:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5], $temp[6], $temp[7]);
+            case 7:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5], $temp[6]);
+            case 6:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4], $temp[5]);
+            case 5:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3], $temp[4]);
+            default:
+                return pack('N*', $temp[0], $temp[1], $temp[2], $temp[3]);
+        }
+    }
+
+    /**
+     * Setup the key (expansion)
+     *
+     * @see Crypt_Base::_setupKey()
+     * @access private
+     */
+    function _setupKey()
+    {
+        // Each number in $rcon is equal to the previous number multiplied by two in Rijndael's finite field.
+        // See http://en.wikipedia.org/wiki/Finite_field_arithmetic#Multiplicative_inverse
+        static $rcon = array(0,
+            0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000,
+            0x20000000, 0x40000000, 0x80000000, 0x1B000000, 0x36000000,
+            0x6C000000, 0xD8000000, 0xAB000000, 0x4D000000, 0x9A000000,
+            0x2F000000, 0x5E000000, 0xBC000000, 0x63000000, 0xC6000000,
+            0x97000000, 0x35000000, 0x6A000000, 0xD4000000, 0xB3000000,
+            0x7D000000, 0xFA000000, 0xEF000000, 0xC5000000, 0x91000000
+        );
+
+        $this->key = str_pad(substr($this->key, 0, $this->key_size), $this->key_size, "\0");
+
+        if (isset($this->kl['key']) && $this->key === $this->kl['key'] && $this->key_size === $this->kl['key_size'] && $this->block_size === $this->kl['block_size']) {
+            // already expanded
+            return;
+        }
+        $this->kl = array('key' => $this->key, 'key_size' => $this->key_size, 'block_size' => $this->block_size);
+
+        $this->Nk = $this->key_size >> 2;
+        // see Rijndael-ammended.pdf#page=44
+        $this->Nr = max($this->Nk, $this->Nb) + 6;
+
+        // shift offsets for Nb = 5, 7 are defined in Rijndael-ammended.pdf#page=44,
+        //     "Table 8: Shift offsets in Shiftrow for the alternative block lengths"
+        // shift offsets for Nb = 4, 6, 8 are defined in Rijndael-ammended.pdf#page=14,
+        //     "Table 2: Shift offsets for different block lengths"
+        switch ($this->Nb) {
+            case 4:
+            case 5:
+            case 6:
+                $this->c = array(0, 1, 2, 3);
+                break;
+            case 7:
+                $this->c = array(0, 1, 2, 4);
+                break;
+            case 8:
+                $this->c = array(0, 1, 3, 4);
+        }
+
+        $w = array_values(unpack('N*words', $this->key));
+
+        $length = $this->Nb * ($this->Nr + 1);
+        for ($i = $this->Nk; $i < $length; $i++) {
+            $temp = $w[$i - 1];
+            if ($i % $this->Nk == 0) {
+                // according to <http://php.net/language.types.integer>, "the size of an integer is platform-dependent".
+                // on a 32-bit machine, it's 32-bits, and on a 64-bit machine, it's 64-bits. on a 32-bit machine,
+                // 0xFFFFFFFF << 8 == 0xFFFFFF00, but on a 64-bit machine, it equals 0xFFFFFFFF00. as such, doing 'and'
+                // with 0xFFFFFFFF (or 0xFFFFFF00) on a 32-bit machine is unnecessary, but on a 64-bit machine, it is.
+                $temp = (($temp << 8) & 0xFFFFFF00) | (($temp >> 24) & 0x000000FF); // rotWord
+                $temp = $this->_subWord($temp) ^ $rcon[$i / $this->Nk];
+            } else if ($this->Nk > 6 && $i % $this->Nk == 4) {
+                $temp = $this->_subWord($temp);
+            }
+            $w[$i] = $w[$i - $this->Nk] ^ $temp;
+        }
+
+        // convert the key schedule from a vector of $Nb * ($Nr + 1) length to a matrix with $Nr + 1 rows and $Nb columns
+        // and generate the inverse key schedule.  more specifically,
+        // according to <http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf#page=23> (section 5.3.3),
+        // "The key expansion for the Inverse Cipher is defined as follows:
+        //        1. Apply the Key Expansion.
+        //        2. Apply InvMixColumn to all Round Keys except the first and the last one."
+        // also, see fips-197.pdf#page=27, "5.3.5 Equivalent Inverse Cipher"
+        $temp = $this->w = $this->dw = array();
+        for ($i = $row = $col = 0; $i < $length; $i++, $col++) {
+            if ($col == $this->Nb) {
+                if ($row == 0) {
+                    $this->dw[0] = $this->w[0];
+                } else {
+                    // subWord + invMixColumn + invSubWord = invMixColumn
+                    $j = 0;
+                    while ($j < $this->Nb) {
+                        $dw = $this->_subWord($this->w[$row][$j]);
+                        $temp[$j] = $this->dt0[$dw >> 24 & 0x000000FF] ^
+                                    $this->dt1[$dw >> 16 & 0x000000FF] ^
+                                    $this->dt2[$dw >>  8 & 0x000000FF] ^
+                                    $this->dt3[$dw       & 0x000000FF];
+                        $j++;
+                    }
+                    $this->dw[$row] = $temp;
+                }
+
+                $col = 0;
+                $row++;
+            }
+            $this->w[$row][$col] = $w[$i];
+        }
+
+        $this->dw[$row] = $this->w[$row];
+
+        // In case of $this->use_inline_crypt === true we have to use 1-dim key arrays (both ascending)
+        if ($this->use_inline_crypt) {
+            $this->dw = array_reverse($this->dw);
+            $w  = array_pop($this->w);
+            $dw = array_pop($this->dw);
+            foreach ($this->w as $r => $wr) {
+                foreach ($wr as $c => $wc) {
+                    $w[]  = $wc;
+                    $dw[] = $this->dw[$r][$c];
+                }
+            }
+            $this->w  = $w;
+            $this->dw = $dw;
+        }
+    }
+
+    /**
+     * Performs S-Box substitutions
+     *
+     * @access private
+     * @param Integer $word
+     */
+    function _subWord($word)
+    {
+        $sbox = $this->sbox;
+
+        return  $sbox[$word       & 0x000000FF]        |
+               ($sbox[$word >>  8 & 0x000000FF] <<  8) |
+               ($sbox[$word >> 16 & 0x000000FF] << 16) |
+               ($sbox[$word >> 24 & 0x000000FF] << 24);
+    }
+
+    /**
+     * Setup the performance-optimized function for de/encrypt()
+     *
+     * @see Crypt_Base::_setupInlineCrypt()
+     * @access private
+     */
+    function _setupInlineCrypt()
+    {
+        // Note: _setupInlineCrypt() will be called only if $this->changed === true
+        // So here we are'nt under the same heavy timing-stress as we are in _de/encryptBlock() or de/encrypt().
+        // However...the here generated function- $code, stored as php callback in $this->inline_crypt, must work as fast as even possible.
+
+        $lambda_functions =& Crypt_Rijndael::_getLambdaFunctions();
+
+        // The first 10 generated $lambda_functions will use the key-words hardcoded for better performance.
+        // For memory reason we limit those ultra-optimized functions.
+        // After that, we use pure (extracted) integer vars for the key-words which is faster than accessing them via array.
+        if (count($lambda_functions) < 10) {
+            $w  = $this->w;
+            $dw = $this->dw;
+            $init_encrypt = '';
+            $init_decrypt = '';
+        } else {
+            for ($i = 0, $cw = count($this->w); $i < $cw; ++$i) {
+                $w[]  = '$w['  . $i . ']';
+                $dw[] = '$dw[' . $i . ']';
+            }
+            $init_encrypt = '$w = $self->w;';
+            $init_decrypt = '$dw = $self->dw;';
+        }
+
+        $code_hash = md5(str_pad("Crypt_Rijndael, {$this->mode}, {$this->block_size}, ", 32, "\0") . implode(',', $w));
+
+        if (!isset($lambda_functions[$code_hash])) {
+            $Nr = $this->Nr;
+            $Nb = $this->Nb;
+            $c  = $this->c;
+
+            // Generating encrypt code:
+            $init_encrypt.= '
+                static $t0, $t1, $t2, $t3, $sbox;
+                if (!$t0) {
+                    for ($i = 0; $i < 256; ++$i) {
+                        $t0[$i]    = (int)$self->t0[$i];
+                        $t1[$i]    = (int)$self->t1[$i];
+                        $t2[$i]    = (int)$self->t2[$i];
+                        $t3[$i]    = (int)$self->t3[$i];
+                        $sbox[$i]  = (int)$self->sbox[$i];
+                    }
+                }
+            ';
+
+            $s  = 'e';
+            $e  = 's';
+            $wc = $Nb - 1;
+
+            // Preround: addRoundKey
+            $encrypt_block = '$in = unpack("N*", $in);'."\n";
+            for ($i = 0; $i < $Nb; ++$i) {
+                $encrypt_block .= '$s'.$i.' = $in['.($i + 1).'] ^ '.$w[++$wc].";\n";
+            }
+
+            // Mainrounds: shiftRows + subWord + mixColumns + addRoundKey
+            for ($round = 1; $round < $Nr; ++$round) {
+                list($s, $e) = array($e, $s);
+                for ($i = 0; $i < $Nb; ++$i) {
+                    $encrypt_block.=
+                        '$'.$e.$i.' =
+                        $t0[($'.$s.$i                  .' >> 24) & 0xff] ^
+                        $t1[($'.$s.(($i + $c[1]) % $Nb).' >> 16) & 0xff] ^
+                        $t2[($'.$s.(($i + $c[2]) % $Nb).' >>  8) & 0xff] ^
+                        $t3[ $'.$s.(($i + $c[3]) % $Nb).'        & 0xff] ^
+                        '.$w[++$wc].";\n";
+                }
+            }
+
+            // Finalround: subWord + shiftRows + addRoundKey
+            for ($i = 0; $i < $Nb; ++$i) {
+                $encrypt_block.=
+                    '$'.$e.$i.' =
+                     $sbox[ $'.$e.$i.'        & 0xff]        |
+                    ($sbox[($'.$e.$i.' >>  8) & 0xff] <<  8) |
+                    ($sbox[($'.$e.$i.' >> 16) & 0xff] << 16) |
+                    ($sbox[($'.$e.$i.' >> 24) & 0xff] << 24);'."\n";
+            }
+            $encrypt_block .= '$in = pack("N*"'."\n";
+            for ($i = 0; $i < $Nb; ++$i) {
+                $encrypt_block.= ',
+                    ($'.$e.$i                  .' & 0xFF000000) ^
+                    ($'.$e.(($i + $c[1]) % $Nb).' & 0x00FF0000) ^
+                    ($'.$e.(($i + $c[2]) % $Nb).' & 0x0000FF00) ^
+                    ($'.$e.(($i + $c[3]) % $Nb).' & 0x000000FF) ^
+                    '.$w[$i]."\n";
+            }
+            $encrypt_block .= ');';
+
+            // Generating decrypt code:
+            $init_decrypt.= '
+                static $dt0, $dt1, $dt2, $dt3, $isbox;
+                if (!$dt0) {
+                    for ($i = 0; $i < 256; ++$i) {
+                        $dt0[$i]   = (int)$self->dt0[$i];
+                        $dt1[$i]   = (int)$self->dt1[$i];
+                        $dt2[$i]   = (int)$self->dt2[$i];
+                        $dt3[$i]   = (int)$self->dt3[$i];
+                        $isbox[$i] = (int)$self->isbox[$i];
+                    }
+                }
+            ';
+
+            $s  = 'e';
+            $e  = 's';
+            $wc = $Nb - 1;
+
+            // Preround: addRoundKey
+            $decrypt_block = '$in = unpack("N*", $in);'."\n";
+            for ($i = 0; $i < $Nb; ++$i) {
+                $decrypt_block .= '$s'.$i.' = $in['.($i + 1).'] ^ '.$dw[++$wc].';'."\n";
+            }
+
+            // Mainrounds: shiftRows + subWord + mixColumns + addRoundKey
+            for ($round = 1; $round < $Nr; ++$round) {
+                list($s, $e) = array($e, $s);
+                for ($i = 0; $i < $Nb; ++$i) {
+                    $decrypt_block.=
+                        '$'.$e.$i.' =
+                        $dt0[($'.$s.$i                        .' >> 24) & 0xff] ^
+                        $dt1[($'.$s.(($Nb + $i - $c[1]) % $Nb).' >> 16) & 0xff] ^
+                        $dt2[($'.$s.(($Nb + $i - $c[2]) % $Nb).' >>  8) & 0xff] ^
+                        $dt3[ $'.$s.(($Nb + $i - $c[3]) % $Nb).'        & 0xff] ^
+                        '.$dw[++$wc].";\n";
+                }
+            }
+
+            // Finalround: subWord + shiftRows + addRoundKey
+            for ($i = 0; $i < $Nb; ++$i) {
+                $decrypt_block.=
+                    '$'.$e.$i.' =
+                     $isbox[ $'.$e.$i.'        & 0xff]        |
+                    ($isbox[($'.$e.$i.' >>  8) & 0xff] <<  8) |
+                    ($isbox[($'.$e.$i.' >> 16) & 0xff] << 16) |
+                    ($isbox[($'.$e.$i.' >> 24) & 0xff] << 24);'."\n";
+            }
+            $decrypt_block .= '$in = pack("N*"'."\n";
+            for ($i = 0; $i < $Nb; ++$i) {
+                $decrypt_block.= ',
+                    ($'.$e.$i.                        ' & 0xFF000000) ^
+                    ($'.$e.(($Nb + $i - $c[1]) % $Nb).' & 0x00FF0000) ^
+                    ($'.$e.(($Nb + $i - $c[2]) % $Nb).' & 0x0000FF00) ^
+                    ($'.$e.(($Nb + $i - $c[3]) % $Nb).' & 0x000000FF) ^
+                    '.$dw[$i]."\n";
+            }
+            $decrypt_block .= ');';
+
+            $lambda_functions[$code_hash] = $this->_createInlineCryptFunction(
+                array(
+                   'init_crypt'    => '',
+                   'init_encrypt'  => $init_encrypt,
+                   'init_decrypt'  => $init_decrypt,
+                   'encrypt_block' => $encrypt_block,
+                   'decrypt_block' => $decrypt_block
+                )
+            );
+        }
+        $this->inline_crypt = $lambda_functions[$code_hash];
+    }
+}
+
+// vim: ts=4:sw=4:et:
+// vim6: fdl=1:
diff --git a/inc/phpseclib/LICENSE b/inc/phpseclib/LICENSE
new file mode 100644
index 000000000..6ecd9b9be
--- /dev/null
+++ b/inc/phpseclib/LICENSE
@@ -0,0 +1,21 @@
+Copyright 2007-2012 TerraFrost and other contributors
+http://phpseclib.sourceforge.net/
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
+LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
\ No newline at end of file
diff --git a/inc/phpseclib/Math_BigInteger.php b/inc/phpseclib/Math_BigInteger.php
new file mode 100644
index 000000000..a37662da9
--- /dev/null
+++ b/inc/phpseclib/Math_BigInteger.php
@@ -0,0 +1,3651 @@
+<?php
+/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */
+
+/**
+ * Pure-PHP arbitrary precision integer arithmetic library.
+ *
+ * Supports base-2, base-10, base-16, and base-256 numbers.  Uses the GMP or BCMath extensions, if available,
+ * and an internal implementation, otherwise.
+ *
+ * PHP versions 4 and 5
+ *
+ * {@internal (all DocBlock comments regarding implementation - such as the one that follows - refer to the 
+ * {@link MATH_BIGINTEGER_MODE_INTERNAL MATH_BIGINTEGER_MODE_INTERNAL} mode)
+ *
+ * Math_BigInteger uses base-2**26 to perform operations such as multiplication and division and
+ * base-2**52 (ie. two base 2**26 digits) to perform addition and subtraction.  Because the largest possible
+ * value when multiplying two base-2**26 numbers together is a base-2**52 number, double precision floating
+ * point numbers - numbers that should be supported on most hardware and whose significand is 53 bits - are
+ * used.  As a consequence, bitwise operators such as >> and << cannot be used, nor can the modulo operator %,
+ * which only supports integers.  Although this fact will slow this library down, the fact that such a high
+ * base is being used should more than compensate.
+ *
+ * When PHP version 6 is officially released, we'll be able to use 64-bit integers.  This should, once again,
+ * allow bitwise operators, and will increase the maximum possible base to 2**31 (or 2**62 for addition /
+ * subtraction).
+ *
+ * Numbers are stored in {@link http://en.wikipedia.org/wiki/Endianness little endian} format.  ie.
+ * (new Math_BigInteger(pow(2, 26)))->value = array(0, 1)
+ *
+ * Useful resources are as follows:
+ *
+ *  - {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf Handbook of Applied Cryptography (HAC)}
+ *  - {@link http://math.libtomcrypt.com/files/tommath.pdf Multi-Precision Math (MPM)}
+ *  - Java's BigInteger classes.  See /j2se/src/share/classes/java/math in jdk-1_5_0-src-jrl.zip
+ *
+ * Here's an example of how to use this library:
+ * <code>
+ * <?php
+ *    include('Math/BigInteger.php');
+ *
+ *    $a = new Math_BigInteger(2);
+ *    $b = new Math_BigInteger(3);
+ *
+ *    $c = $a->add($b);
+ *
+ *    echo $c->toString(); // outputs 5
+ * ?>
+ * </code>
+ *
+ * LICENSE: Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ * 
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ * 
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *
+ * @category   Math
+ * @package    Math_BigInteger
+ * @author     Jim Wigginton <terrafrost@php.net>
+ * @copyright  MMVI Jim Wigginton
+ * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link       http://pear.php.net/package/Math_BigInteger
+ */
+
+/**#@+
+ * Reduction constants
+ *
+ * @access private
+ * @see Math_BigInteger::_reduce()
+ */
+/**
+ * @see Math_BigInteger::_montgomery()
+ * @see Math_BigInteger::_prepMontgomery()
+ */
+define('MATH_BIGINTEGER_MONTGOMERY', 0);
+/**
+ * @see Math_BigInteger::_barrett()
+ */
+define('MATH_BIGINTEGER_BARRETT', 1);
+/**
+ * @see Math_BigInteger::_mod2()
+ */
+define('MATH_BIGINTEGER_POWEROF2', 2);
+/**
+ * @see Math_BigInteger::_remainder()
+ */
+define('MATH_BIGINTEGER_CLASSIC', 3);
+/**
+ * @see Math_BigInteger::__clone()
+ */
+define('MATH_BIGINTEGER_NONE', 4);
+/**#@-*/
+
+/**#@+
+ * Array constants
+ *
+ * Rather than create a thousands and thousands of new Math_BigInteger objects in repeated function calls to add() and
+ * multiply() or whatever, we'll just work directly on arrays, taking them in as parameters and returning them.
+ *
+ * @access private
+ */
+/**
+ * $result[MATH_BIGINTEGER_VALUE] contains the value.
+ */
+define('MATH_BIGINTEGER_VALUE', 0);
+/**
+ * $result[MATH_BIGINTEGER_SIGN] contains the sign.
+ */
+define('MATH_BIGINTEGER_SIGN', 1);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Math_BigInteger::_montgomery()
+ * @see Math_BigInteger::_barrett()
+ */
+/**
+ * Cache constants
+ *
+ * $cache[MATH_BIGINTEGER_VARIABLE] tells us whether or not the cached data is still valid.
+ */
+define('MATH_BIGINTEGER_VARIABLE', 0);
+/**
+ * $cache[MATH_BIGINTEGER_DATA] contains the cached data.
+ */
+define('MATH_BIGINTEGER_DATA', 1);
+/**#@-*/
+
+/**#@+
+ * Mode constants.
+ *
+ * @access private
+ * @see Math_BigInteger::Math_BigInteger()
+ */
+/**
+ * To use the pure-PHP implementation
+ */
+define('MATH_BIGINTEGER_MODE_INTERNAL', 1);
+/**
+ * To use the BCMath library
+ *
+ * (if enabled; otherwise, the internal implementation will be used)
+ */
+define('MATH_BIGINTEGER_MODE_BCMATH', 2);
+/**
+ * To use the GMP library
+ *
+ * (if present; otherwise, either the BCMath or the internal implementation will be used)
+ */
+define('MATH_BIGINTEGER_MODE_GMP', 3);
+/**#@-*/
+
+/**
+ * Karatsuba Cutoff
+ *
+ * At what point do we switch between Karatsuba multiplication and schoolbook long multiplication?
+ *
+ * @access private
+ */
+define('MATH_BIGINTEGER_KARATSUBA_CUTOFF', 25);
+
+/**
+ * Pure-PHP arbitrary precision integer arithmetic library. Supports base-2, base-10, base-16, and base-256
+ * numbers.
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @version 1.0.0RC4
+ * @access  public
+ * @package Math_BigInteger
+ */
+class Math_BigInteger {
+    /**
+     * Holds the BigInteger's value.
+     *
+     * @var Array
+     * @access private
+     */
+    var $value;
+
+    /**
+     * Holds the BigInteger's magnitude.
+     *
+     * @var Boolean
+     * @access private
+     */
+    var $is_negative = false;
+
+    /**
+     * Random number generator function
+     *
+     * @see setRandomGenerator()
+     * @access private
+     */
+    var $generator = 'mt_rand';
+
+    /**
+     * Precision
+     *
+     * @see setPrecision()
+     * @access private
+     */
+    var $precision = -1;
+
+    /**
+     * Precision Bitmask
+     *
+     * @see setPrecision()
+     * @access private
+     */
+    var $bitmask = false;
+
+    /**
+     * Mode independent value used for serialization.
+     *
+     * If the bcmath or gmp extensions are installed $this->value will be a non-serializable resource, hence the need for 
+     * a variable that'll be serializable regardless of whether or not extensions are being used.  Unlike $this->value,
+     * however, $this->hex is only calculated when $this->__sleep() is called.
+     *
+     * @see __sleep()
+     * @see __wakeup()
+     * @var String
+     * @access private
+     */
+    var $hex;
+
+    /**
+     * Converts base-2, base-10, base-16, and binary strings (base-256) to BigIntegers.
+     *
+     * If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using
+     * two's compliment.  The sole exception to this is -10, which is treated the same as 10 is.
+     *
+     * Here's an example:
+     * <code>
+     * &lt;?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('0x32', 16); // 50 in base-16
+     *
+     *    echo $a->toString(); // outputs 50
+     * ?&gt;
+     * </code>
+     *
+     * @param optional $x base-10 number or base-$base number if $base set.
+     * @param optional integer $base
+     * @return Math_BigInteger
+     * @access public
+     */
+    function Math_BigInteger($x = 0, $base = 10)
+    {
+        if ( !defined('MATH_BIGINTEGER_MODE') ) {
+            switch (true) {
+                case extension_loaded('gmp'):
+                    define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_GMP);
+                    break;
+                case extension_loaded('bcmath'):
+                    define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_BCMATH);
+                    break;
+                default:
+                    define('MATH_BIGINTEGER_MODE', MATH_BIGINTEGER_MODE_INTERNAL);
+            }
+        }
+
+        if (function_exists('openssl_public_encrypt') && !defined('MATH_BIGINTEGER_OPENSSL_DISABLE') && !defined('MATH_BIGINTEGER_OPENSSL_ENABLED')) {
+            define('MATH_BIGINTEGER_OPENSSL_ENABLED', true);
+        }
+
+        if (!defined('PHP_INT_SIZE')) {
+            define('PHP_INT_SIZE', 4);
+        }
+
+        if (!defined('MATH_BIGINTEGER_BASE') && MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_INTERNAL) {
+            switch (PHP_INT_SIZE) {
+                case 8: // use 64-bit integers if int size is 8 bytes
+                    define('MATH_BIGINTEGER_BASE',       31);
+                    define('MATH_BIGINTEGER_BASE_FULL',  0x80000000);
+                    define('MATH_BIGINTEGER_MAX_DIGIT',  0x7FFFFFFF);
+                    define('MATH_BIGINTEGER_MSB',        0x40000000);
+                    // 10**9 is the closest we can get to 2**31 without passing it
+                    define('MATH_BIGINTEGER_MAX10',      1000000000);
+                    define('MATH_BIGINTEGER_MAX10_LEN',  9);
+                    // the largest digit that may be used in addition / subtraction
+                    define('MATH_BIGINTEGER_MAX_DIGIT2', pow(2, 62));
+                    break;
+                //case 4: // use 64-bit floats if int size is 4 bytes
+                default:
+                    define('MATH_BIGINTEGER_BASE',       26);
+                    define('MATH_BIGINTEGER_BASE_FULL',  0x4000000);
+                    define('MATH_BIGINTEGER_MAX_DIGIT',  0x3FFFFFF);
+                    define('MATH_BIGINTEGER_MSB',        0x2000000);
+                    // 10**7 is the closest to 2**26 without passing it
+                    define('MATH_BIGINTEGER_MAX10',      10000000);
+                    define('MATH_BIGINTEGER_MAX10_LEN',  7);
+                    // the largest digit that may be used in addition / subtraction
+                    // we do pow(2, 52) instead of using 4503599627370496 directly because some
+                    // PHP installations will truncate 4503599627370496.
+                    define('MATH_BIGINTEGER_MAX_DIGIT2', pow(2, 52));
+            }
+        }
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                if (is_resource($x) && get_resource_type($x) == 'GMP integer') {
+                    $this->value = $x;
+                    return;
+                }
+                $this->value = gmp_init(0);
+                break;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $this->value = '0';
+                break;
+            default:
+                $this->value = array();
+        }
+
+        // '0' counts as empty() but when the base is 256 '0' is equal to ord('0') or 48
+        // '0' is the only value like this per http://php.net/empty
+        if (empty($x) && (abs($base) != 256 || $x !== '0')) {
+            return;
+        }
+
+        switch ($base) {
+            case -256:
+                if (ord($x[0]) & 0x80) {
+                    $x = ~$x;
+                    $this->is_negative = true;
+                }
+            case  256:
+                switch ( MATH_BIGINTEGER_MODE ) {
+                    case MATH_BIGINTEGER_MODE_GMP:
+                        $sign = $this->is_negative ? '-' : '';
+                        $this->value = gmp_init($sign . '0x' . bin2hex($x));
+                        break;
+                    case MATH_BIGINTEGER_MODE_BCMATH:
+                        // round $len to the nearest 4 (thanks, DavidMJ!)
+                        $len = (strlen($x) + 3) & 0xFFFFFFFC;
+
+                        $x = str_pad($x, $len, chr(0), STR_PAD_LEFT);
+
+                        for ($i = 0; $i < $len; $i+= 4) {
+                            $this->value = bcmul($this->value, '4294967296', 0); // 4294967296 == 2**32
+                            $this->value = bcadd($this->value, 0x1000000 * ord($x[$i]) + ((ord($x[$i + 1]) << 16) | (ord($x[$i + 2]) << 8) | ord($x[$i + 3])), 0);
+                        }
+
+                        if ($this->is_negative) {
+                            $this->value = '-' . $this->value;
+                        }
+
+                        break;
+                    // converts a base-2**8 (big endian / msb) number to base-2**26 (little endian / lsb)
+                    default:
+                        while (strlen($x)) {
+                            $this->value[] = $this->_bytes2int($this->_base256_rshift($x, MATH_BIGINTEGER_BASE));
+                        }
+                }
+
+                if ($this->is_negative) {
+                    if (MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL) {
+                        $this->is_negative = false;
+                    }
+                    $temp = $this->add(new Math_BigInteger('-1'));
+                    $this->value = $temp->value;
+                }
+                break;
+            case  16:
+            case -16:
+                if ($base > 0 && $x[0] == '-') {
+                    $this->is_negative = true;
+                    $x = substr($x, 1);
+                }
+
+                $x = preg_replace('#^(?:0x)?([A-Fa-f0-9]*).*#', '$1', $x);
+
+                $is_negative = false;
+                if ($base < 0 && hexdec($x[0]) >= 8) {
+                    $this->is_negative = $is_negative = true;
+                    $x = bin2hex(~pack('H*', $x));
+                }
+
+                switch ( MATH_BIGINTEGER_MODE ) {
+                    case MATH_BIGINTEGER_MODE_GMP:
+                        $temp = $this->is_negative ? '-0x' . $x : '0x' . $x;
+                        $this->value = gmp_init($temp);
+                        $this->is_negative = false;
+                        break;
+                    case MATH_BIGINTEGER_MODE_BCMATH:
+                        $x = ( strlen($x) & 1 ) ? '0' . $x : $x;
+                        $temp = new Math_BigInteger(pack('H*', $x), 256);
+                        $this->value = $this->is_negative ? '-' . $temp->value : $temp->value;
+                        $this->is_negative = false;
+                        break;
+                    default:
+                        $x = ( strlen($x) & 1 ) ? '0' . $x : $x;
+                        $temp = new Math_BigInteger(pack('H*', $x), 256);
+                        $this->value = $temp->value;
+                }
+
+                if ($is_negative) {
+                    $temp = $this->add(new Math_BigInteger('-1'));
+                    $this->value = $temp->value;
+                }
+                break;
+            case  10:
+            case -10:
+                // (?<!^)(?:-).*: find any -'s that aren't at the beginning and then any characters that follow that
+                // (?<=^|-)0*: find any 0's that are preceded by the start of the string or by a - (ie. octals)
+                // [^-0-9].*: find any non-numeric characters and then any characters that follow that
+                $x = preg_replace('#(?<!^)(?:-).*|(?<=^|-)0*|[^-0-9].*#', '', $x);
+
+                switch ( MATH_BIGINTEGER_MODE ) {
+                    case MATH_BIGINTEGER_MODE_GMP:
+                        $this->value = gmp_init($x);
+                        break;
+                    case MATH_BIGINTEGER_MODE_BCMATH:
+                        // explicitly casting $x to a string is necessary, here, since doing $x[0] on -1 yields different
+                        // results then doing it on '-1' does (modInverse does $x[0])
+                        $this->value = $x === '-' ? '0' : (string) $x;
+                        break;
+                    default:
+                        $temp = new Math_BigInteger();
+
+                        $multiplier = new Math_BigInteger();
+                        $multiplier->value = array(MATH_BIGINTEGER_MAX10);
+
+                        if ($x[0] == '-') {
+                            $this->is_negative = true;
+                            $x = substr($x, 1);
+                        }
+
+                        $x = str_pad($x, strlen($x) + ((MATH_BIGINTEGER_MAX10_LEN - 1) * strlen($x)) % MATH_BIGINTEGER_MAX10_LEN, 0, STR_PAD_LEFT);
+
+                        while (strlen($x)) {
+                            $temp = $temp->multiply($multiplier);
+                            $temp = $temp->add(new Math_BigInteger($this->_int2bytes(substr($x, 0, MATH_BIGINTEGER_MAX10_LEN)), 256));
+                            $x = substr($x, MATH_BIGINTEGER_MAX10_LEN);
+                        }
+
+                        $this->value = $temp->value;
+                }
+                break;
+            case  2: // base-2 support originally implemented by Lluis Pamies - thanks!
+            case -2:
+                if ($base > 0 && $x[0] == '-') {
+                    $this->is_negative = true;
+                    $x = substr($x, 1);
+                }
+
+                $x = preg_replace('#^([01]*).*#', '$1', $x);
+                $x = str_pad($x, strlen($x) + (3 * strlen($x)) % 4, 0, STR_PAD_LEFT);
+
+                $str = '0x';
+                while (strlen($x)) {
+                    $part = substr($x, 0, 4);
+                    $str.= dechex(bindec($part));
+                    $x = substr($x, 4);
+                }
+
+                if ($this->is_negative) {
+                    $str = '-' . $str;
+                }
+
+                $temp = new Math_BigInteger($str, 8 * $base); // ie. either -16 or +16
+                $this->value = $temp->value;
+                $this->is_negative = $temp->is_negative;
+
+                break;
+            default:
+                // base not supported, so we'll let $this == 0
+        }
+    }
+
+    /**
+     * Converts a BigInteger to a byte string (eg. base-256).
+     *
+     * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
+     * saved as two's compliment.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('65');
+     *
+     *    echo $a->toBytes(); // outputs chr(65)
+     * ?>
+     * </code>
+     *
+     * @param Boolean $twos_compliment
+     * @return String
+     * @access public
+     * @internal Converts a base-2**26 number to base-2**8
+     */
+    function toBytes($twos_compliment = false)
+    {
+        if ($twos_compliment) {
+            $comparison = $this->compare(new Math_BigInteger());
+            if ($comparison == 0) {
+                return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
+            }
+
+            $temp = $comparison < 0 ? $this->add(new Math_BigInteger(1)) : $this->copy();
+            $bytes = $temp->toBytes();
+
+            if (empty($bytes)) { // eg. if the number we're trying to convert is -1
+                $bytes = chr(0);
+            }
+
+            if (ord($bytes[0]) & 0x80) {
+                $bytes = chr(0) . $bytes;
+            }
+
+            return $comparison < 0 ? ~$bytes : $bytes;
+        }
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                if (gmp_cmp($this->value, gmp_init(0)) == 0) {
+                    return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
+                }
+
+                $temp = gmp_strval(gmp_abs($this->value), 16);
+                $temp = ( strlen($temp) & 1 ) ? '0' . $temp : $temp;
+                $temp = pack('H*', $temp);
+
+                return $this->precision > 0 ?
+                    substr(str_pad($temp, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :
+                    ltrim($temp, chr(0));
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                if ($this->value === '0') {
+                    return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
+                }
+
+                $value = '';
+                $current = $this->value;
+
+                if ($current[0] == '-') {
+                    $current = substr($current, 1);
+                }
+
+                while (bccomp($current, '0', 0) > 0) {
+                    $temp = bcmod($current, '16777216');
+                    $value = chr($temp >> 16) . chr($temp >> 8) . chr($temp) . $value;
+                    $current = bcdiv($current, '16777216', 0);
+                }
+
+                return $this->precision > 0 ?
+                    substr(str_pad($value, $this->precision >> 3, chr(0), STR_PAD_LEFT), -($this->precision >> 3)) :
+                    ltrim($value, chr(0));
+        }
+
+        if (!count($this->value)) {
+            return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
+        }
+        $result = $this->_int2bytes($this->value[count($this->value) - 1]);
+
+        $temp = $this->copy();
+
+        for ($i = count($temp->value) - 2; $i >= 0; --$i) {
+            $temp->_base256_lshift($result, MATH_BIGINTEGER_BASE);
+            $result = $result | str_pad($temp->_int2bytes($temp->value[$i]), strlen($result), chr(0), STR_PAD_LEFT);
+        }
+
+        return $this->precision > 0 ?
+            str_pad(substr($result, -(($this->precision + 7) >> 3)), ($this->precision + 7) >> 3, chr(0), STR_PAD_LEFT) :
+            $result;
+    }
+
+    /**
+     * Converts a BigInteger to a hex string (eg. base-16)).
+     *
+     * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
+     * saved as two's compliment.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('65');
+     *
+     *    echo $a->toHex(); // outputs '41'
+     * ?>
+     * </code>
+     *
+     * @param Boolean $twos_compliment
+     * @return String
+     * @access public
+     * @internal Converts a base-2**26 number to base-2**8
+     */
+    function toHex($twos_compliment = false)
+    {
+        return bin2hex($this->toBytes($twos_compliment));
+    }
+
+    /**
+     * Converts a BigInteger to a bit string (eg. base-2).
+     *
+     * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
+     * saved as two's compliment.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('65');
+     *
+     *    echo $a->toBits(); // outputs '1000001'
+     * ?>
+     * </code>
+     *
+     * @param Boolean $twos_compliment
+     * @return String
+     * @access public
+     * @internal Converts a base-2**26 number to base-2**2
+     */
+    function toBits($twos_compliment = false)
+    {
+        $hex = $this->toHex($twos_compliment);
+        $bits = '';
+        for ($i = strlen($hex) - 8, $start = strlen($hex) & 7; $i >= $start; $i-=8) {
+            $bits = str_pad(decbin(hexdec(substr($hex, $i, 8))), 32, '0', STR_PAD_LEFT) . $bits;
+        }
+        if ($start) { // hexdec('') == 0
+            $bits = str_pad(decbin(hexdec(substr($hex, 0, $start))), 8, '0', STR_PAD_LEFT) . $bits;
+        }
+        $result = $this->precision > 0 ? substr($bits, -$this->precision) : ltrim($bits, '0');
+
+        if ($twos_compliment && $this->compare(new Math_BigInteger()) > 0 && $this->precision <= 0) {
+            return '0' . $result;
+        }
+
+        return $result;
+    }
+
+    /**
+     * Converts a BigInteger to a base-10 number.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('50');
+     *
+     *    echo $a->toString(); // outputs 50
+     * ?>
+     * </code>
+     *
+     * @return String
+     * @access public
+     * @internal Converts a base-2**26 number to base-10**7 (which is pretty much base-10)
+     */
+    function toString()
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                return gmp_strval($this->value);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                if ($this->value === '0') {
+                    return '0';
+                }
+
+                return ltrim($this->value, '0');
+        }
+
+        if (!count($this->value)) {
+            return '0';
+        }
+
+        $temp = $this->copy();
+        $temp->is_negative = false;
+
+        $divisor = new Math_BigInteger();
+        $divisor->value = array(MATH_BIGINTEGER_MAX10);
+        $result = '';
+        while (count($temp->value)) {
+            list($temp, $mod) = $temp->divide($divisor);
+            $result = str_pad(isset($mod->value[0]) ? $mod->value[0] : '', MATH_BIGINTEGER_MAX10_LEN, '0', STR_PAD_LEFT) . $result;
+        }
+        $result = ltrim($result, '0');
+        if (empty($result)) {
+            $result = '0';
+        }
+
+        if ($this->is_negative) {
+            $result = '-' . $result;
+        }
+
+        return $result;
+    }
+
+    /**
+     * Copy an object
+     *
+     * PHP5 passes objects by reference while PHP4 passes by value.  As such, we need a function to guarantee
+     * that all objects are passed by value, when appropriate.  More information can be found here:
+     *
+     * {@link http://php.net/language.oop5.basic#51624}
+     *
+     * @access public
+     * @see __clone()
+     * @return Math_BigInteger
+     */
+    function copy()
+    {
+        $temp = new Math_BigInteger();
+        $temp->value = $this->value;
+        $temp->is_negative = $this->is_negative;
+        $temp->generator = $this->generator;
+        $temp->precision = $this->precision;
+        $temp->bitmask = $this->bitmask;
+        return $temp;
+    }
+
+    /**
+     *  __toString() magic method
+     *
+     * Will be called, automatically, if you're supporting just PHP5.  If you're supporting PHP4, you'll need to call
+     * toString().
+     *
+     * @access public
+     * @internal Implemented per a suggestion by Techie-Michael - thanks!
+     */
+    function __toString()
+    {
+        return $this->toString();
+    }
+
+    /**
+     * __clone() magic method
+     *
+     * Although you can call Math_BigInteger::__toString() directly in PHP5, you cannot call Math_BigInteger::__clone()
+     * directly in PHP5.  You can in PHP4 since it's not a magic method, but in PHP5, you have to call it by using the PHP5
+     * only syntax of $y = clone $x.  As such, if you're trying to write an application that works on both PHP4 and PHP5,
+     * call Math_BigInteger::copy(), instead.
+     *
+     * @access public
+     * @see copy()
+     * @return Math_BigInteger
+     */
+    function __clone()
+    {
+        return $this->copy();
+    }
+
+    /**
+     *  __sleep() magic method
+     *
+     * Will be called, automatically, when serialize() is called on a Math_BigInteger object.
+     *
+     * @see __wakeup()
+     * @access public
+     */
+    function __sleep()
+    {
+        $this->hex = $this->toHex(true);
+        $vars = array('hex');
+        if ($this->generator != 'mt_rand') {
+            $vars[] = 'generator';
+        }
+        if ($this->precision > 0) {
+            $vars[] = 'precision';
+        }
+        return $vars;
+        
+    }
+
+    /**
+     *  __wakeup() magic method
+     *
+     * Will be called, automatically, when unserialize() is called on a Math_BigInteger object.
+     *
+     * @see __sleep()
+     * @access public
+     */
+    function __wakeup()
+    {
+        $temp = new Math_BigInteger($this->hex, -16);
+        $this->value = $temp->value;
+        $this->is_negative = $temp->is_negative;
+        $this->setRandomGenerator($this->generator);
+        if ($this->precision > 0) {
+            // recalculate $this->bitmask
+            $this->setPrecision($this->precision);
+        }
+    }
+
+    /**
+     * Adds two BigIntegers.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('10');
+     *    $b = new Math_BigInteger('20');
+     *
+     *    $c = $a->add($b);
+     *
+     *    echo $c->toString(); // outputs 30
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $y
+     * @return Math_BigInteger
+     * @access public
+     * @internal Performs base-2**52 addition
+     */
+    function add($y)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_add($this->value, $y->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp = new Math_BigInteger();
+                $temp->value = bcadd($this->value, $y->value, 0);
+
+                return $this->_normalize($temp);
+        }
+
+        $temp = $this->_add($this->value, $this->is_negative, $y->value, $y->is_negative);
+
+        $result = new Math_BigInteger();
+        $result->value = $temp[MATH_BIGINTEGER_VALUE];
+        $result->is_negative = $temp[MATH_BIGINTEGER_SIGN];
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Performs addition.
+     *
+     * @param Array $x_value
+     * @param Boolean $x_negative
+     * @param Array $y_value
+     * @param Boolean $y_negative
+     * @return Array
+     * @access private
+     */
+    function _add($x_value, $x_negative, $y_value, $y_negative)
+    {
+        $x_size = count($x_value);
+        $y_size = count($y_value);
+
+        if ($x_size == 0) {
+            return array(
+                MATH_BIGINTEGER_VALUE => $y_value,
+                MATH_BIGINTEGER_SIGN => $y_negative
+            );
+        } else if ($y_size == 0) {
+            return array(
+                MATH_BIGINTEGER_VALUE => $x_value,
+                MATH_BIGINTEGER_SIGN => $x_negative
+            );
+        }
+
+        // subtract, if appropriate
+        if ( $x_negative != $y_negative ) {
+            if ( $x_value == $y_value ) {
+                return array(
+                    MATH_BIGINTEGER_VALUE => array(),
+                    MATH_BIGINTEGER_SIGN => false
+                );
+            }
+
+            $temp = $this->_subtract($x_value, false, $y_value, false);
+            $temp[MATH_BIGINTEGER_SIGN] = $this->_compare($x_value, false, $y_value, false) > 0 ?
+                                          $x_negative : $y_negative;
+
+            return $temp;
+        }
+
+        if ($x_size < $y_size) {
+            $size = $x_size;
+            $value = $y_value;
+        } else {
+            $size = $y_size;
+            $value = $x_value;
+        }
+
+        $value[] = 0; // just in case the carry adds an extra digit
+
+        $carry = 0;
+        for ($i = 0, $j = 1; $j < $size; $i+=2, $j+=2) {
+            $sum = $x_value[$j] * MATH_BIGINTEGER_BASE_FULL + $x_value[$i] + $y_value[$j] * MATH_BIGINTEGER_BASE_FULL + $y_value[$i] + $carry;
+            $carry = $sum >= MATH_BIGINTEGER_MAX_DIGIT2; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
+            $sum = $carry ? $sum - MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
+
+            $temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
+
+            $value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp); // eg. a faster alternative to fmod($sum, 0x4000000)
+            $value[$j] = $temp;
+        }
+
+        if ($j == $size) { // ie. if $y_size is odd
+            $sum = $x_value[$i] + $y_value[$i] + $carry;
+            $carry = $sum >= MATH_BIGINTEGER_BASE_FULL;
+            $value[$i] = $carry ? $sum - MATH_BIGINTEGER_BASE_FULL : $sum;
+            ++$i; // ie. let $i = $j since we've just done $value[$i]
+        }
+
+        if ($carry) {
+            for (; $value[$i] == MATH_BIGINTEGER_MAX_DIGIT; ++$i) {
+                $value[$i] = 0;
+            }
+            ++$value[$i];
+        }
+
+        return array(
+            MATH_BIGINTEGER_VALUE => $this->_trim($value),
+            MATH_BIGINTEGER_SIGN => $x_negative
+        );
+    }
+
+    /**
+     * Subtracts two BigIntegers.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('10');
+     *    $b = new Math_BigInteger('20');
+     *
+     *    $c = $a->subtract($b);
+     *
+     *    echo $c->toString(); // outputs -10
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $y
+     * @return Math_BigInteger
+     * @access public
+     * @internal Performs base-2**52 subtraction
+     */
+    function subtract($y)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_sub($this->value, $y->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp = new Math_BigInteger();
+                $temp->value = bcsub($this->value, $y->value, 0);
+
+                return $this->_normalize($temp);
+        }
+
+        $temp = $this->_subtract($this->value, $this->is_negative, $y->value, $y->is_negative);
+
+        $result = new Math_BigInteger();
+        $result->value = $temp[MATH_BIGINTEGER_VALUE];
+        $result->is_negative = $temp[MATH_BIGINTEGER_SIGN];
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Performs subtraction.
+     *
+     * @param Array $x_value
+     * @param Boolean $x_negative
+     * @param Array $y_value
+     * @param Boolean $y_negative
+     * @return Array
+     * @access private
+     */
+    function _subtract($x_value, $x_negative, $y_value, $y_negative)
+    {
+        $x_size = count($x_value);
+        $y_size = count($y_value);
+
+        if ($x_size == 0) {
+            return array(
+                MATH_BIGINTEGER_VALUE => $y_value,
+                MATH_BIGINTEGER_SIGN => !$y_negative
+            );
+        } else if ($y_size == 0) {
+            return array(
+                MATH_BIGINTEGER_VALUE => $x_value,
+                MATH_BIGINTEGER_SIGN => $x_negative
+            );
+        }
+
+        // add, if appropriate (ie. -$x - +$y or +$x - -$y)
+        if ( $x_negative != $y_negative ) {
+            $temp = $this->_add($x_value, false, $y_value, false);
+            $temp[MATH_BIGINTEGER_SIGN] = $x_negative;
+
+            return $temp;
+        }
+
+        $diff = $this->_compare($x_value, $x_negative, $y_value, $y_negative);
+
+        if ( !$diff ) {
+            return array(
+                MATH_BIGINTEGER_VALUE => array(),
+                MATH_BIGINTEGER_SIGN => false
+            );
+        }
+
+        // switch $x and $y around, if appropriate.
+        if ( (!$x_negative && $diff < 0) || ($x_negative && $diff > 0) ) {
+            $temp = $x_value;
+            $x_value = $y_value;
+            $y_value = $temp;
+
+            $x_negative = !$x_negative;
+
+            $x_size = count($x_value);
+            $y_size = count($y_value);
+        }
+
+        // at this point, $x_value should be at least as big as - if not bigger than - $y_value
+
+        $carry = 0;
+        for ($i = 0, $j = 1; $j < $y_size; $i+=2, $j+=2) {
+            $sum = $x_value[$j] * MATH_BIGINTEGER_BASE_FULL + $x_value[$i] - $y_value[$j] * MATH_BIGINTEGER_BASE_FULL - $y_value[$i] - $carry;
+            $carry = $sum < 0; // eg. floor($sum / 2**52); only possible values (in any base) are 0 and 1
+            $sum = $carry ? $sum + MATH_BIGINTEGER_MAX_DIGIT2 : $sum;
+
+            $temp = (int) ($sum / MATH_BIGINTEGER_BASE_FULL);
+
+            $x_value[$i] = (int) ($sum - MATH_BIGINTEGER_BASE_FULL * $temp);
+            $x_value[$j] = $temp;
+        }
+
+        if ($j == $y_size) { // ie. if $y_size is odd
+            $sum = $x_value[$i] - $y_value[$i] - $carry;
+            $carry = $sum < 0;
+            $x_value[$i] = $carry ? $sum + MATH_BIGINTEGER_BASE_FULL : $sum;
+            ++$i;
+        }
+
+        if ($carry) {
+            for (; !$x_value[$i]; ++$i) {
+                $x_value[$i] = MATH_BIGINTEGER_MAX_DIGIT;
+            }
+            --$x_value[$i];
+        }
+
+        return array(
+            MATH_BIGINTEGER_VALUE => $this->_trim($x_value),
+            MATH_BIGINTEGER_SIGN => $x_negative
+        );
+    }
+
+    /**
+     * Multiplies two BigIntegers
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('10');
+     *    $b = new Math_BigInteger('20');
+     *
+     *    $c = $a->multiply($b);
+     *
+     *    echo $c->toString(); // outputs 200
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $x
+     * @return Math_BigInteger
+     * @access public
+     */
+    function multiply($x)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_mul($this->value, $x->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp = new Math_BigInteger();
+                $temp->value = bcmul($this->value, $x->value, 0);
+
+                return $this->_normalize($temp);
+        }
+
+        $temp = $this->_multiply($this->value, $this->is_negative, $x->value, $x->is_negative);
+
+        $product = new Math_BigInteger();
+        $product->value = $temp[MATH_BIGINTEGER_VALUE];
+        $product->is_negative = $temp[MATH_BIGINTEGER_SIGN];
+
+        return $this->_normalize($product);
+    }
+
+    /**
+     * Performs multiplication.
+     *
+     * @param Array $x_value
+     * @param Boolean $x_negative
+     * @param Array $y_value
+     * @param Boolean $y_negative
+     * @return Array
+     * @access private
+     */
+    function _multiply($x_value, $x_negative, $y_value, $y_negative)
+    {
+        //if ( $x_value == $y_value ) {
+        //    return array(
+        //        MATH_BIGINTEGER_VALUE => $this->_square($x_value),
+        //        MATH_BIGINTEGER_SIGN => $x_sign != $y_value
+        //    );
+        //}
+
+        $x_length = count($x_value);
+        $y_length = count($y_value);
+
+        if ( !$x_length || !$y_length ) { // a 0 is being multiplied
+            return array(
+                MATH_BIGINTEGER_VALUE => array(),
+                MATH_BIGINTEGER_SIGN => false
+            );
+        }
+
+        return array(
+            MATH_BIGINTEGER_VALUE => min($x_length, $y_length) < 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF ?
+                $this->_trim($this->_regularMultiply($x_value, $y_value)) :
+                $this->_trim($this->_karatsuba($x_value, $y_value)),
+            MATH_BIGINTEGER_SIGN => $x_negative != $y_negative
+        );
+    }
+
+    /**
+     * Performs long multiplication on two BigIntegers
+     *
+     * Modeled after 'multiply' in MutableBigInteger.java.
+     *
+     * @param Array $x_value
+     * @param Array $y_value
+     * @return Array
+     * @access private
+     */
+    function _regularMultiply($x_value, $y_value)
+    {
+        $x_length = count($x_value);
+        $y_length = count($y_value);
+
+        if ( !$x_length || !$y_length ) { // a 0 is being multiplied
+            return array();
+        }
+
+        if ( $x_length < $y_length ) {
+            $temp = $x_value;
+            $x_value = $y_value;
+            $y_value = $temp;
+
+            $x_length = count($x_value);
+            $y_length = count($y_value);
+        }
+
+        $product_value = $this->_array_repeat(0, $x_length + $y_length);
+
+        // the following for loop could be removed if the for loop following it
+        // (the one with nested for loops) initially set $i to 0, but
+        // doing so would also make the result in one set of unnecessary adds,
+        // since on the outermost loops first pass, $product->value[$k] is going
+        // to always be 0
+
+        $carry = 0;
+
+        for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0
+            $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
+            $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+            $product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+        }
+
+        $product_value[$j] = $carry;
+
+        // the above for loop is what the previous comment was talking about.  the
+        // following for loop is the "one with nested for loops"
+        for ($i = 1; $i < $y_length; ++$i) {
+            $carry = 0;
+
+            for ($j = 0, $k = $i; $j < $x_length; ++$j, ++$k) {
+                $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
+                $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+                $product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+            }
+
+            $product_value[$k] = $carry;
+        }
+
+        return $product_value;
+    }
+
+    /**
+     * Performs Karatsuba multiplication on two BigIntegers
+     *
+     * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and
+     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=120 MPM 5.2.3}.
+     *
+     * @param Array $x_value
+     * @param Array $y_value
+     * @return Array
+     * @access private
+     */
+    function _karatsuba($x_value, $y_value)
+    {
+        $m = min(count($x_value) >> 1, count($y_value) >> 1);
+
+        if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) {
+            return $this->_regularMultiply($x_value, $y_value);
+        }
+
+        $x1 = array_slice($x_value, $m);
+        $x0 = array_slice($x_value, 0, $m);
+        $y1 = array_slice($y_value, $m);
+        $y0 = array_slice($y_value, 0, $m);
+
+        $z2 = $this->_karatsuba($x1, $y1);
+        $z0 = $this->_karatsuba($x0, $y0);
+
+        $z1 = $this->_add($x1, false, $x0, false);
+        $temp = $this->_add($y1, false, $y0, false);
+        $z1 = $this->_karatsuba($z1[MATH_BIGINTEGER_VALUE], $temp[MATH_BIGINTEGER_VALUE]);
+        $temp = $this->_add($z2, false, $z0, false);
+        $z1 = $this->_subtract($z1, false, $temp[MATH_BIGINTEGER_VALUE], false);
+
+        $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2);
+        $z1[MATH_BIGINTEGER_VALUE] = array_merge(array_fill(0, $m, 0), $z1[MATH_BIGINTEGER_VALUE]);
+
+        $xy = $this->_add($z2, false, $z1[MATH_BIGINTEGER_VALUE], $z1[MATH_BIGINTEGER_SIGN]);
+        $xy = $this->_add($xy[MATH_BIGINTEGER_VALUE], $xy[MATH_BIGINTEGER_SIGN], $z0, false);
+
+        return $xy[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * Performs squaring
+     *
+     * @param Array $x
+     * @return Array
+     * @access private
+     */
+    function _square($x = false)
+    {
+        return count($x) < 2 * MATH_BIGINTEGER_KARATSUBA_CUTOFF ?
+            $this->_trim($this->_baseSquare($x)) :
+            $this->_trim($this->_karatsubaSquare($x));
+    }
+
+    /**
+     * Performs traditional squaring on two BigIntegers
+     *
+     * Squaring can be done faster than multiplying a number by itself can be.  See
+     * {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=7 HAC 14.2.4} /
+     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=141 MPM 5.3} for more information.
+     *
+     * @param Array $value
+     * @return Array
+     * @access private
+     */
+    function _baseSquare($value)
+    {
+        if ( empty($value) ) {
+            return array();
+        }
+        $square_value = $this->_array_repeat(0, 2 * count($value));
+
+        for ($i = 0, $max_index = count($value) - 1; $i <= $max_index; ++$i) {
+            $i2 = $i << 1;
+
+            $temp = $square_value[$i2] + $value[$i] * $value[$i];
+            $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+            $square_value[$i2] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+
+            // note how we start from $i+1 instead of 0 as we do in multiplication.
+            for ($j = $i + 1, $k = $i2 + 1; $j <= $max_index; ++$j, ++$k) {
+                $temp = $square_value[$k] + 2 * $value[$j] * $value[$i] + $carry;
+                $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+                $square_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+            }
+
+            // the following line can yield values larger 2**15.  at this point, PHP should switch
+            // over to floats.
+            $square_value[$i + $max_index + 1] = $carry;
+        }
+
+        return $square_value;
+    }
+
+    /**
+     * Performs Karatsuba "squaring" on two BigIntegers
+     *
+     * See {@link http://en.wikipedia.org/wiki/Karatsuba_algorithm Karatsuba algorithm} and
+     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=151 MPM 5.3.4}.
+     *
+     * @param Array $value
+     * @return Array
+     * @access private
+     */
+    function _karatsubaSquare($value)
+    {
+        $m = count($value) >> 1;
+
+        if ($m < MATH_BIGINTEGER_KARATSUBA_CUTOFF) {
+            return $this->_baseSquare($value);
+        }
+
+        $x1 = array_slice($value, $m);
+        $x0 = array_slice($value, 0, $m);
+
+        $z2 = $this->_karatsubaSquare($x1);
+        $z0 = $this->_karatsubaSquare($x0);
+
+        $z1 = $this->_add($x1, false, $x0, false);
+        $z1 = $this->_karatsubaSquare($z1[MATH_BIGINTEGER_VALUE]);
+        $temp = $this->_add($z2, false, $z0, false);
+        $z1 = $this->_subtract($z1, false, $temp[MATH_BIGINTEGER_VALUE], false);
+
+        $z2 = array_merge(array_fill(0, 2 * $m, 0), $z2);
+        $z1[MATH_BIGINTEGER_VALUE] = array_merge(array_fill(0, $m, 0), $z1[MATH_BIGINTEGER_VALUE]);
+
+        $xx = $this->_add($z2, false, $z1[MATH_BIGINTEGER_VALUE], $z1[MATH_BIGINTEGER_SIGN]);
+        $xx = $this->_add($xx[MATH_BIGINTEGER_VALUE], $xx[MATH_BIGINTEGER_SIGN], $z0, false);
+
+        return $xx[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * Divides two BigIntegers.
+     *
+     * Returns an array whose first element contains the quotient and whose second element contains the
+     * "common residue".  If the remainder would be positive, the "common residue" and the remainder are the
+     * same.  If the remainder would be negative, the "common residue" is equal to the sum of the remainder
+     * and the divisor (basically, the "common residue" is the first positive modulo).
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('10');
+     *    $b = new Math_BigInteger('20');
+     *
+     *    list($quotient, $remainder) = $a->divide($b);
+     *
+     *    echo $quotient->toString(); // outputs 0
+     *    echo "\r\n";
+     *    echo $remainder->toString(); // outputs 10
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $y
+     * @return Array
+     * @access public
+     * @internal This function is based off of {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=9 HAC 14.20}.
+     */
+    function divide($y)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $quotient = new Math_BigInteger();
+                $remainder = new Math_BigInteger();
+
+                list($quotient->value, $remainder->value) = gmp_div_qr($this->value, $y->value);
+
+                if (gmp_sign($remainder->value) < 0) {
+                    $remainder->value = gmp_add($remainder->value, gmp_abs($y->value));
+                }
+
+                return array($this->_normalize($quotient), $this->_normalize($remainder));
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $quotient = new Math_BigInteger();
+                $remainder = new Math_BigInteger();
+
+                $quotient->value = bcdiv($this->value, $y->value, 0);
+                $remainder->value = bcmod($this->value, $y->value);
+
+                if ($remainder->value[0] == '-') {
+                    $remainder->value = bcadd($remainder->value, $y->value[0] == '-' ? substr($y->value, 1) : $y->value, 0);
+                }
+
+                return array($this->_normalize($quotient), $this->_normalize($remainder));
+        }
+
+        if (count($y->value) == 1) {
+            list($q, $r) = $this->_divide_digit($this->value, $y->value[0]);
+            $quotient = new Math_BigInteger();
+            $remainder = new Math_BigInteger();
+            $quotient->value = $q;
+            $remainder->value = array($r);
+            $quotient->is_negative = $this->is_negative != $y->is_negative;
+            return array($this->_normalize($quotient), $this->_normalize($remainder));
+        }
+
+        static $zero;
+        if ( !isset($zero) ) {
+            $zero = new Math_BigInteger();
+        }
+
+        $x = $this->copy();
+        $y = $y->copy();
+
+        $x_sign = $x->is_negative;
+        $y_sign = $y->is_negative;
+
+        $x->is_negative = $y->is_negative = false;
+
+        $diff = $x->compare($y);
+
+        if ( !$diff ) {
+            $temp = new Math_BigInteger();
+            $temp->value = array(1);
+            $temp->is_negative = $x_sign != $y_sign;
+            return array($this->_normalize($temp), $this->_normalize(new Math_BigInteger()));
+        }
+
+        if ( $diff < 0 ) {
+            // if $x is negative, "add" $y.
+            if ( $x_sign ) {
+                $x = $y->subtract($x);
+            }
+            return array($this->_normalize(new Math_BigInteger()), $this->_normalize($x));
+        }
+
+        // normalize $x and $y as described in HAC 14.23 / 14.24
+        $msb = $y->value[count($y->value) - 1];
+        for ($shift = 0; !($msb & MATH_BIGINTEGER_MSB); ++$shift) {
+            $msb <<= 1;
+        }
+        $x->_lshift($shift);
+        $y->_lshift($shift);
+        $y_value = &$y->value;
+
+        $x_max = count($x->value) - 1;
+        $y_max = count($y->value) - 1;
+
+        $quotient = new Math_BigInteger();
+        $quotient_value = &$quotient->value;
+        $quotient_value = $this->_array_repeat(0, $x_max - $y_max + 1);
+
+        static $temp, $lhs, $rhs;
+        if (!isset($temp)) {
+            $temp = new Math_BigInteger();
+            $lhs =  new Math_BigInteger();
+            $rhs =  new Math_BigInteger();
+        }
+        $temp_value = &$temp->value;
+        $rhs_value =  &$rhs->value;
+
+        // $temp = $y << ($x_max - $y_max-1) in base 2**26
+        $temp_value = array_merge($this->_array_repeat(0, $x_max - $y_max), $y_value);
+
+        while ( $x->compare($temp) >= 0 ) {
+            // calculate the "common residue"
+            ++$quotient_value[$x_max - $y_max];
+            $x = $x->subtract($temp);
+            $x_max = count($x->value) - 1;
+        }
+
+        for ($i = $x_max; $i >= $y_max + 1; --$i) {
+            $x_value = &$x->value;
+            $x_window = array(
+                isset($x_value[$i]) ? $x_value[$i] : 0,
+                isset($x_value[$i - 1]) ? $x_value[$i - 1] : 0,
+                isset($x_value[$i - 2]) ? $x_value[$i - 2] : 0
+            );
+            $y_window = array(
+                $y_value[$y_max],
+                ( $y_max > 0 ) ? $y_value[$y_max - 1] : 0
+            );
+
+            $q_index = $i - $y_max - 1;
+            if ($x_window[0] == $y_window[0]) {
+                $quotient_value[$q_index] = MATH_BIGINTEGER_MAX_DIGIT;
+            } else {
+                $quotient_value[$q_index] = (int) (
+                    ($x_window[0] * MATH_BIGINTEGER_BASE_FULL + $x_window[1])
+                    /
+                    $y_window[0]
+                );
+            }
+
+            $temp_value = array($y_window[1], $y_window[0]);
+
+            $lhs->value = array($quotient_value[$q_index]);
+            $lhs = $lhs->multiply($temp);
+
+            $rhs_value = array($x_window[2], $x_window[1], $x_window[0]);
+
+            while ( $lhs->compare($rhs) > 0 ) {
+                --$quotient_value[$q_index];
+
+                $lhs->value = array($quotient_value[$q_index]);
+                $lhs = $lhs->multiply($temp);
+            }
+
+            $adjust = $this->_array_repeat(0, $q_index);
+            $temp_value = array($quotient_value[$q_index]);
+            $temp = $temp->multiply($y);
+            $temp_value = &$temp->value;
+            $temp_value = array_merge($adjust, $temp_value);
+
+            $x = $x->subtract($temp);
+
+            if ($x->compare($zero) < 0) {
+                $temp_value = array_merge($adjust, $y_value);
+                $x = $x->add($temp);
+
+                --$quotient_value[$q_index];
+            }
+
+            $x_max = count($x_value) - 1;
+        }
+
+        // unnormalize the remainder
+        $x->_rshift($shift);
+
+        $quotient->is_negative = $x_sign != $y_sign;
+
+        // calculate the "common residue", if appropriate
+        if ( $x_sign ) {
+            $y->_rshift($shift);
+            $x = $y->subtract($x);
+        }
+
+        return array($this->_normalize($quotient), $this->_normalize($x));
+    }
+
+    /**
+     * Divides a BigInteger by a regular integer
+     *
+     * abc / x = a00 / x + b0 / x + c / x
+     *
+     * @param Array $dividend
+     * @param Array $divisor
+     * @return Array
+     * @access private
+     */
+    function _divide_digit($dividend, $divisor)
+    {
+        $carry = 0;
+        $result = array();
+
+        for ($i = count($dividend) - 1; $i >= 0; --$i) {
+            $temp = MATH_BIGINTEGER_BASE_FULL * $carry + $dividend[$i];
+            $result[$i] = (int) ($temp / $divisor);
+            $carry = (int) ($temp - $divisor * $result[$i]);
+        }
+
+        return array($result, $carry);
+    }
+
+    /**
+     * Performs modular exponentiation.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger('10');
+     *    $b = new Math_BigInteger('20');
+     *    $c = new Math_BigInteger('30');
+     *
+     *    $c = $a->modPow($b, $c);
+     *
+     *    echo $c->toString(); // outputs 10
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $e
+     * @param Math_BigInteger $n
+     * @return Math_BigInteger
+     * @access public
+     * @internal The most naive approach to modular exponentiation has very unreasonable requirements, and
+     *    and although the approach involving repeated squaring does vastly better, it, too, is impractical
+     *    for our purposes.  The reason being that division - by far the most complicated and time-consuming
+     *    of the basic operations (eg. +,-,*,/) - occurs multiple times within it.
+     *
+     *    Modular reductions resolve this issue.  Although an individual modular reduction takes more time
+     *    then an individual division, when performed in succession (with the same modulo), they're a lot faster.
+     *
+     *    The two most commonly used modular reductions are Barrett and Montgomery reduction.  Montgomery reduction,
+     *    although faster, only works when the gcd of the modulo and of the base being used is 1.  In RSA, when the
+     *    base is a power of two, the modulo - a product of two primes - is always going to have a gcd of 1 (because
+     *    the product of two odd numbers is odd), but what about when RSA isn't used?
+     *
+     *    In contrast, Barrett reduction has no such constraint.  As such, some bigint implementations perform a
+     *    Barrett reduction after every operation in the modpow function.  Others perform Barrett reductions when the
+     *    modulo is even and Montgomery reductions when the modulo is odd.  BigInteger.java's modPow method, however,
+     *    uses a trick involving the Chinese Remainder Theorem to factor the even modulo into two numbers - one odd and
+     *    the other, a power of two - and recombine them, later.  This is the method that this modPow function uses.
+     *    {@link http://islab.oregonstate.edu/papers/j34monex.pdf Montgomery Reduction with Even Modulus} elaborates.
+     */
+    function modPow($e, $n)
+    {
+        $n = $this->bitmask !== false && $this->bitmask->compare($n) < 0 ? $this->bitmask : $n->abs();
+
+        if ($e->compare(new Math_BigInteger()) < 0) {
+            $e = $e->abs();
+
+            $temp = $this->modInverse($n);
+            if ($temp === false) {
+                return false;
+            }
+
+            return $this->_normalize($temp->modPow($e, $n));
+        }
+
+        if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_GMP ) {
+            $temp = new Math_BigInteger();
+            $temp->value = gmp_powm($this->value, $e->value, $n->value);
+
+            return $this->_normalize($temp);
+        }
+
+        if ($this->compare(new Math_BigInteger()) < 0 || $this->compare($n) > 0) {
+            list(, $temp) = $this->divide($n);
+            return $temp->modPow($e, $n);
+        }
+
+        if (defined('MATH_BIGINTEGER_OPENSSL_ENABLED')) {
+            $components = array(
+                'modulus' => $n->toBytes(true),
+                'publicExponent' => $e->toBytes(true)
+            );
+
+            $components = array(
+                'modulus' => pack('Ca*a*', 2, $this->_encodeASN1Length(strlen($components['modulus'])), $components['modulus']),
+                'publicExponent' => pack('Ca*a*', 2, $this->_encodeASN1Length(strlen($components['publicExponent'])), $components['publicExponent'])
+            );
+
+            $RSAPublicKey = pack('Ca*a*a*',
+                48, $this->_encodeASN1Length(strlen($components['modulus']) + strlen($components['publicExponent'])),
+                $components['modulus'], $components['publicExponent']
+            );
+
+            $rsaOID = pack('H*', '300d06092a864886f70d0101010500'); // hex version of MA0GCSqGSIb3DQEBAQUA
+            $RSAPublicKey = chr(0) . $RSAPublicKey;
+            $RSAPublicKey = chr(3) . $this->_encodeASN1Length(strlen($RSAPublicKey)) . $RSAPublicKey;
+
+            $encapsulated = pack('Ca*a*',
+                48, $this->_encodeASN1Length(strlen($rsaOID . $RSAPublicKey)), $rsaOID . $RSAPublicKey
+            );
+
+            $RSAPublicKey = "-----BEGIN PUBLIC KEY-----\r\n" .
+                             chunk_split(base64_encode($encapsulated)) .
+                             '-----END PUBLIC KEY-----';
+
+            $plaintext = str_pad($this->toBytes(), strlen($n->toBytes(true)) - 1, "\0", STR_PAD_LEFT);
+
+            if (openssl_public_encrypt($plaintext, $result, $RSAPublicKey, OPENSSL_NO_PADDING)) {
+                return new Math_BigInteger($result, 256);
+            }
+        }
+
+        if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH ) {
+                $temp = new Math_BigInteger();
+                $temp->value = bcpowmod($this->value, $e->value, $n->value, 0);
+
+                return $this->_normalize($temp);
+        }
+
+        if ( empty($e->value) ) {
+            $temp = new Math_BigInteger();
+            $temp->value = array(1);
+            return $this->_normalize($temp);
+        }
+
+        if ( $e->value == array(1) ) {
+            list(, $temp) = $this->divide($n);
+            return $this->_normalize($temp);
+        }
+
+        if ( $e->value == array(2) ) {
+            $temp = new Math_BigInteger();
+            $temp->value = $this->_square($this->value);
+            list(, $temp) = $temp->divide($n);
+            return $this->_normalize($temp);
+        }
+
+        return $this->_normalize($this->_slidingWindow($e, $n, MATH_BIGINTEGER_BARRETT));
+
+        // is the modulo odd?
+        if ( $n->value[0] & 1 ) {
+            return $this->_normalize($this->_slidingWindow($e, $n, MATH_BIGINTEGER_MONTGOMERY));
+        }
+        // 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+= 26 * $i;
+                break;
+            }
+        }
+        // at this point, 2^$j * $n/(2^$j) == $n
+
+        $mod1 = $n->copy();
+        $mod1->_rshift($j);
+        $mod2 = new Math_BigInteger();
+        $mod2->value = array(1);
+        $mod2->_lshift($j);
+
+        $part1 = ( $mod1->value != array(1) ) ? $this->_slidingWindow($e, $mod1, MATH_BIGINTEGER_MONTGOMERY) : new Math_BigInteger();
+        $part2 = $this->_slidingWindow($e, $mod2, MATH_BIGINTEGER_POWEROF2);
+
+        $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);
+        list(, $result) = $result->divide($n);
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Performs modular exponentiation.
+     *
+     * Alias for Math_BigInteger::modPow()
+     *
+     * @param Math_BigInteger $e
+     * @param Math_BigInteger $n
+     * @return Math_BigInteger
+     * @access public
+     */
+    function powMod($e, $n)
+    {
+        return $this->modPow($e, $n);
+    }
+
+    /**
+     * Sliding Window k-ary Modular Exponentiation
+     *
+     * Based on {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=27 HAC 14.85} /
+     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=210 MPM 7.7}.  In a departure from those algorithims,
+     * however, this function performs a modular reduction after every multiplication and squaring operation.
+     * As such, this function has the same preconditions that the reductions being used do.
+     *
+     * @param Math_BigInteger $e
+     * @param Math_BigInteger $n
+     * @param Integer $mode
+     * @return Math_BigInteger
+     * @access private
+     */
+    function _slidingWindow($e, $n, $mode)
+    {
+        static $window_ranges = array(7, 25, 81, 241, 673, 1793); // from BigInteger.java's oddModPow function
+        //static $window_ranges = array(0, 7, 36, 140, 450, 1303, 3529); // from MPM 7.3.1
+
+        $e_value = $e->value;
+        $e_length = count($e_value) - 1;
+        $e_bits = decbin($e_value[$e_length]);
+        for ($i = $e_length - 1; $i >= 0; --$i) {
+            $e_bits.= str_pad(decbin($e_value[$i]), MATH_BIGINTEGER_BASE, '0', STR_PAD_LEFT);
+        }
+
+        $e_length = strlen($e_bits);
+
+        // calculate the appropriate window size.
+        // $window_size == 3 if $window_ranges is between 25 and 81, for example.
+        for ($i = 0, $window_size = 1; $e_length > $window_ranges[$i] && $i < count($window_ranges); ++$window_size, ++$i);
+
+        $n_value = $n->value;
+
+        // precompute $this^0 through $this^$window_size
+        $powers = array();
+        $powers[1] = $this->_prepareReduce($this->value, $n_value, $mode);
+        $powers[2] = $this->_squareReduce($powers[1], $n_value, $mode);
+
+        // we do every other number since substr($e_bits, $i, $j+1) (see below) is supposed to end
+        // in a 1.  ie. it's supposed to be odd.
+        $temp = 1 << ($window_size - 1);
+        for ($i = 1; $i < $temp; ++$i) {
+            $i2 = $i << 1;
+            $powers[$i2 + 1] = $this->_multiplyReduce($powers[$i2 - 1], $powers[2], $n_value, $mode);
+        }
+
+        $result = array(1);
+        $result = $this->_prepareReduce($result, $n_value, $mode);
+
+        for ($i = 0; $i < $e_length; ) {
+            if ( !$e_bits[$i] ) {
+                $result = $this->_squareReduce($result, $n_value, $mode);
+                ++$i;
+            } else {
+                for ($j = $window_size - 1; $j > 0; --$j) {
+                    if ( !empty($e_bits[$i + $j]) ) {
+                        break;
+                    }
+                }
+
+                for ($k = 0; $k <= $j; ++$k) {// eg. the length of substr($e_bits, $i, $j+1)
+                    $result = $this->_squareReduce($result, $n_value, $mode);
+                }
+
+                $result = $this->_multiplyReduce($result, $powers[bindec(substr($e_bits, $i, $j + 1))], $n_value, $mode);
+
+                $i+=$j + 1;
+            }
+        }
+
+        $temp = new Math_BigInteger();
+        $temp->value = $this->_reduce($result, $n_value, $mode);
+
+        return $temp;
+    }
+
+    /**
+     * Modular reduction
+     *
+     * For most $modes this will return the remainder.
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @param Integer $mode
+     * @return Array
+     */
+    function _reduce($x, $n, $mode)
+    {
+        switch ($mode) {
+            case MATH_BIGINTEGER_MONTGOMERY:
+                return $this->_montgomery($x, $n);
+            case MATH_BIGINTEGER_BARRETT:
+                return $this->_barrett($x, $n);
+            case MATH_BIGINTEGER_POWEROF2:
+                $lhs = new Math_BigInteger();
+                $lhs->value = $x;
+                $rhs = new Math_BigInteger();
+                $rhs->value = $n;
+                return $x->_mod2($n);
+            case MATH_BIGINTEGER_CLASSIC:
+                $lhs = new Math_BigInteger();
+                $lhs->value = $x;
+                $rhs = new Math_BigInteger();
+                $rhs->value = $n;
+                list(, $temp) = $lhs->divide($rhs);
+                return $temp->value;
+            case MATH_BIGINTEGER_NONE:
+                return $x;
+            default:
+                // an invalid $mode was provided
+        }
+    }
+
+    /**
+     * Modular reduction preperation
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @param Integer $mode
+     * @return Array
+     */
+    function _prepareReduce($x, $n, $mode)
+    {
+        if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
+            return $this->_prepMontgomery($x, $n);
+        }
+        return $this->_reduce($x, $n, $mode);
+    }
+
+    /**
+     * Modular multiply
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $y
+     * @param Array $n
+     * @param Integer $mode
+     * @return Array
+     */
+    function _multiplyReduce($x, $y, $n, $mode)
+    {
+        if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
+            return $this->_montgomeryMultiply($x, $y, $n);
+        }
+        $temp = $this->_multiply($x, false, $y, false);
+        return $this->_reduce($temp[MATH_BIGINTEGER_VALUE], $n, $mode);
+    }
+
+    /**
+     * Modular square
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @param Integer $mode
+     * @return Array
+     */
+    function _squareReduce($x, $n, $mode)
+    {
+        if ($mode == MATH_BIGINTEGER_MONTGOMERY) {
+            return $this->_montgomeryMultiply($x, $x, $n);
+        }
+        return $this->_reduce($this->_square($x), $n, $mode);
+    }
+
+    /**
+     * Modulos for Powers of Two
+     *
+     * Calculates $x%$n, where $n = 2**$e, for some $e.  Since this is basically the same as doing $x & ($n-1),
+     * we'll just use this function as a wrapper for doing that.
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Math_BigInteger
+     * @return Math_BigInteger
+     */
+    function _mod2($n)
+    {
+        $temp = new Math_BigInteger();
+        $temp->value = array(1);
+        return $this->bitwise_and($n->subtract($temp));
+    }
+
+    /**
+     * 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.
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $n
+     * @param Array $m
+     * @return Array
+     */
+    function _barrett($n, $m)
+    {
+        static $cache = array(
+            MATH_BIGINTEGER_VARIABLE => array(),
+            MATH_BIGINTEGER_DATA => array()
+        );
+
+        $m_length = count($m);
+
+        // if ($this->_compare($n, $this->_square($m)) >= 0) {
+        if (count($n) > 2 * $m_length) {
+            $lhs = new Math_BigInteger();
+            $rhs = new Math_BigInteger();
+            $lhs->value = $n;
+            $rhs->value = $m;
+            list(, $temp) = $lhs->divide($rhs);
+            return $temp->value;
+        }
+
+        // if (m.length >> 1) + 2 <= m.length then m is too small and n can't be reduced
+        if ($m_length < 5) {
+            return $this->_regularBarrett($n, $m);
+        }
+
+        // n = 2 * m.length
+
+        if ( ($key = array_search($m, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
+            $key = count($cache[MATH_BIGINTEGER_VARIABLE]);
+            $cache[MATH_BIGINTEGER_VARIABLE][] = $m;
+
+            $lhs = new Math_BigInteger();
+            $lhs_value = &$lhs->value;
+            $lhs_value = $this->_array_repeat(0, $m_length + ($m_length >> 1));
+            $lhs_value[] = 1;
+            $rhs = new Math_BigInteger();
+            $rhs->value = $m;
+
+            list($u, $m1) = $lhs->divide($rhs);
+            $u = $u->value;
+            $m1 = $m1->value;
+
+            $cache[MATH_BIGINTEGER_DATA][] = array(
+                'u' => $u, // m.length >> 1 (technically (m.length >> 1) + 1)
+                'm1'=> $m1 // m.length
+            );
+        } else {
+            extract($cache[MATH_BIGINTEGER_DATA][$key]);
+        }
+
+        $cutoff = $m_length + ($m_length >> 1);
+        $lsd = array_slice($n, 0, $cutoff); // m.length + (m.length >> 1)
+        $msd = array_slice($n, $cutoff);    // m.length >> 1
+        $lsd = $this->_trim($lsd);
+        $temp = $this->_multiply($msd, false, $m1, false);
+        $n = $this->_add($lsd, false, $temp[MATH_BIGINTEGER_VALUE], false); // m.length + (m.length >> 1) + 1
+
+        if ($m_length & 1) {
+            return $this->_regularBarrett($n[MATH_BIGINTEGER_VALUE], $m);
+        }
+
+        // (m.length + (m.length >> 1) + 1) - (m.length - 1) == (m.length >> 1) + 2
+        $temp = array_slice($n[MATH_BIGINTEGER_VALUE], $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 = $this->_multiply($temp, false, $u, false);
+        // 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)
+        $temp = array_slice($temp[MATH_BIGINTEGER_VALUE], ($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 = $this->_multiply($temp, false, $m, false);
+
+        // 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 = $this->_subtract($n[MATH_BIGINTEGER_VALUE], false, $temp[MATH_BIGINTEGER_VALUE], false);
+
+        while ($this->_compare($result[MATH_BIGINTEGER_VALUE], $result[MATH_BIGINTEGER_SIGN], $m, false) >= 0) {
+            $result = $this->_subtract($result[MATH_BIGINTEGER_VALUE], $result[MATH_BIGINTEGER_SIGN], $m, false);
+        }
+
+        return $result[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * (Regular) Barrett Modular Reduction
+     *
+     * For numbers with more than four digits Math_BigInteger::_barrett() is faster.  The difference between that and this
+     * is that this function does not fold the denominator into a smaller form.
+     *
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @return Array
+     */
+    function _regularBarrett($x, $n)
+    {
+        static $cache = array(
+            MATH_BIGINTEGER_VARIABLE => array(),
+            MATH_BIGINTEGER_DATA => array()
+        );
+
+        $n_length = count($n);
+
+        if (count($x) > 2 * $n_length) {
+            $lhs = new Math_BigInteger();
+            $rhs = new Math_BigInteger();
+            $lhs->value = $x;
+            $rhs->value = $n;
+            list(, $temp) = $lhs->divide($rhs);
+            return $temp->value;
+        }
+
+        if ( ($key = array_search($n, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
+            $key = count($cache[MATH_BIGINTEGER_VARIABLE]);
+            $cache[MATH_BIGINTEGER_VARIABLE][] = $n;
+            $lhs = new Math_BigInteger();
+            $lhs_value = &$lhs->value;
+            $lhs_value = $this->_array_repeat(0, 2 * $n_length);
+            $lhs_value[] = 1;
+            $rhs = new Math_BigInteger();
+            $rhs->value = $n;
+            list($temp, ) = $lhs->divide($rhs); // m.length
+            $cache[MATH_BIGINTEGER_DATA][] = $temp->value;
+        }
+
+        // 2 * m.length - (m.length - 1) = m.length + 1
+        $temp = array_slice($x, $n_length - 1);
+        // (m.length + 1) + m.length = 2 * m.length + 1
+        $temp = $this->_multiply($temp, false, $cache[MATH_BIGINTEGER_DATA][$key], false);
+        // (2 * m.length + 1) - (m.length - 1) = m.length + 2
+        $temp = array_slice($temp[MATH_BIGINTEGER_VALUE], $n_length + 1);
+
+        // m.length + 1
+        $result = array_slice($x, 0, $n_length + 1);
+        // m.length + 1
+        $temp = $this->_multiplyLower($temp, false, $n, false, $n_length + 1);
+        // $temp == array_slice($temp->_multiply($temp, false, $n, false)->value, 0, $n_length + 1)
+
+        if ($this->_compare($result, false, $temp[MATH_BIGINTEGER_VALUE], $temp[MATH_BIGINTEGER_SIGN]) < 0) {
+            $corrector_value = $this->_array_repeat(0, $n_length + 1);
+            $corrector_value[] = 1;
+            $result = $this->_add($result, false, $corrector_value, false);
+            $result = $result[MATH_BIGINTEGER_VALUE];
+        }
+
+        // at this point, we're subtracting a number with m.length + 1 digits from another number with m.length + 1 digits
+        $result = $this->_subtract($result, false, $temp[MATH_BIGINTEGER_VALUE], $temp[MATH_BIGINTEGER_SIGN]);
+        while ($this->_compare($result[MATH_BIGINTEGER_VALUE], $result[MATH_BIGINTEGER_SIGN], $n, false) > 0) {
+            $result = $this->_subtract($result[MATH_BIGINTEGER_VALUE], $result[MATH_BIGINTEGER_SIGN], $n, false);
+        }
+
+        return $result[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * Performs long multiplication up to $stop digits
+     *
+     * If you're going to be doing array_slice($product->value, 0, $stop), some cycles can be saved.
+     *
+     * @see _regularBarrett()
+     * @param Array $x_value
+     * @param Boolean $x_negative
+     * @param Array $y_value
+     * @param Boolean $y_negative
+     * @param Integer $stop
+     * @return Array
+     * @access private
+     */
+    function _multiplyLower($x_value, $x_negative, $y_value, $y_negative, $stop)
+    {
+        $x_length = count($x_value);
+        $y_length = count($y_value);
+
+        if ( !$x_length || !$y_length ) { // a 0 is being multiplied
+            return array(
+                MATH_BIGINTEGER_VALUE => array(),
+                MATH_BIGINTEGER_SIGN => false
+            );
+        }
+
+        if ( $x_length < $y_length ) {
+            $temp = $x_value;
+            $x_value = $y_value;
+            $y_value = $temp;
+
+            $x_length = count($x_value);
+            $y_length = count($y_value);
+        }
+
+        $product_value = $this->_array_repeat(0, $x_length + $y_length);
+
+        // the following for loop could be removed if the for loop following it
+        // (the one with nested for loops) initially set $i to 0, but
+        // doing so would also make the result in one set of unnecessary adds,
+        // since on the outermost loops first pass, $product->value[$k] is going
+        // to always be 0
+
+        $carry = 0;
+
+        for ($j = 0; $j < $x_length; ++$j) { // ie. $i = 0, $k = $i
+            $temp = $x_value[$j] * $y_value[0] + $carry; // $product_value[$k] == 0
+            $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+            $product_value[$j] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+        }
+
+        if ($j < $stop) {
+            $product_value[$j] = $carry;
+        }
+
+        // the above for loop is what the previous comment was talking about.  the
+        // following for loop is the "one with nested for loops"
+
+        for ($i = 1; $i < $y_length; ++$i) {
+            $carry = 0;
+
+            for ($j = 0, $k = $i; $j < $x_length && $k < $stop; ++$j, ++$k) {
+                $temp = $product_value[$k] + $x_value[$j] * $y_value[$i] + $carry;
+                $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+                $product_value[$k] = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * $carry);
+            }
+
+            if ($k < $stop) {
+                $product_value[$k] = $carry;
+            }
+        }
+
+        return array(
+            MATH_BIGINTEGER_VALUE => $this->_trim($product_value),
+            MATH_BIGINTEGER_SIGN => $x_negative != $y_negative
+        );
+    }
+
+    /**
+     * Montgomery Modular Reduction
+     *
+     * ($x->_prepMontgomery($n))->_montgomery($n) yields $x % $n.
+     * {@link http://math.libtomcrypt.com/files/tommath.pdf#page=170 MPM 6.3} provides insights on how this can be
+     * improved upon (basically, by using the comba method).  gcd($n, 2) must be equal to one for this function
+     * to work correctly.
+     *
+     * @see _prepMontgomery()
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @return Array
+     */
+    function _montgomery($x, $n)
+    {
+        static $cache = array(
+            MATH_BIGINTEGER_VARIABLE => array(),
+            MATH_BIGINTEGER_DATA => array()
+        );
+
+        if ( ($key = array_search($n, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
+            $key = count($cache[MATH_BIGINTEGER_VARIABLE]);
+            $cache[MATH_BIGINTEGER_VARIABLE][] = $x;
+            $cache[MATH_BIGINTEGER_DATA][] = $this->_modInverse67108864($n);
+        }
+
+        $k = count($n);
+
+        $result = array(MATH_BIGINTEGER_VALUE => $x);
+
+        for ($i = 0; $i < $k; ++$i) {
+            $temp = $result[MATH_BIGINTEGER_VALUE][$i] * $cache[MATH_BIGINTEGER_DATA][$key];
+            $temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
+            $temp = $this->_regularMultiply(array($temp), $n);
+            $temp = array_merge($this->_array_repeat(0, $i), $temp);
+            $result = $this->_add($result[MATH_BIGINTEGER_VALUE], false, $temp, false);
+        }
+
+        $result[MATH_BIGINTEGER_VALUE] = array_slice($result[MATH_BIGINTEGER_VALUE], $k);
+
+        if ($this->_compare($result, false, $n, false) >= 0) {
+            $result = $this->_subtract($result[MATH_BIGINTEGER_VALUE], false, $n, false);
+        }
+
+        return $result[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * 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}
+     *
+     * @see _prepMontgomery()
+     * @see _montgomery()
+     * @access private
+     * @param Array $x
+     * @param Array $y
+     * @param Array $m
+     * @return Array
+     */
+    function _montgomeryMultiply($x, $y, $m)
+    {
+        $temp = $this->_multiply($x, false, $y, false);
+        return $this->_montgomery($temp[MATH_BIGINTEGER_VALUE], $m);
+
+        static $cache = array(
+            MATH_BIGINTEGER_VARIABLE => array(),
+            MATH_BIGINTEGER_DATA => array()
+        );
+
+        if ( ($key = array_search($m, $cache[MATH_BIGINTEGER_VARIABLE])) === false ) {
+            $key = count($cache[MATH_BIGINTEGER_VARIABLE]);
+            $cache[MATH_BIGINTEGER_VARIABLE][] = $m;
+            $cache[MATH_BIGINTEGER_DATA][] = $this->_modInverse67108864($m);
+        }
+
+        $n = max(count($x), count($y), count($m));
+        $x = array_pad($x, $n, 0);
+        $y = array_pad($y, $n, 0);
+        $m = array_pad($m, $n, 0);
+        $a = array(MATH_BIGINTEGER_VALUE => $this->_array_repeat(0, $n + 1));
+        for ($i = 0; $i < $n; ++$i) {
+            $temp = $a[MATH_BIGINTEGER_VALUE][0] + $x[$i] * $y[0];
+            $temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
+            $temp = $temp * $cache[MATH_BIGINTEGER_DATA][$key];
+            $temp = (int) ($temp - MATH_BIGINTEGER_BASE_FULL * ((int) ($temp / MATH_BIGINTEGER_BASE_FULL)));
+            $temp = $this->_add($this->_regularMultiply(array($x[$i]), $y), false, $this->_regularMultiply(array($temp), $m), false);
+            $a = $this->_add($a[MATH_BIGINTEGER_VALUE], false, $temp[MATH_BIGINTEGER_VALUE], false);
+            $a[MATH_BIGINTEGER_VALUE] = array_slice($a[MATH_BIGINTEGER_VALUE], 1);
+        }
+        if ($this->_compare($a[MATH_BIGINTEGER_VALUE], false, $m, false) >= 0) {
+            $a = $this->_subtract($a[MATH_BIGINTEGER_VALUE], false, $m, false);
+        }
+        return $a[MATH_BIGINTEGER_VALUE];
+    }
+
+    /**
+     * Prepare a number for use in Montgomery Modular Reductions
+     *
+     * @see _montgomery()
+     * @see _slidingWindow()
+     * @access private
+     * @param Array $x
+     * @param Array $n
+     * @return Array
+     */
+    function _prepMontgomery($x, $n)
+    {
+        $lhs = new Math_BigInteger();
+        $lhs->value = array_merge($this->_array_repeat(0, count($n)), $x);
+        $rhs = new Math_BigInteger();
+        $rhs->value = $n;
+
+        list(, $temp) = $lhs->divide($rhs);
+        return $temp->value;
+    }
+
+    /**
+     * Modular Inverse of a number mod 2**26 (eg. 67108864)
+     *
+     * Based off of the bnpInvDigit function implemented and justified in the following URL:
+     *
+     * {@link http://www-cs-students.stanford.edu/~tjw/jsbn/jsbn.js}
+     *
+     * The following URL provides more info:
+     *
+     * {@link http://groups.google.com/group/sci.crypt/msg/7a137205c1be7d85}
+     *
+     * As for why we do all the bitmasking...  strange things can happen when converting from floats to ints. For
+     * instance, on some computers, var_dump((int) -4294967297) yields int(-1) and on others, it yields 
+     * int(-2147483648).  To avoid problems stemming from this, we use bitmasks to guarantee that ints aren't
+     * auto-converted to floats.  The outermost bitmask is present because without it, there's no guarantee that
+     * the "residue" returned would be the so-called "common residue".  We use fmod, in the last step, because the
+     * maximum possible $x is 26 bits and the maximum $result is 16 bits.  Thus, we have to be able to handle up to
+     * 40 bits, which only 64-bit floating points will support.
+     *
+     * Thanks to Pedro Gimeno Fortea for input!
+     *
+     * @see _montgomery()
+     * @access private
+     * @param Array $x
+     * @return Integer
+     */
+    function _modInverse67108864($x) // 2**26 == 67,108,864
+    {
+        $x = -$x[0];
+        $result = $x & 0x3; // x**-1 mod 2**2
+        $result = ($result * (2 - $x * $result)) & 0xF; // x**-1 mod 2**4
+        $result = ($result * (2 - ($x & 0xFF) * $result))  & 0xFF; // x**-1 mod 2**8
+        $result = ($result * ((2 - ($x & 0xFFFF) * $result) & 0xFFFF)) & 0xFFFF; // x**-1 mod 2**16
+        $result = fmod($result * (2 - fmod($x * $result, MATH_BIGINTEGER_BASE_FULL)), MATH_BIGINTEGER_BASE_FULL); // x**-1 mod 2**26
+        return $result & MATH_BIGINTEGER_MAX_DIGIT;
+    }
+
+    /**
+     * Calculates modular inverses.
+     *
+     * Say you have (30 mod 17 * x mod 17) mod 17 == 1.  x can be found using modular inverses.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger(30);
+     *    $b = new Math_BigInteger(17);
+     *
+     *    $c = $a->modInverse($b);
+     *    echo $c->toString(); // outputs 4
+     *
+     *    echo "\r\n";
+     *
+     *    $d = $a->multiply($c);
+     *    list(, $d) = $d->divide($b);
+     *    echo $d; // outputs 1 (as per the definition of modular inverse)
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $n
+     * @return mixed false, if no modular inverse exists, Math_BigInteger, otherwise.
+     * @access public
+     * @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=21 HAC 14.64} for more information.
+     */
+    function modInverse($n)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_invert($this->value, $n->value);
+
+                return ( $temp->value === false ) ? false : $this->_normalize($temp);
+        }
+
+        static $zero, $one;
+        if (!isset($zero)) {
+            $zero = new Math_BigInteger();
+            $one = new Math_BigInteger(1);
+        }
+
+        // $x mod -$n == $x mod $n.
+        $n = $n->abs();
+
+        if ($this->compare($zero) < 0) {
+            $temp = $this->abs();
+            $temp = $temp->modInverse($n);
+            return $this->_normalize($n->subtract($temp));
+        }
+
+        extract($this->extendedGCD($n));
+
+        if (!$gcd->equals($one)) {
+            return false;
+        }
+
+        $x = $x->compare($zero) < 0 ? $x->add($n) : $x;
+
+        return $this->compare($zero) < 0 ? $this->_normalize($n->subtract($x)) : $this->_normalize($x);
+    }
+
+    /**
+     * Calculates the greatest common divisor and Bezout's identity.
+     *
+     * Say you have 693 and 609.  The GCD is 21.  Bezout's identity states that there exist integers x and y such that
+     * 693*x + 609*y == 21.  In point of fact, there are actually an infinite number of x and y combinations and which
+     * combination is returned is dependant upon which mode is in use.  See
+     * {@link http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity Bezout's identity - Wikipedia} for more information.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger(693);
+     *    $b = new Math_BigInteger(609);
+     *
+     *    extract($a->extendedGCD($b));
+     *
+     *    echo $gcd->toString() . "\r\n"; // outputs 21
+     *    echo $a->toString() * $x->toString() + $b->toString() * $y->toString(); // outputs 21
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $n
+     * @return Math_BigInteger
+     * @access public
+     * @internal Calculates the GCD using the binary xGCD algorithim described in
+     *    {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=19 HAC 14.61}.  As the text above 14.61 notes,
+     *    the more traditional algorithim requires "relatively costly multiple-precision divisions".
+     */
+    function extendedGCD($n)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                extract(gmp_gcdext($this->value, $n->value));
+
+                return array(
+                    'gcd' => $this->_normalize(new Math_BigInteger($g)),
+                    'x'   => $this->_normalize(new Math_BigInteger($s)),
+                    'y'   => $this->_normalize(new Math_BigInteger($t))
+                );
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                // it might be faster to use the binary xGCD algorithim here, as well, but (1) that algorithim works
+                // best when the base is a power of 2 and (2) i don't think it'd make much difference, anyway.  as is,
+                // the basic extended euclidean algorithim is what we're using.
+
+                $u = $this->value;
+                $v = $n->value;
+
+                $a = '1';
+                $b = '0';
+                $c = '0';
+                $d = '1';
+
+                while (bccomp($v, '0', 0) != 0) {
+                    $q = bcdiv($u, $v, 0);
+
+                    $temp = $u;
+                    $u = $v;
+                    $v = bcsub($temp, bcmul($v, $q, 0), 0);
+
+                    $temp = $a;
+                    $a = $c;
+                    $c = bcsub($temp, bcmul($a, $q, 0), 0);
+
+                    $temp = $b;
+                    $b = $d;
+                    $d = bcsub($temp, bcmul($b, $q, 0), 0);
+                }
+
+                return array(
+                    'gcd' => $this->_normalize(new Math_BigInteger($u)),
+                    'x'   => $this->_normalize(new Math_BigInteger($a)),
+                    'y'   => $this->_normalize(new Math_BigInteger($b))
+                );
+        }
+
+        $y = $n->copy();
+        $x = $this->copy();
+        $g = new Math_BigInteger();
+        $g->value = array(1);
+
+        while ( !(($x->value[0] & 1)|| ($y->value[0] & 1)) ) {
+            $x->_rshift(1);
+            $y->_rshift(1);
+            $g->_lshift(1);
+        }
+
+        $u = $x->copy();
+        $v = $y->copy();
+
+        $a = new Math_BigInteger();
+        $b = new Math_BigInteger();
+        $c = new Math_BigInteger();
+        $d = new Math_BigInteger();
+
+        $a->value = $d->value = $g->value = array(1);
+        $b->value = $c->value = array();
+
+        while ( !empty($u->value) ) {
+            while ( !($u->value[0] & 1) ) {
+                $u->_rshift(1);
+                if ( (!empty($a->value) && ($a->value[0] & 1)) || (!empty($b->value) && ($b->value[0] & 1)) ) {
+                    $a = $a->add($y);
+                    $b = $b->subtract($x);
+                }
+                $a->_rshift(1);
+                $b->_rshift(1);
+            }
+
+            while ( !($v->value[0] & 1) ) {
+                $v->_rshift(1);
+                if ( (!empty($d->value) && ($d->value[0] & 1)) || (!empty($c->value) && ($c->value[0] & 1)) ) {
+                    $c = $c->add($y);
+                    $d = $d->subtract($x);
+                }
+                $c->_rshift(1);
+                $d->_rshift(1);
+            }
+
+            if ($u->compare($v) >= 0) {
+                $u = $u->subtract($v);
+                $a = $a->subtract($c);
+                $b = $b->subtract($d);
+            } else {
+                $v = $v->subtract($u);
+                $c = $c->subtract($a);
+                $d = $d->subtract($b);
+            }
+        }
+
+        return array(
+            'gcd' => $this->_normalize($g->multiply($v)),
+            'x'   => $this->_normalize($c),
+            'y'   => $this->_normalize($d)
+        );
+    }
+
+    /**
+     * Calculates the greatest common divisor
+     *
+     * Say you have 693 and 609.  The GCD is 21.
+     *
+     * Here's an example:
+     * <code>
+     * <?php
+     *    include('Math/BigInteger.php');
+     *
+     *    $a = new Math_BigInteger(693);
+     *    $b = new Math_BigInteger(609);
+     *
+     *    $gcd = a->extendedGCD($b);
+     *
+     *    echo $gcd->toString() . "\r\n"; // outputs 21
+     * ?>
+     * </code>
+     *
+     * @param Math_BigInteger $n
+     * @return Math_BigInteger
+     * @access public
+     */
+    function gcd($n)
+    {
+        extract($this->extendedGCD($n));
+        return $gcd;
+    }
+
+    /**
+     * Absolute value.
+     *
+     * @return Math_BigInteger
+     * @access public
+     */
+    function abs()
+    {
+        $temp = new Math_BigInteger();
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp->value = gmp_abs($this->value);
+                break;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp->value = (bccomp($this->value, '0', 0) < 0) ? substr($this->value, 1) : $this->value;
+                break;
+            default:
+                $temp->value = $this->value;
+        }
+
+        return $temp;
+    }
+
+    /**
+     * Compares two numbers.
+     *
+     * Although one might think !$x->compare($y) means $x != $y, it, in fact, means the opposite.  The reason for this is
+     * demonstrated thusly:
+     *
+     * $x  > $y: $x->compare($y)  > 0
+     * $x  < $y: $x->compare($y)  < 0
+     * $x == $y: $x->compare($y) == 0
+     *
+     * Note how the same comparison operator is used.  If you want to test for equality, use $x->equals($y).
+     *
+     * @param Math_BigInteger $y
+     * @return Integer < 0 if $this is less than $y; > 0 if $this is greater than $y, and 0 if they are equal.
+     * @access public
+     * @see equals()
+     * @internal Could return $this->subtract($x), but that's not as fast as what we do do.
+     */
+    function compare($y)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                return gmp_cmp($this->value, $y->value);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                return bccomp($this->value, $y->value, 0);
+        }
+
+        return $this->_compare($this->value, $this->is_negative, $y->value, $y->is_negative);
+    }
+
+    /**
+     * Compares two numbers.
+     *
+     * @param Array $x_value
+     * @param Boolean $x_negative
+     * @param Array $y_value
+     * @param Boolean $y_negative
+     * @return Integer
+     * @see compare()
+     * @access private
+     */
+    function _compare($x_value, $x_negative, $y_value, $y_negative)
+    {
+        if ( $x_negative != $y_negative ) {
+            return ( !$x_negative && $y_negative ) ? 1 : -1;
+        }
+
+        $result = $x_negative ? -1 : 1;
+
+        if ( count($x_value) != count($y_value) ) {
+            return ( count($x_value) > count($y_value) ) ? $result : -$result;
+        }
+        $size = max(count($x_value), count($y_value));
+
+        $x_value = array_pad($x_value, $size, 0);
+        $y_value = array_pad($y_value, $size, 0);
+
+        for ($i = count($x_value) - 1; $i >= 0; --$i) {
+            if ($x_value[$i] != $y_value[$i]) {
+                return ( $x_value[$i] > $y_value[$i] ) ? $result : -$result;
+            }
+        }
+
+        return 0;
+    }
+
+    /**
+     * Tests the equality of two numbers.
+     *
+     * If you need to see if one number is greater than or less than another number, use Math_BigInteger::compare()
+     *
+     * @param Math_BigInteger $x
+     * @return Boolean
+     * @access public
+     * @see compare()
+     */
+    function equals($x)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                return gmp_cmp($this->value, $x->value) == 0;
+            default:
+                return $this->value === $x->value && $this->is_negative == $x->is_negative;
+        }
+    }
+
+    /**
+     * Set Precision
+     *
+     * Some bitwise operations give different results depending on the precision being used.  Examples include left
+     * shift, not, and rotates.
+     *
+     * @param Integer $bits
+     * @access public
+     */
+    function setPrecision($bits)
+    {
+        $this->precision = $bits;
+        if ( MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_BCMATH ) {
+            $this->bitmask = new Math_BigInteger(chr((1 << ($bits & 0x7)) - 1) . str_repeat(chr(0xFF), $bits >> 3), 256);
+        } else {
+            $this->bitmask = new Math_BigInteger(bcpow('2', $bits, 0));
+        }
+
+        $temp = $this->_normalize($this);
+        $this->value = $temp->value;
+    }
+
+    /**
+     * Logical And
+     *
+     * @param Math_BigInteger $x
+     * @access public
+     * @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat>
+     * @return Math_BigInteger
+     */
+    function bitwise_and($x)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_and($this->value, $x->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $left = $this->toBytes();
+                $right = $x->toBytes();
+
+                $length = max(strlen($left), strlen($right));
+
+                $left = str_pad($left, $length, chr(0), STR_PAD_LEFT);
+                $right = str_pad($right, $length, chr(0), STR_PAD_LEFT);
+
+                return $this->_normalize(new Math_BigInteger($left & $right, 256));
+        }
+
+        $result = $this->copy();
+
+        $length = min(count($x->value), count($this->value));
+
+        $result->value = array_slice($result->value, 0, $length);
+
+        for ($i = 0; $i < $length; ++$i) {
+            $result->value[$i]&= $x->value[$i];
+        }
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Logical Or
+     *
+     * @param Math_BigInteger $x
+     * @access public
+     * @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat>
+     * @return Math_BigInteger
+     */
+    function bitwise_or($x)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_or($this->value, $x->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $left = $this->toBytes();
+                $right = $x->toBytes();
+
+                $length = max(strlen($left), strlen($right));
+
+                $left = str_pad($left, $length, chr(0), STR_PAD_LEFT);
+                $right = str_pad($right, $length, chr(0), STR_PAD_LEFT);
+
+                return $this->_normalize(new Math_BigInteger($left | $right, 256));
+        }
+
+        $length = max(count($this->value), count($x->value));
+        $result = $this->copy();
+        $result->value = array_pad($result->value, $length, 0);
+        $x->value = array_pad($x->value, $length, 0);
+
+        for ($i = 0; $i < $length; ++$i) {
+            $result->value[$i]|= $x->value[$i];
+        }
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Logical Exclusive-Or
+     *
+     * @param Math_BigInteger $x
+     * @access public
+     * @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat>
+     * @return Math_BigInteger
+     */
+    function bitwise_xor($x)
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                $temp = new Math_BigInteger();
+                $temp->value = gmp_xor($this->value, $x->value);
+
+                return $this->_normalize($temp);
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $left = $this->toBytes();
+                $right = $x->toBytes();
+
+                $length = max(strlen($left), strlen($right));
+
+                $left = str_pad($left, $length, chr(0), STR_PAD_LEFT);
+                $right = str_pad($right, $length, chr(0), STR_PAD_LEFT);
+
+                return $this->_normalize(new Math_BigInteger($left ^ $right, 256));
+        }
+
+        $length = max(count($this->value), count($x->value));
+        $result = $this->copy();
+        $result->value = array_pad($result->value, $length, 0);
+        $x->value = array_pad($x->value, $length, 0);
+
+        for ($i = 0; $i < $length; ++$i) {
+            $result->value[$i]^= $x->value[$i];
+        }
+
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Logical Not
+     *
+     * @access public
+     * @internal Implemented per a request by Lluis Pamies i Juarez <lluis _a_ pamies.cat>
+     * @return Math_BigInteger
+     */
+    function bitwise_not()
+    {
+        // calculuate "not" without regard to $this->precision
+        // (will always result in a smaller number.  ie. ~1 isn't 1111 1110 - it's 0)
+        $temp = $this->toBytes();
+        $pre_msb = decbin(ord($temp[0]));
+        $temp = ~$temp;
+        $msb = decbin(ord($temp[0]));
+        if (strlen($msb) == 8) {
+            $msb = substr($msb, strpos($msb, '0'));
+        }
+        $temp[0] = chr(bindec($msb));
+
+        // see if we need to add extra leading 1's
+        $current_bits = strlen($pre_msb) + 8 * strlen($temp) - 8;
+        $new_bits = $this->precision - $current_bits;
+        if ($new_bits <= 0) {
+            return $this->_normalize(new Math_BigInteger($temp, 256));
+        }
+
+        // generate as many leading 1's as we need to.
+        $leading_ones = chr((1 << ($new_bits & 0x7)) - 1) . str_repeat(chr(0xFF), $new_bits >> 3);
+        $this->_base256_lshift($leading_ones, $current_bits);
+
+        $temp = str_pad($temp, ceil($this->bits / 8), chr(0), STR_PAD_LEFT);
+
+        return $this->_normalize(new Math_BigInteger($leading_ones | $temp, 256));
+    }
+
+    /**
+     * Logical Right Shift
+     *
+     * Shifts BigInteger's by $shift bits, effectively dividing by 2**$shift.
+     *
+     * @param Integer $shift
+     * @return Math_BigInteger
+     * @access public
+     * @internal The only version that yields any speed increases is the internal version.
+     */
+    function bitwise_rightShift($shift)
+    {
+        $temp = new Math_BigInteger();
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                static $two;
+
+                if (!isset($two)) {
+                    $two = gmp_init('2');
+                }
+
+                $temp->value = gmp_div_q($this->value, gmp_pow($two, $shift));
+
+                break;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp->value = bcdiv($this->value, bcpow('2', $shift, 0), 0);
+
+                break;
+            default: // could just replace _lshift with this, but then all _lshift() calls would need to be rewritten
+                     // and I don't want to do that...
+                $temp->value = $this->value;
+                $temp->_rshift($shift);
+        }
+
+        return $this->_normalize($temp);
+    }
+
+    /**
+     * Logical Left Shift
+     *
+     * Shifts BigInteger's by $shift bits, effectively multiplying by 2**$shift.
+     *
+     * @param Integer $shift
+     * @return Math_BigInteger
+     * @access public
+     * @internal The only version that yields any speed increases is the internal version.
+     */
+    function bitwise_leftShift($shift)
+    {
+        $temp = new Math_BigInteger();
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                static $two;
+
+                if (!isset($two)) {
+                    $two = gmp_init('2');
+                }
+
+                $temp->value = gmp_mul($this->value, gmp_pow($two, $shift));
+
+                break;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                $temp->value = bcmul($this->value, bcpow('2', $shift, 0), 0);
+
+                break;
+            default: // could just replace _rshift with this, but then all _lshift() calls would need to be rewritten
+                     // and I don't want to do that...
+                $temp->value = $this->value;
+                $temp->_lshift($shift);
+        }
+
+        return $this->_normalize($temp);
+    }
+
+    /**
+     * Logical Left Rotate
+     *
+     * Instead of the top x bits being dropped they're appended to the shifted bit string.
+     *
+     * @param Integer $shift
+     * @return Math_BigInteger
+     * @access public
+     */
+    function bitwise_leftRotate($shift)
+    {
+        $bits = $this->toBytes();
+
+        if ($this->precision > 0) {
+            $precision = $this->precision;
+            if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH ) {
+                $mask = $this->bitmask->subtract(new Math_BigInteger(1));
+                $mask = $mask->toBytes();
+            } else {
+                $mask = $this->bitmask->toBytes();
+            }
+        } else {
+            $temp = ord($bits[0]);
+            for ($i = 0; $temp >> $i; ++$i);
+            $precision = 8 * strlen($bits) - 8 + $i;
+            $mask = chr((1 << ($precision & 0x7)) - 1) . str_repeat(chr(0xFF), $precision >> 3);
+        }
+
+        if ($shift < 0) {
+            $shift+= $precision;
+        }
+        $shift%= $precision;
+
+        if (!$shift) {
+            return $this->copy();
+        }
+
+        $left = $this->bitwise_leftShift($shift);
+        $left = $left->bitwise_and(new Math_BigInteger($mask, 256));
+        $right = $this->bitwise_rightShift($precision - $shift);
+        $result = MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_BCMATH ? $left->bitwise_or($right) : $left->add($right);
+        return $this->_normalize($result);
+    }
+
+    /**
+     * Logical Right Rotate
+     *
+     * Instead of the bottom x bits being dropped they're prepended to the shifted bit string.
+     *
+     * @param Integer $shift
+     * @return Math_BigInteger
+     * @access public
+     */
+    function bitwise_rightRotate($shift)
+    {
+        return $this->bitwise_leftRotate(-$shift);
+    }
+
+    /**
+     * Set random number generator function
+     *
+     * This function is deprecated.
+     *
+     * @param String $generator
+     * @access public
+     */
+    function setRandomGenerator($generator)
+    {
+    }
+
+    /**
+     * Generate a random number
+     *
+     * @param optional Integer $min
+     * @param optional Integer $max
+     * @return Math_BigInteger
+     * @access public
+     */
+    function random($min = false, $max = false)
+    {
+        if ($min === false) {
+            $min = new Math_BigInteger(0);
+        }
+
+        if ($max === false) {
+            $max = new Math_BigInteger(0x7FFFFFFF);
+        }
+
+        $compare = $max->compare($min);
+
+        if (!$compare) {
+            return $this->_normalize($min);
+        } else if ($compare < 0) {
+            // if $min is bigger then $max, swap $min and $max
+            $temp = $max;
+            $max = $min;
+            $min = $temp;
+        }
+
+        $max = $max->subtract($min);
+        $max = ltrim($max->toBytes(), chr(0));
+        $size = strlen($max) - 1;
+
+        $crypt_random = function_exists('crypt_random_string') || (!class_exists('Crypt_Random') && function_exists('crypt_random_string'));
+        if ($crypt_random) {
+            $random = crypt_random_string($size);
+        } else {
+            $random = '';
+
+            if ($size & 1) {
+                $random.= chr(mt_rand(0, 255));
+            }
+
+            $blocks = $size >> 1;
+            for ($i = 0; $i < $blocks; ++$i) {
+                // mt_rand(-2147483648, 0x7FFFFFFF) always produces -2147483648 on some systems
+                $random.= pack('n', mt_rand(0, 0xFFFF));
+            }
+        }
+
+        $fragment = new Math_BigInteger($random, 256);
+        $leading = $fragment->compare(new Math_BigInteger(substr($max, 1), 256)) > 0 ?
+            ord($max[0]) - 1 : ord($max[0]);
+
+        if (!$crypt_random) {
+            $msb = chr(mt_rand(0, $leading));
+        } else {
+            $cutoff = floor(0xFF / $leading) * $leading;
+            while (true) {
+                $msb = ord(crypt_random_string(1));
+                if ($msb <= $cutoff) {
+                    $msb%= $leading;
+                    break;
+                }
+            }
+            $msb = chr($msb);
+        }
+
+        $random = new Math_BigInteger($msb . $random, 256);
+
+        return $this->_normalize($random->add($min));
+    }
+
+    /**
+     * Generate a random prime number.
+     *
+     * If there's not a prime within the given range, false will be returned.  If more than $timeout seconds have elapsed,
+     * give up and return false.
+     *
+     * @param optional Integer $min
+     * @param optional Integer $max
+     * @param optional Integer $timeout
+     * @return Math_BigInteger
+     * @access public
+     * @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=15 HAC 4.44}.
+     */
+    function randomPrime($min = false, $max = false, $timeout = false)
+    {
+        if ($min === false) {
+            $min = new Math_BigInteger(0);
+        }
+
+        if ($max === false) {
+            $max = new Math_BigInteger(0x7FFFFFFF);
+        }
+
+        $compare = $max->compare($min);
+
+        if (!$compare) {
+            return $min->isPrime() ? $min : false;
+        } else if ($compare < 0) {
+            // if $min is bigger then $max, swap $min and $max
+            $temp = $max;
+            $max = $min;
+            $min = $temp;
+        }
+
+        static $one, $two;
+        if (!isset($one)) {
+            $one = new Math_BigInteger(1);
+            $two = new Math_BigInteger(2);
+        }
+
+        $start = time();
+
+        $x = $this->random($min, $max);
+
+        // gmp_nextprime() requires PHP 5 >= 5.2.0 per <http://php.net/gmp-nextprime>.
+        if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_GMP && function_exists('gmp_nextprime') ) {
+            $p = new Math_BigInteger();
+            $p->value = gmp_nextprime($x->value);
+
+            if ($p->compare($max) <= 0) {
+                return $p;
+            }
+
+            if (!$min->equals($x)) {
+                $x = $x->subtract($one);
+            }
+
+            return $x->randomPrime($min, $x);
+        }
+
+        if ($x->equals($two)) {
+            return $x;
+        }
+
+        $x->_make_odd();
+        if ($x->compare($max) > 0) {
+            // if $x > $max then $max is even and if $min == $max then no prime number exists between the specified range
+            if ($min->equals($max)) {
+                return false;
+            }
+            $x = $min->copy();
+            $x->_make_odd();
+        }
+
+        $initial_x = $x->copy();
+
+        while (true) {
+            if ($timeout !== false && time() - $start > $timeout) {
+                return false;
+            }
+
+            if ($x->isPrime()) {
+                return $x;
+            }
+
+            $x = $x->add($two);
+
+            if ($x->compare($max) > 0) {
+                $x = $min->copy();
+                if ($x->equals($two)) {
+                    return $x;
+                }
+                $x->_make_odd();
+            }
+
+            if ($x->equals($initial_x)) {
+                return false;
+            }
+        }
+    }
+
+    /**
+     * Make the current number odd
+     *
+     * If the current number is odd it'll be unchanged.  If it's even, one will be added to it.
+     *
+     * @see randomPrime()
+     * @access private
+     */
+    function _make_odd()
+    {
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                gmp_setbit($this->value, 0);
+                break;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                if ($this->value[strlen($this->value) - 1] % 2 == 0) {
+                    $this->value = bcadd($this->value, '1');
+                }
+                break;
+            default:
+                $this->value[0] |= 1;
+        }
+    }
+
+    /**
+     * Checks a numer to see if it's prime
+     *
+     * Assuming the $t parameter is not set, this function has an error rate of 2**-80.  The main motivation for the
+     * $t parameter is distributability.  Math_BigInteger::randomPrime() can be distributed accross multiple pageloads
+     * on a website instead of just one.
+     *
+     * @param optional Integer $t
+     * @return Boolean
+     * @access public
+     * @internal Uses the
+     *     {@link http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test Miller-Rabin primality test}.  See 
+     *     {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=8 HAC 4.24}.
+     */
+    function isPrime($t = false)
+    {
+        $length = strlen($this->toBytes());
+
+        if (!$t) {
+            // see HAC 4.49 "Note (controlling the error probability)"
+                 if ($length >= 163) { $t =  2; } // floor(1300 / 8)
+            else if ($length >= 106) { $t =  3; } // floor( 850 / 8)
+            else if ($length >= 81 ) { $t =  4; } // floor( 650 / 8)
+            else if ($length >= 68 ) { $t =  5; } // floor( 550 / 8)
+            else if ($length >= 56 ) { $t =  6; } // floor( 450 / 8)
+            else if ($length >= 50 ) { $t =  7; } // floor( 400 / 8)
+            else if ($length >= 43 ) { $t =  8; } // floor( 350 / 8)
+            else if ($length >= 37 ) { $t =  9; } // floor( 300 / 8)
+            else if ($length >= 31 ) { $t = 12; } // floor( 250 / 8)
+            else if ($length >= 25 ) { $t = 15; } // floor( 200 / 8)
+            else if ($length >= 18 ) { $t = 18; } // floor( 150 / 8)
+            else                     { $t = 27; }
+        }
+
+        // ie. gmp_testbit($this, 0)
+        // ie. isEven() or !isOdd()
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                return gmp_prob_prime($this->value, $t) != 0;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                if ($this->value === '2') {
+                    return true;
+                }
+                if ($this->value[strlen($this->value) - 1] % 2 == 0) {
+                    return false;
+                }
+                break;
+            default:
+                if ($this->value == array(2)) {
+                    return true;
+                }
+                if (~$this->value[0] & 1) {
+                    return false;
+                }
+        }
+
+        static $primes, $zero, $one, $two;
+
+        if (!isset($primes)) {
+            $primes = array(
+                3,    5,    7,    11,   13,   17,   19,   23,   29,   31,   37,   41,   43,   47,   53,   59,   
+                61,   67,   71,   73,   79,   83,   89,   97,   101,  103,  107,  109,  113,  127,  131,  137,  
+                139,  149,  151,  157,  163,  167,  173,  179,  181,  191,  193,  197,  199,  211,  223,  227,  
+                229,  233,  239,  241,  251,  257,  263,  269,  271,  277,  281,  283,  293,  307,  311,  313,  
+                317,  331,  337,  347,  349,  353,  359,  367,  373,  379,  383,  389,  397,  401,  409,  419,  
+                421,  431,  433,  439,  443,  449,  457,  461,  463,  467,  479,  487,  491,  499,  503,  509,  
+                521,  523,  541,  547,  557,  563,  569,  571,  577,  587,  593,  599,  601,  607,  613,  617,  
+                619,  631,  641,  643,  647,  653,  659,  661,  673,  677,  683,  691,  701,  709,  719,  727,  
+                733,  739,  743,  751,  757,  761,  769,  773,  787,  797,  809,  811,  821,  823,  827,  829,  
+                839,  853,  857,  859,  863,  877,  881,  883,  887,  907,  911,  919,  929,  937,  941,  947,  
+                953,  967,  971,  977,  983,  991,  997
+            );
+
+            if ( MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL ) {
+                for ($i = 0; $i < count($primes); ++$i) {
+                    $primes[$i] = new Math_BigInteger($primes[$i]);
+                }
+            }
+
+            $zero = new Math_BigInteger();
+            $one = new Math_BigInteger(1);
+            $two = new Math_BigInteger(2);
+        }
+
+        if ($this->equals($one)) {
+            return false;
+        }
+
+        // see HAC 4.4.1 "Random search for probable primes"
+        if ( MATH_BIGINTEGER_MODE != MATH_BIGINTEGER_MODE_INTERNAL ) {
+            foreach ($primes as $prime) {
+                list(, $r) = $this->divide($prime);
+                if ($r->equals($zero)) {
+                    return $this->equals($prime);
+                }
+            }
+        } else {
+            $value = $this->value;
+            foreach ($primes as $prime) {
+                list(, $r) = $this->_divide_digit($value, $prime);
+                if (!$r) {
+                    return count($value) == 1 && $value[0] == $prime;
+                }
+            }
+        }
+
+        $n   = $this->copy();
+        $n_1 = $n->subtract($one);
+        $n_2 = $n->subtract($two);
+
+        $r = $n_1->copy();
+        $r_value = $r->value;
+        // ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
+        if ( MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_BCMATH ) {
+            $s = 0;
+            // if $n was 1, $r would be 0 and this would be an infinite loop, hence our $this->equals($one) check earlier
+            while ($r->value[strlen($r->value) - 1] % 2 == 0) {
+                $r->value = bcdiv($r->value, '2', 0);
+                ++$s;
+            }
+        } else {
+            for ($i = 0, $r_length = count($r_value); $i < $r_length; ++$i) {
+                $temp = ~$r_value[$i] & 0xFFFFFF;
+                for ($j = 1; ($temp >> $j) & 1; ++$j);
+                if ($j != 25) {
+                    break;
+                }
+            }
+            $s = 26 * $i + $j - 1;
+            $r->_rshift($s);
+        }
+
+        for ($i = 0; $i < $t; ++$i) {
+            $a = $this->random($two, $n_2);
+            $y = $a->modPow($r, $n);
+
+            if (!$y->equals($one) && !$y->equals($n_1)) {
+                for ($j = 1; $j < $s && !$y->equals($n_1); ++$j) {
+                    $y = $y->modPow($two, $n);
+                    if ($y->equals($one)) {
+                        return false;
+                    }
+                }
+
+                if (!$y->equals($n_1)) {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    /**
+     * Logical Left Shift
+     *
+     * Shifts BigInteger's by $shift bits.
+     *
+     * @param Integer $shift
+     * @access private
+     */
+    function _lshift($shift)
+    {
+        if ( $shift == 0 ) {
+            return;
+        }
+
+        $num_digits = (int) ($shift / MATH_BIGINTEGER_BASE);
+        $shift %= MATH_BIGINTEGER_BASE;
+        $shift = 1 << $shift;
+
+        $carry = 0;
+
+        for ($i = 0; $i < count($this->value); ++$i) {
+            $temp = $this->value[$i] * $shift + $carry;
+            $carry = (int) ($temp / MATH_BIGINTEGER_BASE_FULL);
+            $this->value[$i] = (int) ($temp - $carry * MATH_BIGINTEGER_BASE_FULL);
+        }
+
+        if ( $carry ) {
+            $this->value[] = $carry;
+        }
+
+        while ($num_digits--) {
+            array_unshift($this->value, 0);
+        }
+    }
+
+    /**
+     * Logical Right Shift
+     *
+     * Shifts BigInteger's by $shift bits.
+     *
+     * @param Integer $shift
+     * @access private
+     */
+    function _rshift($shift)
+    {
+        if ($shift == 0) {
+            return;
+        }
+
+        $num_digits = (int) ($shift / MATH_BIGINTEGER_BASE);
+        $shift %= MATH_BIGINTEGER_BASE;
+        $carry_shift = MATH_BIGINTEGER_BASE - $shift;
+        $carry_mask = (1 << $shift) - 1;
+
+        if ( $num_digits ) {
+            $this->value = array_slice($this->value, $num_digits);
+        }
+
+        $carry = 0;
+
+        for ($i = count($this->value) - 1; $i >= 0; --$i) {
+            $temp = $this->value[$i] >> $shift | $carry;
+            $carry = ($this->value[$i] & $carry_mask) << $carry_shift;
+            $this->value[$i] = $temp;
+        }
+
+        $this->value = $this->_trim($this->value);
+    }
+
+    /**
+     * Normalize
+     *
+     * Removes leading zeros and truncates (if necessary) to maintain the appropriate precision
+     *
+     * @param Math_BigInteger
+     * @return Math_BigInteger
+     * @see _trim()
+     * @access private
+     */
+    function _normalize($result)
+    {
+        $result->precision = $this->precision;
+        $result->bitmask = $this->bitmask;
+
+        switch ( MATH_BIGINTEGER_MODE ) {
+            case MATH_BIGINTEGER_MODE_GMP:
+                if (!empty($result->bitmask->value)) {
+                    $result->value = gmp_and($result->value, $result->bitmask->value);
+                }
+
+                return $result;
+            case MATH_BIGINTEGER_MODE_BCMATH:
+                if (!empty($result->bitmask->value)) {
+                    $result->value = bcmod($result->value, $result->bitmask->value);
+                }
+
+                return $result;
+        }
+
+        $value = &$result->value;
+
+        if ( !count($value) ) {
+            return $result;
+        }
+
+        $value = $this->_trim($value);
+
+        if (!empty($result->bitmask->value)) {
+            $length = min(count($value), count($this->bitmask->value));
+            $value = array_slice($value, 0, $length);
+
+            for ($i = 0; $i < $length; ++$i) {
+                $value[$i] = $value[$i] & $this->bitmask->value[$i];
+            }
+        }
+
+        return $result;
+    }
+
+    /**
+     * Trim
+     *
+     * Removes leading zeros
+     *
+     * @param Array $value
+     * @return Math_BigInteger
+     * @access private
+     */
+    function _trim($value)
+    {
+        for ($i = count($value) - 1; $i >= 0; --$i) {
+            if ( $value[$i] ) {
+                break;
+            }
+            unset($value[$i]);
+        }
+
+        return $value;
+    }
+
+    /**
+     * Array Repeat
+     *
+     * @param $input Array
+     * @param $multiplier mixed
+     * @return Array
+     * @access private
+     */
+    function _array_repeat($input, $multiplier)
+    {
+        return ($multiplier) ? array_fill(0, $multiplier, $input) : array();
+    }
+
+    /**
+     * Logical Left Shift
+     *
+     * Shifts binary strings $shift bits, essentially multiplying by 2**$shift.
+     *
+     * @param $x String
+     * @param $shift Integer
+     * @return String
+     * @access private
+     */
+    function _base256_lshift(&$x, $shift)
+    {
+        if ($shift == 0) {
+            return;
+        }
+
+        $num_bytes = $shift >> 3; // eg. floor($shift/8)
+        $shift &= 7; // eg. $shift % 8
+
+        $carry = 0;
+        for ($i = strlen($x) - 1; $i >= 0; --$i) {
+            $temp = ord($x[$i]) << $shift | $carry;
+            $x[$i] = chr($temp);
+            $carry = $temp >> 8;
+        }
+        $carry = ($carry != 0) ? chr($carry) : '';
+        $x = $carry . $x . str_repeat(chr(0), $num_bytes);
+    }
+
+    /**
+     * Logical Right Shift
+     *
+     * Shifts binary strings $shift bits, essentially dividing by 2**$shift and returning the remainder.
+     *
+     * @param $x String
+     * @param $shift Integer
+     * @return String
+     * @access private
+     */
+    function _base256_rshift(&$x, $shift)
+    {
+        if ($shift == 0) {
+            $x = ltrim($x, chr(0));
+            return '';
+        }
+
+        $num_bytes = $shift >> 3; // eg. floor($shift/8)
+        $shift &= 7; // eg. $shift % 8
+
+        $remainder = '';
+        if ($num_bytes) {
+            $start = $num_bytes > strlen($x) ? -strlen($x) : -$num_bytes;
+            $remainder = substr($x, $start);
+            $x = substr($x, 0, -$num_bytes);
+        }
+
+        $carry = 0;
+        $carry_shift = 8 - $shift;
+        for ($i = 0; $i < strlen($x); ++$i) {
+            $temp = (ord($x[$i]) >> $shift) | $carry;
+            $carry = (ord($x[$i]) << $carry_shift) & 0xFF;
+            $x[$i] = chr($temp);
+        }
+        $x = ltrim($x, chr(0));
+
+        $remainder = chr($carry >> $carry_shift) . $remainder;
+
+        return ltrim($remainder, chr(0));
+    }
+
+    // one quirk about how the following functions are implemented is that PHP defines N to be an unsigned long
+    // at 32-bits, while java's longs are 64-bits.
+
+    /**
+     * Converts 32-bit integers to bytes.
+     *
+     * @param Integer $x
+     * @return String
+     * @access private
+     */
+    function _int2bytes($x)
+    {
+        return ltrim(pack('N', $x), chr(0));
+    }
+
+    /**
+     * Converts bytes to 32-bit integers
+     *
+     * @param String $x
+     * @return Integer
+     * @access private
+     */
+    function _bytes2int($x)
+    {
+        $temp = unpack('Nint', str_pad($x, 4, chr(0), STR_PAD_LEFT));
+        return $temp['int'];
+    }
+
+    /**
+     * DER-encode an integer
+     *
+     * The ability to DER-encode integers is needed to create RSA public keys for use with OpenSSL
+     *
+     * @see modPow()
+     * @access private
+     * @param Integer $length
+     * @return String
+     */
+    function _encodeASN1Length($length)
+    {
+        if ($length <= 0x7F) {
+            return chr($length);
+        }
+
+        $temp = ltrim(pack('N', $length), chr(0));
+        return pack('Ca*', 0x80 | strlen($temp), $temp);
+    }
+}
diff --git a/inc/phpseclib/update.sh b/inc/phpseclib/update.sh
new file mode 100755
index 000000000..ff3747a14
--- /dev/null
+++ b/inc/phpseclib/update.sh
@@ -0,0 +1,8 @@
+#!/bin/sh
+
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/LICENSE -O LICENSE
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/phpseclib/Math/BigInteger.php -O Math_BigInteger.php
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/phpseclib/Crypt/AES.php -O Crypt_AES.php
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/phpseclib/Crypt/Rijndael.php -O Crypt_Rijndael.php
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/phpseclib/Crypt/Base.php -O Crypt_Base.php
+wget -nv https://raw.github.com/phpseclib/phpseclib/master/phpseclib/Crypt/Hash.php -O Crypt_Hash.php