/Crypt/RSA.php

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<?php
/* vim: set expandtab tabstop=4 shiftwidth=4 softtabstop=4: */

/**
 * 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: This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston,
 * MA  02111-1307  USA
 *
 * @category   Crypt
 * @package    Crypt_RSA
 * @author     Jim Wigginton <terrafrost@php.net>
 * @copyright  MMIX Jim Wigginton
 * @license    http://www.opensource.org/licenses/mit-license.html  MIT License
 * @version    $Id: RSA.php,v 1.19 2010/09/12 21:58:54 terrafrost Exp $
 * @link       http://phpseclib.sourceforge.net
 */

/**
 * Include Math_BigInteger
 */
require_once('Math/BigInteger.php');

/**
 * Include Crypt_Random
 */
require_once('Crypt/Random.php');

/**
 * Include Crypt_Hash
 */
require_once('Crypt/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
 * compatability 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
 * compatability 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 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);
/**#@-*/

/**#@+
 * @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);
/**#@-*/

/**#@+
 * @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', 1);
/**
 * PKCS#1 formatted public key
 */
define('CRYPT_RSA_PUBLIC_FORMAT_PKCS1', 2);
/**
 * OpenSSH formatted public key
 *
 * Place in $HOME/.ssh/authorized_keys
 */
define('CRYPT_RSA_PUBLIC_FORMAT_OPENSSH', 3);
/**#@-*/

/**
 * Pure-PHP PKCS#1 compliant implementation of RSA.
 *
 * @author  Jim Wigginton <terrafrost@php.net>
 * @version 0.1.0
 * @access  public
 * @package Crypt_RSA
 */
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_PKCS1;

    /**
     * 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 = '';

    /**
     * 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 ( !defined('CRYPT_RSA_MODE') ) {
            switch (true) {
                //case extension_loaded('openssl') && version_compare(PHP_VERSION, '4.2.0', '>='):
                //    define('CRYPT_RSA_MODE', CRYPT_RSA_MODE_OPENSSL);
                //    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 ( CRYPT_RSA_MODE == CRYPT_RSA_MODE_OPENSSL ) {
            $rsa = openssl_pkey_new(array('private_key_bits' => $bits));
            openssl_pkey_export($rsa, $privatekey);
            $publickey = openssl_pkey_get_details($rsa);
            $publickey = $publickey['key'];

            if ($this->privateKeyFormat != CRYPT_RSA_PRIVATE_FORMAT_PKCS1) {
                $privatekey = call_user_func_array(array($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)));
            }

            return array(
                'privatekey' => $privatekey,
                'publickey' => $publickey,
                'partialkey' => false
            );
        }

        static $e;
        if (!isset($e)) {
            if (!defined('CRYPT_RSA_EXPONENT')) {
                // http://en.wikipedia.org/wiki/65537_%28number%29
                define('CRYPT_RSA_EXPONENT', '65537');
            }
            if (!defined('CRYPT_RSA_COMMENT')) {
                define('CRYPT_RSA_COMMENT', 'phpseclib-generated-key');
            }
            // per <http://cseweb.ucsd.edu/~hovav/dist/survey.pdf#page=5>, this number ought not result in primes smaller
            // than 256 bits.
            if (!defined('CRYPT_RSA_SMALLEST_PRIME')) {
                define('CRYPT_RSA_SMALLEST_PRIME', 4096);
            }

            $e = new Math_BigInteger(CRYPT_RSA_EXPONENT);
        }

        extract($this->_generateMinMax($bits));
        $absoluteMin = $min;
        $temp = $bits >> 1;
        if ($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();
        $generator->setRandomGenerator('crypt_random');

        $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($lcm) = $lcm['top']->divide($lcm['bottom']);
            $gcd = $lcm->gcd($e);
            $i0 = 1;
        } while (!$gcd->equals($this->one));

        $d = $e->modInverse($lcm);

        $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)
    {
        $num_primes = count($primes);
        $raw = array(
            'version' => $num_primes == 2 ? chr(0) : chr(1), // two-prime vs. multi
            'modulus' => $n->toBytes(true),
            'publicExponent' => $e->toBytes(true),
            'privateExponent' => $d->toBytes(true),
            'prime1' => $primes[1]->toBytes(true),
            'prime2' => $primes[2]->toBytes(true),
            'exponent1' => $exponents[1]->toBytes(true),
            'exponent2' => $exponents[2]->toBytes(true),
            'coefficient' => $coefficients[2]->toBytes(true)
        );

        // if the format in question does not support multi-prime rsa and multi-prime rsa was used,
        // call _convertPublicKey() instead.
        switch ($this->privateKeyFormat) {
            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 (!empty($this->password)) {
                    $iv = $this->_random(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')) {
                        require_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))) .
                                     '-----END RSA PRIVATE KEY-----';
                } else {
                    $RSAPrivateKey = "-----BEGIN RSA PRIVATE KEY-----\r\n" .
                                     chunk_split(base64_encode($RSAPrivateKey)) .
                                     '-----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)
    {
        $modulus = $n->toBytes(true);
        $publicExponent = $e->toBytes(true);

        switch ($this->publicKeyFormat) {
            case CRYPT_RSA_PUBLIC_FORMAT_RAW:
                return array('e' => $e->copy(), 'n' => $n->copy());
            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) . ' ' . CRYPT_RSA_COMMENT;

                return $RSAPublicKey;
            default: // eg. 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']
                );

                $RSAPublicKey = "-----BEGIN PUBLIC KEY-----\r\n" .
                                 chunk_split(base64_encode($RSAPublicKey)) .
                                 '-----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, $type)
    {
        switch ($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 $components;
            case CRYPT_RSA_PRIVATE_FORMAT_PKCS1:
            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
                    $symkey.= substr(pack('H*', md5($symkey . $this->password . $iv)), 0, 8);
                    $ciphertext = preg_replace('#.+(\r|\n|\r\n)\1|[\r\n]|-.+-#s', '', $key);
                    $ciphertext = preg_match('#^[a-zA-Z\d/+]*={0,2}$#', $ciphertext) ? base64_decode($ciphertext) : false;
                    if ($ciphertext === false) {
                        $ciphertext = $key;
                    }
                    switch ($matches[1]) {
                        case 'AES-128-CBC':
                            if (!class_exists('Crypt_AES')) {
                                require_once('Crypt/AES.php');
                            }
                            $symkey = substr($symkey, 0, 16);
                            break;
                        case 'DES-EDE3-CFB':
                            if (!class_exists('Crypt_TripleDES')) {
                                require_once('Crypt/TripleDES.php');
                            }
                            $crypto = new Crypt_TripleDES(CRYPT_DES_MODE_CFB);
                            break;
                        case 'DES-EDE3-CBC':
                            if (!class_exists('Crypt_TripleDES')) {
                                require_once('Crypt/TripleDES.php');
                            }
                            $crypto = new Crypt_TripleDES();
                            break;
                        case 'DES-CBC':
                            if (!class_exists('Crypt_DES')) {
                                require_once('Crypt/DES.php');
                            }
                            $crypto = new Crypt_DES();
                            break;
                        default:
                            return false;
                    }
                    $crypto->setKey($symkey);
                    $crypto->setIV($iv);
                    $decoded = $crypto->decrypt($ciphertext);
                } else {
                    $decoded = preg_replace('#-.+-|[\r\n]#', '', $key);
                    $decoded = preg_match('#^[a-zA-Z\d/+]*={0,2}$#', $decoded) ? base64_decode($decoded) : false;
                }

                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($key));
                if ($tag == CRYPT_RSA_ASN1_SEQUENCE) {
                    /* 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 */
                    $this->_string_shift($key, $this->_decodeLength($key));
                    $this->_string_shift($key); // skip over the BIT STRING tag
                    $this->_decodeLength($key); // skip over the BIT 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 teh 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)
                    $this->_string_shift($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:
                $key = base64_decode(preg_replace('#^ssh-rsa | .+$#', '', $key));
                if ($key === false) {
                    return false;
                }

                $cleanup = substr($key, 0, 11) == "\0\0\0\7ssh-rsa";

                extract(unpack('Nlength', $this->_string_shift($key, 4)));
                $publicExponent = new Math_BigInteger($this->_string_shift($key, $length), -256);
                extract(unpack('Nlength', $this->_string_shift($key, 4)));
                $modulus = new Math_BigInteger($this->_string_shift($key, $length), -256);

                if ($cleanup && strlen($key)) {
                    extract(unpack('Nlength', $this->_string_shift($key, 4)));
                    return array(
                        'modulus' => new Math_BigInteger($this->_string_shift($key, $length), -256),
                        'publicExponent' => $modulus
                    );
                } else {
                    return array(
                        'modulus' => $modulus,
                        'publicExponent' => $publicExponent
                    );
                }
        }
    }

    /**
     * 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 = CRYPT_RSA_PRIVATE_FORMAT_PKCS1)
    {
        $components = $this->_parseKey($key, $type);
        if ($components === false) {
            return false;
        }

        $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;
        }

        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 true.
     *
     * @see createKey()
     * @see loadKey()
     * @access public
     * @param String $password
     */
    function setPassword($password)
    {
        $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.
     *
     * 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
     * @param Integer $type optional
     * @return Boolean
     */
    function setPublicKey($key, $type = CRYPT_RSA_PUBLIC_FORMAT_PKCS1)
    {
        $components = $this->_parseKey($key, $type);

        if (empty($this->modulus) || !$this->modulus->equals($components['modulus'])) {
            user_error('Trying to load a public key?  Use loadKey() instead.  It\'s called loadKey() and not loadPrivateKey() for a reason.', E_USER_NOTICE);
            return false;
        }

        $this->publicExponent = $components['publicExponent'];

        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_PKCS1)
    {
        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;
    }

    /**
     * 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 § 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 § 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;
    }

    /**
     * Generates a random string x bytes long
     *
     * @access public
     * @param Integer $bytes
     * @param optional Integer $nonzero
     * @return String
     */
    function _random($bytes, $nonzero = false)
    {
        $temp = '';
        if ($nonzero) {
            for ($i = 0; $i < $bytes; $i++) {
                $temp.= chr(crypt_random(1, 255));
            }
        } else {
            $ints = ($bytes + 1) >> 2;
            for ($i = 0; $i < $ints; $i++) {
                $temp.= pack('N', crypt_random());
            }
            $temp = substr($temp, 0, $bytes);
        }
        return $temp;
    }

    /**
     * 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) > $xLen) {
            user_error('Integer too large', E_USER_NOTICE);
            return false;
        }
        return str_pad($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);
            $one->setRandomGenerator('crypt_random');

            $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;
    }

    /**
     * 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', E_USER_NOTICE);
            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', E_USER_NOTICE);
            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
     …