/vendors/phpseclib/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: 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  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
 */
if (!class_exists('Math_BigInteger')) {
    require_once('Math/BigInteger.php');
}

/**
 * Include Crypt_Random
 */
// the class_exists() will only be called if the crypt_random 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 require_once from being called outside
// of the auto loader
if (!function_exists('crypt_random') && !class_exists('Crypt_Random') && !function_exists('crypt_random')) {
    require_once('Crypt/Random.php');
}

/**
 * Include Crypt_Hash
 */
if (!class_exists('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 Bit String
 */
define('CRYPT_RSA_ASN1_BITSTRING', 3); 
/**
 * 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);
/**
 * PuTTY formatted private key
 */
define('CRYPT_RSA_PRIVATE_FORMAT_PUTTY', 1);
/**
 * XML formatted private key
 */
define('CRYPT_RSA_PRIVATE_FORMAT_XML', 2);
/**#@-*/

/**#@+
 * @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
 */
define('CRYPT_RSA_PUBLIC_FORMAT_PKCS1', 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);
/**#@-*/

/**
 * 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 = '';

    /**
     * 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;

    /**
     * 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);
            }
        }

        if (!defined('CRYPT_RSA_COMMENT')) {
            define('CRYPT_RSA_COMMENT', 'phpseclib-generated-key');
        }

        $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) {
            $rsa = openssl_pkey_new(array(
                'private_key_bits' => $bits,
                'config' => dirname(__FILE__) . '/../openssl.cnf'
            ));

            openssl_pkey_export($rsa, $privatekey, NULL, array('config' => dirname(__FILE__) . '/../openssl.cnf'));
            $publickey = openssl_pkey_get_details($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)));
            }

            // 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();
        $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 ($this->privateKeyFormat) {
            case CRYPT_RSA_PRIVATE_FORMAT_XML:
                if ($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)) ? 'aes256-cbc' : 'none';
                $key.= $encryption;
                $key.= "\r\nComment: " . CRYPT_RSA_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), $encryption,
                              strlen(CRYPT_RSA_COMMENT), CRYPT_RSA_COMMENT, strlen($public), $public
                );
                $public = base64_encode($public);
                $key.= "Public-Lines: " . ((strlen($public) + 32) >> 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)) {
                    $source.= pack('Na*', strlen($private), $private);
                    $hashkey = 'putty-private-key-file-mac-key';
                } else {
                    $private.= $this->_random(16 - (strlen($private) & 15));
                    $source.= pack('Na*', strlen($private), $private);
                    if (!class_exists('Crypt_AES')) {
                        require_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) + 32) >> 6) . "\r\n";
                $key.= chunk_split($private, 64);
                if (!class_exists('Crypt_Hash')) {
                    require_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 (!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' => $n->copy());
            case CRYPT_RSA_PUBLIC_FORMAT_XML:
                return "<RSAKeyValue>\r\n" .
                       '  <Modulus>' . base64_encode($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) . ' ' . 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, $type)
    {
        if ($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_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);
                            $crypto = new Crypt_AES();
                            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));
                /* 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 */

                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) {
                    /* 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));
                    $tag = ord($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:
                $key = base64_decode(preg_replace('#^ssh-rsa | .+$#', '', $key));
                if ($key === false) {
                    return 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' => $modulus
                    );
                } else {
                    return strlen($key) ? false : array(
                        'modulus' => $modulus,
                        'publicExponent' => $publicExponent
                    );
                }
            // 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($xml, '_data_handler');
                if (!xml_parse($xml, $key)) {
                    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]));

                $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')) {
                            require_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;
        }
    }

    /**
     * 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'];
                break;
            default:
                unset($this->current);
        }
        $this->current = '';
    }

    /**
     * Stop Element Handler
     *
     * Called by xml_set_element_handler()
     *
     * @access private
     * @param Resource $parser
     * @param String $name
     */
    function _stop_element_handler($parser, $name)
    {
        //$name = strtoupper($name);
        if ($name == 'RSAKEYVALUE') {
            return;
        }
        $this->current = new Math_BigInteger(base64_decode($this->current), 256);
    }

    /**
     * Data Handler
     *
     * Called by xml_set_character_data_handler()
     *
     * @access private
     * @param Resource $parser
 …