way encryption: I need to store passwords that can be retrieved

I am creating an application that will store passwords, which the user can retrieve and see. The passwords are for a hardware device, so checking against hashes are out of the question.

What I need to know is:

Personally, I would use mcrypt like others posted. But there is much more to note...

$key = $userKey . $serverKey . $userSuppliedKey;

Edit: Here's a PHP class implementation of a strong encryption method:

/**
 * A class to handle secure encryption and decryption of arbitrary data
 *
 * Note that this is not just straight encryption.  It also has a few other
 *  features in it to make the encrypted data far more secure.  Note that any
 *  other implementations used to decrypt data will have to do the same exact
 *  operations.  
 *
 * Security Benefits:
 *
 * - Uses Key stretching
 * - Hides the Initialization Vector
 * - Does HMAC verification of source data
 *
 */
class Encryption {

    /**
     * @var string $cipher The mcrypt cipher to use for this instance
     */
    protected $cipher = '';

    /**
     * @var int $mode The mcrypt cipher mode to use
     */
    protected $mode = '';

    /**
     * @var int $rounds The number of rounds to feed into PBKDF2 for key generation
     */
    protected $rounds = 100;

    /**
     * Constructor!
     *
     * @param string $cipher The MCRYPT_* cypher to use for this instance
     * @param int    $mode   The MCRYPT_MODE_* mode to use for this instance
     * @param int    $rounds The number of PBKDF2 rounds to do on the key
     */
    public function __construct($cipher, $mode, $rounds = 100) {
        $this->cipher = $cipher;
        $this->mode = $mode;
        $this->rounds = (int) $rounds;
    }

    /**
     * Decrypt the data with the provided key
     *
     * @param string $data The encrypted datat to decrypt
     * @param string $key  The key to use for decryption
     * 
     * @returns string|false The returned string if decryption is successful
     *                           false if it is not
     */
    public function decrypt($data, $key) {
        $salt = substr($data, 0, 128);
        $enc = substr($data, 128, -64);
        $mac = substr($data, -64);

        list ($cipherKey, $macKey, $iv) = $this->getKeys($salt, $key);

        if (!hash_equals(hash_hmac('sha512', $enc, $macKey, true), $mac)) {
             return false;
        }

        $dec = mcrypt_decrypt($this->cipher, $cipherKey, $enc, $this->mode, $iv);

        $data = $this->unpad($dec);

        return $data;
    }

    /**
     * Encrypt the supplied data using the supplied key
     * 
     * @param string $data The data to encrypt
     * @param string $key  The key to encrypt with
     *
     * @returns string The encrypted data
     */
    public function encrypt($data, $key) {
        $salt = mcrypt_create_iv(128, MCRYPT_DEV_URANDOM);
        list ($cipherKey, $macKey, $iv) = $this->getKeys($salt, $key);

        $data = $this->pad($data);

        $enc = mcrypt_encrypt($this->cipher, $cipherKey, $data, $this->mode, $iv);

        $mac = hash_hmac('sha512', $enc, $macKey, true);
        return $salt . $enc . $mac;
    }

    /**
     * Generates a set of keys given a random salt and a master key
     *
     * @param string $salt A random string to change the keys each encryption
     * @param string $key  The supplied key to encrypt with
     *
     * @returns array An array of keys (a cipher key, a mac key, and a IV)
     */
    protected function getKeys($salt, $key) {
        $ivSize = mcrypt_get_iv_size($this->cipher, $this->mode);
        $keySize = mcrypt_get_key_size($this->cipher, $this->mode);
        $length = 2 * $keySize + $ivSize;

        $key = $this->pbkdf2('sha512', $key, $salt, $this->rounds, $length);

        $cipherKey = substr($key, 0, $keySize);
        $macKey = substr($key, $keySize, $keySize);
        $iv = substr($key, 2 * $keySize);
        return array($cipherKey, $macKey, $iv);
    }

    /**
     * Stretch the key using the PBKDF2 algorithm
     *
     * @see http://en.wikipedia.org/wiki/PBKDF2
     *
     * @param string $algo   The algorithm to use
     * @param string $key    The key to stretch
     * @param string $salt   A random salt
     * @param int    $rounds The number of rounds to derive
     * @param int    $length The length of the output key
     *
     * @returns string The derived key.
     */
    protected function pbkdf2($algo, $key, $salt, $rounds, $length) {
        $size   = strlen(hash($algo, '', true));
        $len    = ceil($length / $size);
        $result = '';
        for ($i = 1; $i <= $len; $i++) {
            $tmp = hash_hmac($algo, $salt . pack('N', $i), $key, true);
            $res = $tmp;
            for ($j = 1; $j < $rounds; $j++) {
                 $tmp  = hash_hmac($algo, $tmp, $key, true);
                 $res ^= $tmp;
            }
            $result .= $res;
        }
        return substr($result, 0, $length);
    }

    protected function pad($data) {
        $length = mcrypt_get_block_size($this->cipher, $this->mode);
        $padAmount = $length - strlen($data) % $length;
        if ($padAmount == 0) {
            $padAmount = $length;
        }
        return $data . str_repeat(chr($padAmount), $padAmount);
    }

    protected function unpad($data) {
        $length = mcrypt_get_block_size($this->cipher, $this->mode);
        $last = ord($data[strlen($data) - 1]);
        if ($last > $length) return false;
        if (substr($data, -1 * $last) !== str_repeat(chr($last), $last)) {
            return false;
        }
        return substr($data, 0, -1 * $last);
    }
}

Note that I'm using a function added in PHP 5.6: hash_equals . If you're on lower than 5.6, you can use this substitute function which implements a timing-safe comparison function using double HMAC verification:

function hash_equals($a, $b) {
    $key = mcrypt_create_iv(128, MCRYPT_DEV_URANDOM);
    return hash_hmac('sha512', $a, $key) === hash_hmac('sha512', $b, $key);
}

Usage:

$e = new Encryption(MCRYPT_BLOWFISH, MCRYPT_MODE_CBC);
$encryptedData = $e->encrypt($data, $key);

Then, to decrypt:

$e2 = new Encryption(MCRYPT_BLOWFISH, MCRYPT_MODE_CBC);
$data = $e2->decrypt($encryptedData, $key);

Note that I used $e2 the second time to show you different instances will still properly decrypt the data.

Now, how does it work/why use it over another solution:

Now, as to point 3 from the first list, what that would give you is a function like this:

function makeKey($userKey, $serverKey, $userSuppliedKey) {
    $key = hash_hmac('sha512', $userKey, $serverKey);
    $key = hash_hmac('sha512', $key, $userSuppliedKey);
    return $key;
}

You could stretch it in the makeKey() function, but since it's going to be stretched later, there's not really a huge point to doing so.

As far as the storage size, it depends on the plain text. Blowfish uses a 8 byte block size, so you'll have:

So for a 16 character data source, there will be 16 characters of data to be encrypted. So that means the actual encrypted data size is 16 bytes due to padding. Then add the 16 bytes for the salt and 64 bytes for the hmac and the total stored size is 96 bytes. So there's at best a 80 character overhead, and at worst a 87 character overhead...

I hope that helps...

Note: 12/11/12: I just updated this class with a MUCH better encryption method, using better derived keys, and fixing the MAC generation...

How do I encrypt and decrypt a password in PHP? By implementing one of many encryption algorithms. (or using one of many libraries)

What is the safest algorithm to encrypt the passwords with? There are tons of different algorithms, none of which are 100% secure. But many of them are secure enough for commerce and even military purposes

Where do I store the private key? If you have decided to implement public key - cryptography algorithm(eg RSA), you don't store private key. user have private key. your system has public key which could be stored anywhere you wish.

Instead of storing the private key, is it a good idea to require users to enter the private key any time they need a password decrypted? (Users of this application can be trusted) Well if your user can remember ridiculously long prime numbers then - yes, why not. But generally you would need to come up with the system which will allow user to store their key somewhere.

In what ways can the password be stolen and decrypted? What do I need to be aware of? This depends on the algorithm used. However always make sure that you don't send password unencrypted to or from the user. Either encrypt/decrypt it on the client side, or use https(or user other cryptographic means to secure connection between server and client).

However if all you need is to store passwords in encrypted way, I would suggest you to use a simple XOR Cipher. The main problem with this algorithm is that it could be easily broken by frequency analysis. However as generally passwords are not made from long paragraphs of English text I don't think you should worry about it. The second problem with XOR Cipher is that if you have a message in both encrypted and decrypted form you could easily find out password with which it was encrypted. Again, not a big problem in your case as it only affects the user who already was compromised by other means.

The example from the manual is slightly edited for this example):

<?php
$iv_size = mcrypt_get_iv_size(MCRYPT_BLOWFISH, MCRYPT_MODE_ECB);
$iv = mcrypt_create_iv($iv_size, MCRYPT_RAND);
$key = "This is a very secret key";
$pass = "PasswordHere";
echo strlen($pass) . "n";

$crypttext = mcrypt_encrypt(MCRYPT_BLOWFISH, $key, $pass, MCRYPT_MODE_ECB, $iv);
echo strlen($crypttext) . "n";
?>

You would use mcrypt_decrypt to decrypt your password.

I'd put a rider on my answer - I'm not a PHP crypto expert, but, I think what I have answered is standard practice - I welcome comments other may have.

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