In cryptography, a key derivation function (or KDF) derives one or more secret keys from a secret value such as a master key or other known information such as a password or passphrase using a pseudorandom function. For instance, a KDF function can be used to generate encryption or authentication keys from a user password. The Zend\Crypt\Key\Derivation implements a key derivation function using specific adapters.
User passwords are not really suitable to be used as keys in cryptographic algorithms, since users normally choose keys they can write on keyboard. These passwords use only 6 to 7 bits per character (or less). It is highly recommended to use always a KDF function to transform a user’s password in a cryptographic key.
The output of the following key derivation functions is a binary string. If you need to store the value in a database or a different persistent storage, we suggest to convert it in Base64 format, using base64_encode() function, or in hex format, using the bin2hex() function.
Pbkdf2 is a KDF that applies a pseudorandom function, such as a cryptographic hash, to the input password or passphrase along with a salt value and repeats the process many times to produce a derived key, which can then be used as a cryptographic key in subsequent operations. The added computational work makes password cracking much more difficult, and is known as key stretching.
In the example below we show a typical usage of the Pbkdf2 adapter.
1 2 3 4 5 6 7 8 9  use Zend\Crypt\Key\Derivation\Pbkdf2;
use Zend\Math\Rand;
$pass = 'password';
$salt = Rand::getBytes(32, true);
$key = Pbkdf2::calc('sha256', $pass, $salt, 10000, 32);
printf ("Original password: %s\n", $pass);
printf ("Derived key (hex): %s\n", bin2hex($key));

The Pbkdf2 adapter takes the password ($pass) and generate a binary key of 32 bytes. The syntax is calc($hash, $pass, $salt, $iterations, $length) where $hash is the name of the hash function to use, $pass is the password, $salt is a pseudo random value, $iterations is the number of iterations of the algorithm and $length is the size of the key to be generated. We used the Rand::getBytes function of the Zend\Math\Rand class to generate a random string of 32 bytes for the salt, using a strong generator (the true value means the usage of a cryptographically strong generator).
The number of iterations is a very important parameter for the security of the algorithm. Bigger values guarantee more security. There is not a fixed value for that because the number of iterations depends on the CPU power. You should always choose a number of iteration that prevent brute force attacks. For instance, a value of 1‘000‘000 iterations, that is equal to 1 sec of elaboration for the PBKDF2 algorithm, is enough secure using an Intel Core i52500 CPU at 3.3 Ghz.
The SaltedS2k algorithm uses an hash function and a salt to generate a key based on a user’s password. This algorithm doesn’t use a parameter that specify the number of iterations and for that reason it’s considered less secure compared with Pbkdf2. We suggest to use the SaltedS2k algorithm only if you really need it.
Below is reported a usage example of the SaltedS2k adapter to generate a key of 32 bytes.
1 2 3 4 5 6 7 8 9  use Zend\Crypt\Key\Derivation\SaltedS2k;
use Zend\Math\Rand;
$pass = 'password';
$salt = Rand::getBytes(32, true);
$key = SaltedS2k::calc('sha256', $pass, $salt, 32);
printf ("Original password: %s\n", $pass);
printf ("Derived key (hex): %s\n", bin2hex($key));

The scrypt algorithm uses the algorithm Salsa20/8 core and Pbkdf2SHA256 to generate a key based on a user’s password. This algorithm has been designed to be more secure against hardware bruteforce attacks than alternative functions such as Pbkdf2 or bcrypt.
The scrypt algorithm is based on the idea of memoryhard algorithms and sequential memoryhard functions. A memoryhard algorithm is thus an algorithm which asymptotically uses almost as many memory locations as it uses operations[#f1]_. A natural way to reduce the advantage provided by an attacker’s ability to construct highly parallel circuits is to increase the size of a single key derivation circuit — if a circuit is twice as large, only half as many copies can be placed on a given area of silicon — while still operating within the resources available to software implementations, including a powerful CPU and large amounts of RAM.
“From a test executed on modern (2009) hardware, if 5 seconds are spent computing a derived key, the cost of a hardware bruteforce attack against scrypt is roughly 4000 times greater than the cost of a similar attack against bcrypt (to find the same password), and 20000 times greater than a similar attack against Pbkdf2.” Colin Percival (the author of scrypt algorithm)
This algorithm uses 4 parameters to generate a key of 32 bytes:
Below is reported a usage example of the Scrypt adapter.
1 2 3 4 5 6 7 8 9  use Zend\Crypt\Key\Derivation\Scrypt;
use Zend\Math\Rand;
$pass = 'password';
$salt = Rand::getBytes(32, true);
$key = Scrypt::calc($pass, $salt, 2048, 2, 1, 32);
printf ("Original password: %s\n", $pass);
printf ("Derived key (hex): %s\n", bin2hex($key));

Note
Performance of the scrypt implementation
The aim of the scrypt algorithm is to generate secure derived key preventing brute force attacks. Just like the other derivation functions, the more time (and memory) we spent executing the algorithm, the more secure the derived key will be. Unfortunately a pure PHP implementation of the scrypt algorithm is very slow compared with the C implementation (this is always true, if you compare execution time of C with PHP). If you want use a faster scrypt algorithm we suggest to install the scrypt PECL extension. The Scrypt adapter of Zend Framework is able to recognize if the PECL extension is loaded and use it instead of the pure PHP implementation.
[1]  See Colin Percival’s slides on scrypt from BSDCan‘09: http://www.tarsnap.com/scrypt/scryptslides.pdf 
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