PBKDF2 constants

Question

I recently found this PBKDF2 code:

<?php
/*
 * Password Hashing With PBKDF2 (http://crackstation.net/hashing-security.htm).
 * Copyright (c) 2013, Taylor Hornby
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, 
 * this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation 
 * and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE 
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
 * POSSIBILITY OF SUCH DAMAGE.
 */

// These constants may be changed without breaking existing hashes.
define("PBKDF2_HASH_ALGORITHM", "sha256");
define("PBKDF2_ITERATIONS", 1000);
define("PBKDF2_SALT_BYTE_SIZE", 24);
define("PBKDF2_HASH_BYTE_SIZE", 24);

define("HASH_SECTIONS", 4);
define("HASH_ALGORITHM_INDEX", 0);
define("HASH_ITERATION_INDEX", 1);
define("HASH_SALT_INDEX", 2);
define("HASH_PBKDF2_INDEX", 3);

function create_hash($password)
{
    // format: algorithm:iterations:salt:hash
    $salt = base64_encode(mcrypt_create_iv(PBKDF2_SALT_BYTE_SIZE, MCRYPT_DEV_URANDOM));
    return PBKDF2_HASH_ALGORITHM . ":" . PBKDF2_ITERATIONS . ":" .  $salt . ":" .
        base64_encode(pbkdf2(
            PBKDF2_HASH_ALGORITHM,
            $password,
            $salt,
            PBKDF2_ITERATIONS,
            PBKDF2_HASH_BYTE_SIZE,
            true
        ));
}

function validate_password($password, $correct_hash)
{
    $params = explode(":", $correct_hash);
    if(count($params) < HASH_SECTIONS)
       return false;
    $pbkdf2 = base64_decode($params[HASH_PBKDF2_INDEX]);
    return slow_equals(
        $pbkdf2,
        pbkdf2(
            $params[HASH_ALGORITHM_INDEX],
            $password,
            $params[HASH_SALT_INDEX],
            (int)$params[HASH_ITERATION_INDEX],
            strlen($pbkdf2),
            true
        )
    );
}

// Compares two strings $a and $b in length-constant time.
function slow_equals($a, $b)
{
    $diff = strlen($a) ^ strlen($b);
    for($i = 0; $i < strlen($a) && $i < strlen($b); $i++)
    {
        $diff |= ord($a[$i]) ^ ord($b[$i]);
    }
    return $diff === 0;
}

/*
 * PBKDF2 key derivation function as defined by RSA's PKCS #5: https://www.ietf.org/rfc/rfc2898.txt
 * $algorithm - The hash algorithm to use. Recommended: SHA256
 * $password - The password.
 * $salt - A salt that is unique to the password.
 * $count - Iteration count. Higher is better, but slower. Recommended: At least 1000.
 * $key_length - The length of the derived key in bytes.
 * $raw_output - If true, the key is returned in raw binary format. Hex encoded otherwise.
 * Returns: A $key_length-byte key derived from the password and salt.
 *
 * Test vectors can be found here: https://www.ietf.org/rfc/rfc6070.txt
 *
 * This implementation of PBKDF2 was originally created by https://defuse.ca
 * With improvements by http://www.variations-of-shadow.com
 */
function pbkdf2($algorithm, $password, $salt, $count, $key_length, $raw_output = false)
{
    $algorithm = strtolower($algorithm);
    if(!in_array($algorithm, hash_algos(), true))
        trigger_error('PBKDF2 ERROR: Invalid hash algorithm.', E_USER_ERROR);
    if($count <= 0 || $key_length <= 0)
        trigger_error('PBKDF2 ERROR: Invalid parameters.', E_USER_ERROR);

    if (function_exists("hash_pbkdf2")) {
        // The output length is in NIBBLES (4-bits) if $raw_output is false!
        if (!$raw_output) {
            $key_length = $key_length * 2;
        }
        return hash_pbkdf2($algorithm, $password, $salt, $count, $key_length, $raw_output);
    }

    $hash_length = strlen(hash($algorithm, "", true));
    $block_count = ceil($key_length / $hash_length);

    $output = "";
    for($i = 1; $i <= $block_count; $i++) {
        // $i encoded as 4 bytes, big endian.
        $last = $salt . pack("N", $i);
        // first iteration
        $last = $xorsum = hash_hmac($algorithm, $last, $password, true);
        // perform the other $count - 1 iterations
        for ($j = 1; $j < $count; $j++) {
            $xorsum ^= ($last = hash_hmac($algorithm, $last, $password, true));
        }
        $output .= $xorsum;
    }

    if($raw_output)
        return substr($output, 0, $key_length);
    else
        return bin2hex(substr($output, 0, $key_length));
}
?>

However, I did not find anywhere what do these constants do and what are their recommended values:

define("PBKDF2_SALT_BYTE_SIZE", 24);
define("PBKDF2_HASH_BYTE_SIZE", 24);
define("HASH_SECTIONS", 4);
define("HASH_ALGORITHM_INDEX", 0);
define("HASH_ITERATION_INDEX", 1);
define("HASH_SALT_INDEX", 2);
define("HASH_PBKDF2_INDEX", 3);

Can you please explain this to me?

Answer 1

Taking first the second block

define("HASH_SECTIONS", 4);
define("HASH_ALGORITHM_INDEX", 0);
define("HASH_ITERATION_INDEX", 1);
define("HASH_SALT_INDEX", 2);
define("HASH_PBKDF2_INDEX", 3);

it's just a verbose way of specifying the "stringized" storage format. The create_hash function concatenates the hash algorithm, iteration count, salt, and pbkdf2 result (password hash) in that order separated by colons into a single string for storage. validate_password splits that stored string at the colons to get 4 pieces in an array, so the hash algorithm is at index 0 in the array and is accessed using [HASH_ALGORITHM_INDEX] where HASH_ALGORITHM_INDEX is 0, and the iteration count is at index 1 and is accessed using [HASH_ITERATION_INDEX] where HASH_ITERATION_INDEX is 1, etc.

The first block are the actual security parameters:

PBKDF2_ITERATIONS = 1000 was recommended when rfc2898 was written in 2000, but as computer hardware has advanced is now less secure. If you can you should test significantly larger values; try for at least 100k, and a million or more would be better if it doesn't hurt the performance of your system for login (and password-change, but that should be rarer).

PBKDF2_SALT_BYTE_SIZE = 24 is the size in bytes of the salt, which should be large enough to be unique with overwhelming probability for every password you hash; because of the birthday paradox this should span at least the square of the number of passwords plus a safety margin. 24 bytes = 192 bits is generous; it allows I think every atom in the solar system to have a unique password on your system, and I don't think even google plans for that. You could reduce it to 16 or even 12 if you want, and get on average a small increase in performance, but it's probably not worth the trouble. Definitely don't go below 8 or you're at real risk of duplicates.

PBKDF2_HASH_BYTE_SIZE = 24 is the size in bytes of the hash generated. It should be large enough to be well out of brute-force range and like salt unique for every password, but it should not be more than the output size of the hash (and thus HMAC) used, because that differentially increases defense cost for offline attack (where the constanttime equals can't be enforced). For sha256 the output size is 32 bytes so 24 is fine; actually anything from about 16 to 32 is fine. If you wanted to use sha1 you should decrease hash size to 20 bytes, but there's no good reason to use sha1 and doing so will probably attract criticism and perhaps audits that it would be a waste of time to deal with.