How are Crypt and Salt more secure than MD5 against a brute force attack?

Question

I read on PHP.net that MD5 is useless, and they suggest using crypt + salt.

So, I went to their function description and read

<?php
$password = crypt('mypassword'); // let the salt be automatically generated

/* You should pass the entire results of crypt() as the salt for comparing a
   password, to avoid problems when different hashing algorithms are used. (As
   it says above, standard DES-based password hashing uses a 2-character salt,
   but MD5-based hashing uses 12.) */
if (crypt($user_input, $password) == $password) {
   echo "Password verified!";
}
?>

or in my case something like :

$stored_password=fetch_password($user);
if (crypt($_REQUEST['password'],$stored_password)===$stored_password) {
// ok
}

So, when I see that the salt is stored in the hashed password and that you use that hashed password as salt, I think Crypt + Salt is not more secure against a brute force on output (hackers who managed to steal hashed passwords). Is it more secure?

Against a dictionary attack, I can understand its power, but for a brute force attack on hashed passwords, I don't see the advantage.

Answer 1

When applying salt to a string (password in the example) before hashing, the hash now becomes another hash than it would without the salt. Without the salt, you could just use a pre-existing dictionary - now instead you need to create a dictionary to the salt. If you use a user specific salt, each user needs to have it's own dictionary when using brute force. This becomes way more time consuming.

MD5 is a broken algoritm because of its collision vulnerabilities.