It was stated that inclusion of the salt the UNIX password scheme increases the difficulty of guessing by a factor of 4096. Let's use a case to explain why it is asserted that the salt increases security although the salt is stored in plaintext in the same entry as the corresponding ciphertext password. Let's assume that the adversary has obtained a password file containing 4000 entries, each using a unique 12-bit salt.

1. In order to crack all the 4000 hashed passwords in the password file on a UNIX system, how many times does the hash routine, i.e., crypt(3), need to run in the worst case?

2. If the salt is NOT used, how many times does the hash routine, i.e., crypt(3), need to run in the worst case in order to crack all the 4000 hashed passwords?

3. If 24-bit salt is used for this case, does the hash routine need to run more times in the worst case to crack all the 4000 hashed passwords? If so, how many more?