It was stated that the inclusion of the salt in the UNIX password scheme increases the difficulty of guessing by a factor of 4096. But the salt is stored in plaintext in the same entry as the corresponding ciphertext password. Although those two characters are known to the attacker and need not be guessed, the salt still increases security.

1. If there are at most N accounts on the password file, how many bits do we need for the salt?
2. What is the standard salt size for UNIX, how does that get calculated?
3. Would it be possible to thwart all password crackers by increasing the salt size to, say, 24 or 48 bits? (10 points)