$(9$pt$)$ Suppose that on a particular system, all passwords are $8$ characters, there are

$128$ choices for each character, and there is a password file containing the hashes of

$2^{10}$ passwords. Attacker has a dictionary of $2^{30}$ passwords, and the probability that a

randomly selected password is in her dictionary is $\frac{1}{4}.$ Attacker wants to recover Bob's

password with her dictionary.

$($a$)(3$pt$)$ What is the expected work for attacker to crack Bob's password, assuming

the passwords are not salted? To clarify, work is measured in terms of the number

of hashes computed.

$($b$)(3$pt$)$ Repeat part a$,$ assuming the passwords are salted.

Homework $3$

COMP $3632$

$($c$)(3$pt$)$ What is the probability that at least one of the passwords in the password

file appears in attacker's dictionary?