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 $212$ passwords. Trudy has a dictionary of $224$ passwords, and the probability that a randomly selected password is in her dictionary is $1/4.$ Work is measured in terms of the number of hashes computed.

a$.$ Suppose that Trudy wants to recover Alice$$s password. Using her dictionary, what is the expected work for Trudy to crack Alice$$s password, assuming the passwords are not salted?

b$.$ Repeat part a$,$ assuming the passwords are salted.

c$.$ What is the probability that at least one of the passwords in the password file appears in Trudy$$s dictionary? 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 $212$

passwords. Trudy has a dictionary of $224$ passwords, and the probability that

a randomly selected password is in her dictionary is $\frac{1}{4}.$ Work is measured in

terms of the number of hashes computed.

a$.$ Suppose that Trudy wants to recover Alice's password. Using her

dictionary, what is the expected work for Trudy to crack Alice's

password, assuming the passwords are not salted?

b$.$ Repeat part a$,$ assuming the passwords are salted.

c$.$ What is the probability that at least one of the passwords in the

password file appears in Trudy's dictionary?