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 210 passwords. Trudy has a dictionary of 230 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.

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

2. Repeat part a, assuming the passwords are salted.

3. What is the probability that at least one of the passwords in the password file appears in Trudys dictionary?