Suppose all passwords on a given system are 8 characters long and that each character can have any one of 64 different values. The passwords are hashed (with a salt) andstored in a password ?le. Now suppose Trudy has a password cracking programthat can test 64 passwords per second. Trudy also has a dictionary of 2^30 common passwords and the probability that any given password is in her dictionary is 1/4.The password ?le on this system contains 256 password hashes.

a. How many different passwords are possible?
b. How long, on average, will it take Trudy to “crack” the password for the administrator’saccount?
c. What is the probability that at least one of the 256 passwords in the password ?le is in the dictionary?
d. What is the expected work for Trudy to recover any one of the passwords in the password?le?