Suppose all passwords on a given system are 8 characters and that each character can be any one of 64 different values. The passwords are hashed (with a salt) and stored in a password file. Now...

Suppose all passwords on a given system are 8 characters and that each character can be any one of 64 different values. The passwords are hashed (with a salt) and stored in a password file. Now suppose Trudy has a password cracking program that can test 64 passwords per second. Trudy also has a dictionary of 230 common passwords and the probability that any given password is in her dictionary is 1/4. The password file 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 administrator's password?

c. What is the probability that at least one of the 256 passwords in the password file is in the dictionary?

d. What is the expected work for Trudy to recover any one of the passwords in the password file?