In a given system, passwords are required to be 8 to 12 characters in length.

Each character can be any alphanumeric character and passwords are case sensitive.

For authentication matching purposes, all passwords are hashed and stored in a password file.

The password file contains 1024 password hash values, with each belonging to a single user in the system.

Suppose an intruder has gotten access to the password file and the intruder has a dictionary containing 2^16 common passwords and there is a 6.25% chance that any given password is in that dictionary.

In addition, the intruder has a computer that can generate and compare 10^9 hashes per second.

Part A How many different passwords are possible? What if the password was not case sensitive? Explain your answer and show all calculations and results.

Part B How many years would it take to check every possible valid password combination (in both cases above)?

Part C Suppose the intruder wants to recover the password of Bill, who is a user in the system. Right now the intruder only has Bills password hash value in the password file. Using the intruders dictionary, what is the number of hash operations that the intruder expects to compute in order to find out Bills password, given the 6.25% chance that any given password is in the dictionary as mentioned above? Assuming that the intruder has a computer which can generate 109 hashes per second, how long would this take?

Part D What is the probability that at least one of the 1024 passwords kept in the system actually exists in the intruders dictionary?