Problem 1. Password Attacks (20 pt., 5 pt. each) Suppose you could use the 26 lower-case letters in a password and the length of the password is set to 8 characters. Answer the following questions. Hint: On average, it needs to test half of all possible passwords to crack one. a. What is the number of passwords that could be constructed from such a character set? b. Assume a brute-force attack and the attacker knows the length of the password. How long, on average, would it take the attacker to guess such a password if the attacker could test a password every millisecond? Report in second. c. Now assume a dictionary attack. The attacker knows the length of the password and the dictionary contains 100,000 words that have the same length as the password (i.e., 8 characters). How long, on average, would it take the attacker to guess such a password if the attacker could test a password every millisecond? Report in second. d. Lets assume the use of salting. If a password is salted with a 24-bit random number, how big is the dictionary attack search space when using the dictionary in question c?