Suppose a password based authentication system requires the password to be 15 characters long and it should contain exactly two digits, exactly two of the six special characters, namely, {!,@,#,$,%,&} and the rest of the characters can be upper and lower case letters. How many such passwords are possible? (a) Assume that the password file is encrypted and the password file is available for the attacker. If the attacker has access to a supercomputer which can encrypt 1015 passwords per second, how many years will it take for the attacker to determine the password of user using brute force attack? 1 (b) If the password file is salted with a salt of length 128 bits and the slow hash functions used for computing the hash of one password takes 5 seconds on a single node of a super computer. How many years will it take for the attacker to compute the rainbow table of passwords for such a system, if the attacker has access to a super computer containing 10 million such nodes, using brute force attack? (14 points)