Suppose that Alice encrypted a message with a secure cipher that uses a 40-bit key. Trudy knows the ciphertext and Trudy knows the algorithm, but she does not know the plaintext or the key. Trudy plans to do an exhaustive search attack, that is, she will try each possible key until she finds the correct key. a) How many keys, on average, must Trudy try before she finds the correct one? b) How will Trudy know when she has found the correct key? Note that there are too many solutions for Trudy to manually examing each one - she must have some automated approach to determining whether a putative key is correct or not. c) How much work is your automated test in part b) ? d) How many false alarms do you expect from your test in part b)? That is, how often will an incorrect key produce a putative decrypt that will pass your test