34. Suppose you have a private key encryption scheme. Explain why you might want to send a MAC along with the ciphertext when sending messages 35. Suppose you have an ideal random function f: 0,10, 160 a) What is the probability that two random elements lead to a collision? b) How many randomly chosen elements do we need so that the probability that a collision occurs is 1/2 36. Suppose we have a hash function h 0.,11) -> {0,...,7), defined as follows 10 7 11 6 Using this hash function illustrate why it does not satisfy any of the properties that a cryptographic hash function might have (preimage resistance, second preimage resistance, collision resistance)