Problem 1 (Authentication): Consider the following authentication protocol, which uses a classical cryptosystem. Alice generates a random message r, enciphers it with the key k she shares with Bob, and sends the enciphered message {r}k to Bob. Bob deciphers it, adds 1 to r, and sends {r + 1}k back to Alice. Alice deciphers the message and compares it with r. If the difference is 1, she knows that her correspondent shares the same key k and is therefore Bob. If not, she assumes that her correspondent does not share the key k and so is not Bob. Does this protocol authenticate Bob to Alice? If so, Why? Otherwise, explain why not.