Problem 3: Consider the following DES-like encryption method. Start with a message of 2n bits. Divide it into two blocks MoM1 of length n, a left half and a right half. The key K consists of K bits, for some integer k. There is a function f (K, M) that takes an input of k bits K and n bits M and gives an output of n bits. One round of encryption starts with a pair Mj Mj+1. The output is the pair Mj+1Mj+2, where This is done for m rounds, so the ciphertext is MmMm (a) if you have a machine that does the m-round encryption just described, how would you use the same machine, with the same key K, to decrypt the ciphertext MmMm+1? Prove that your decryption method works. (b) Suppose K has n bits and f(K,M) KM, and suppose the encryption process consists of m 2 rounds. If you know only a ciphertext, can you deduce the plaintext and the key? If you know a ciphertext and the corresponding plaintext, can you deduce the key? Explain