(a) Consider a plaintext space M = {M1, M2, M3, M4}, with corresponding ciphertext space C = {C1, C2, C3, C4}. Suppose that each plaintext and each ciphertext is equally likely, i.e. p(Mi) = p(Cj ) = 1/4 for 1 i, j 4. Now suppose that each ciphertext Cj narrows down the choice of corresponding plaintext Mi to two of the four possibilities as follows: C1: M1 or M2 C2: M3 or M4 C3: M2 or M3 C4: M1 or M4 Compute H(M|C).

(b) Suppose a cryptosystem provides perfect secrecy, and that p(M) > 0 for all M M. Prove that H(M|C) = H(M).

(c) Does the example of part (a) provide perfect secrecy? Explain your answer?