Suppose that the key equivocation of a certain cryptosystem vanishes, i.e H(K|C) = 0. Prove that…

Suppose that the key equivocation of a certain cryptosystem vanishes, i.e H(K|C) = 0. Prove that even a single ciphertext uniquely determines the key. (d) Show that the unicity distance of the Hill Cipher over Z26 (with an m × m encryption matrix) is less than m/RL, where RL is the redundancy of the language. (e) Suppose S1 is the Shift Cipher (with equiprobable keys) and S2 is the Shift Cipher where keys are chosen with respect to some probability distribution PK (which may not be equiprobable). Prove that S1 × S2 = S1.