(a) Consider a plaintext space M = {M1,M2,M3,M4}, with corresponding ciphertext space C = {C1,C2,C3,C4}. Suppose that...
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(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 3 Compute H(M|C).
(b) Suppose a cryptosystem provides perfect secrecy, and 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?
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