xercise 2.13b from Introduction to Modern Cryptography, 2nd Edition by Katz & Lindell)

In this problem we consider definitions of perfect secrecy for the encryption of two messages (using the same key). Here we consider distributions over pairs of messages from the message space M; we let M, M2 be random variables denoting the first and second message, respectively. We generate a (single) key k, sample messages (mi, m2) according to the given distribution, and then compute ciphertexts c1 Enck (mi) and c2-Enck (m2); this induces a distribution over pairs of ciphertexts and we let C1, C2 be the corresponding random variables. (b) Say encryption scheme E = (Gen, Enc, Dec) is perfectly secret for two distinct messages if for all distributions over M M where the first and second messages are guaranteed to be different (i.e., stributions over pairs of distinct messages Wi Show an encryption scheme that provably satisfies this definition. Hint: The encryption scheme you propose need not be efficient, though an efficient solution is possible. In this problem we consider definitions of perfect secrecy for the encryption of two messages (using the same key). Here we consider distributions over pairs of messages from the message space M; we let M, M2 be random variables denoting the first and second message, respectively. We generate a (single) key k, sample messages (mi, m2) according to the given distribution, and then compute ciphertexts c1 Enck (mi) and c2-Enck (m2); this induces a distribution over pairs of ciphertexts and we let C1, C2 be the corresponding random variables. (b) Say encryption scheme E = (Gen, Enc, Dec) is perfectly secret for two distinct messages if for all distributions over M M where the first and second messages are guaranteed to be different (i.e., stributions over pairs of distinct messages Wi Show an encryption scheme that provably satisfies this definition. Hint: The encryption scheme you propose need not be efficient, though an efficient solution is possible