Let M denote the message space, K the key space, and C the ciphertext space of a private-key encrypt ...

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Let M denote the message space, K the key space, and C the ciphertext space of a private-key encryption scheme. Define the set of 2-bit strings S := {00, 01, 10}. Consider the following variants of the One-Time Pad (OTP) encryption scheme. (a) The key space is K = {0,1}^(2l) and the key generation algorithm chooses k in K uniformly. The message space is M = S^l, i.e., a restricted set of 2l-bit strings. Encryption works as in the One-Time Pad: Enc_k(m) = k XOR m for k in K and m in M, and decryption works as in the One-Time Pad: Dec_k(c) = k XOR c. (b) The key space is K = S^l and the key generation algorithm chooses k in K uniformly. The message space is also M = S^l. Encryption and decryption work as in the One-Time Pad. For each of the above encryption schemes, state whether or not the scheme satisfies the condition of perfect secrecy, and prove your answer.