Let (Kgen, Enc, Dec) be a semantically secure encryption scheme,that encrypts messages of length l.

Let (Kgen, Enc, Dec) be a semantically secure encryption scheme,that encrypts messages of length l. Show that this scheme alsosatisfies the following properties. 1. Sample a random key K ← Kgen, and encrypt a random message M← {0, 1} l to obtain ciphertext C ← EncK(M). Show that no efficientattacker, given C, can recover the first bit M1 of the message Mwith probability 1. 2. Sample a random key K ← Kgen, and encrypt two random messagesM1 ← {0, 1} l and M2 ← {0, 1} l to obtain two ciphertexts C1 ←EncK(M1) and C2 ← EncK(M2). Show that no efficient attacker, givenC1, C2, can recover the bit of information of whether M1 > M2 orM2 . . .

 
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