Prove that Definition 2.4 implies Definition 2.1. Definition 2.1: An encryption scheme II = (Gen, Enc, Dec) over a message space M is perfectly secret if for every probability distribution over M, every message m e M, and every ciphertext c EC for which Pr[C = c] > 0: Pr[M = mC = c) = Pr[M = m) Definition 2.4: An encryption scheme II = (Gen, Enc, Dec) over a message space M is perfectly secret if for every adversary A it holds that Pr[PrivKXII = 1] = ? Lemma 2.3: An encryption scheme II = (Gen, Enc, Dec) over a message space M is perfectly secret if and only if for every probability distribution over M, every mo, mi e M, and every c E C: Pr[C = CM = mo] = Pr[C = CM = mi] Hint. If a scheme II is not perfectly secret with respect to Definition 2.1, then Lemma 2.3 shows that there exist messages mo, mi e M and c EC for which Pr[C = C|M = mol + Pr[C = CM = mi). Use these me and my to construct an A for which Pr[Privka = 1]>