Problem 1 [Perfect Secrecy] (10 Points) An encryption scheme (Gen, Enc, Dec) with message space M is perfectly secret if for every m, m' e M, every ceC Pr [Enck(m) = c) = Pr [Enck(m') = c] where the probabilities are over the choice of k. Do the following encryption schemes have perfectly secrecy if the key k is sampled uniformly from the key space? Justify your answer. (a) M= {0,1,2,3} K = {0, 1, 2, 3, 4} Enck(m) = k + m (mod 4) Deck(c) = c-k (mod 4) (b) M= {m = m'||0|m' {0,1}l-1} K = {{0, 1}l-1} Enck(m = m'||0) = m' k Deck(c) = ck||0