We wish to encrypt a memoryless source with alphabet M = {0, 1, 2} and P(M = 0) = 1/2, P(M = 1) = p,

We wish to encrypt a memoryless source with alphabet M = {0, 1, 2} and P(M = 0) = 1/2, P(M = 1) = p, P(M = 2) = 1/2 – p, 0 = p = 1/2. Let the key K = (K0, K1, K2) be 9 chosen uniformly from the set of binary 3-tuples. A sequence of messages M1, M2, . . . , Mn is encrypted to a sequence of ciphertexts C1, C2, . . . , Cn by, Ci = Mi + Ki mod 3 (mod 3), ?i, 1 = i = n. a) Find all values of p that give a unicity distance larger than 20. b) Let p = 0. Propose a new cipher for this source that has an infinity unicity distance.