Alice and Bob use the ElGamal scheme with a common prime q=131 and a primitive root a=6. Let Bob's public key be Yu= 3. A. What is the ciphertext of M-9 if Alice chooses the random integer k=4? B. If Alice uses the same k to encrypt two messages M₁ and M₂ as (12, 65) and (12, 64), what is the relation between M₁ and M₂?

1. Let (01, 02, 03,..., 026!} be the set of permutations of the alphabet A = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z}, and consider the simple substitution cryptosystem with ok = A B C D E F G H I J K L M X MTAK ZQB NO LES N O P Q R S T U V W X Y Z IF G R V JH CY UDP W and key k. (a) Compute C = e(AUBUR NUNIV ERSIT YATMO NTGOM ERY, k). (b) Compute M = d(NIZFV SXHNF IHBKF VPXIA KIHVF GP, k).

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Let (M, C, e, d, Ke, Ka) denote the RSA cryptosystem with public key (s, n) = (5, 26051) and private key t = 5141. (a) Compute C = e(200, (5, 26051)). (b) Compute M = d(2,5141)