Problem 2 (20 pts) Simple Cipher Let us assume CT and PT are discrete random variables which can take values from the domain of ciphertext and plaintext, respectively. Consider an example of encrypting the result of a 6-side dice (i.e., M E 11..61), as follows. Uniformly randomly chooses K E 11..61, ciphertext is C (M K) mod 13. The ciphertext space is thus I1..12. We have Pr PT 1) Pr PT 2l Pr PT 3] Pr PT 6l 1/6, and we use a vector notation Pr[PT] (1/6, 1/6, 1/6 to denote this. Assume that you stole a glance at the dice value and saw that there are many dots on it, and hence are quite certain that M is either a 5 or a 6. You then learned the ciphertext Problem 2 (20 pts) Simple Cipher Let us assume CT and PT are discrete random variables which can take values from the domain of ciphertext and plaintext, respectively. Consider an example of encrypting the result of a 6-side dice (i.e., M E 11..61), as follows. Uniformly randomly chooses K E 11..61, ciphertext is C (M K) mod 13. The ciphertext space is thus I1..12. We have Pr PT 1) Pr PT 2l Pr PT 3] Pr PT 6l 1/6, and we use a vector notation Pr[PT] (1/6, 1/6, 1/6 to denote this. Assume that you stole a glance at the dice value and saw that there are many dots on it, and hence are quite certain that M is either a 5 or a 6. You then learned the ciphertext