Question 1: Consider the linear block cipher with block length n and alphabet {0, 1}. On the key space of matrices A ∈ {0, 1} (n,n) with det(A) ≡ 1 (mod 2), choose the uniform distribution. Show that this cryptosystem does not have perfect secrecy. (Use the definition of perfect secrecy, and find a counterexample with n = 2, for instance.) 2: Let n be a positive integer. A Latin square of order n is an n × n array L of the integers 1, 2, . . . , n such that every one of the n integers occurs exactly once in each row and each column of L. An example of a Latin square of order 3 is as follows:  1 2 3 3 1 2 2 3 1  . Given any Latin square L of order n, we can define the following cryptosystem: Take P = C = K = {1, 2, . . . , n}. For 1 ≤ i ≤ n, the encryption function Ei is defined to be Ei (j) = L(i, j). (Hence each row of L gives rise to one encryption function.) Give a complete proof that this Latin square cryptosystem achieves perfect secrecy. (Use Shannon’s theorem).If the question descriptions not clear enough, please check the picture file I posted.