2. Using only basic counting arguments (no formulaso computers) find the number of involutory keys in the Permutation Cipher acting on blocks of length six. Justify rigorously your answer. The definition of involutory key can be found in Hwl. 5. If an encryption function ek is identical to the decryption function dk, then the key k is said to be involutory key. (a) Suppose k = (a,) is a key in an Affine Cipher over Zn. Prove that k is an involutory key if and only if a = 1 and B.(a + 1) = 0) in Zn. (b) Use part(a) to determine all the involutory keys in the Affine Cipher over Z40. Avoid brute force search. 2. Using only basic counting arguments (no formulaso computers) find the number of involutory keys in the Permutation Cipher acting on blocks of length six. Justify rigorously your answer. The definition of involutory key can be found in Hwl. 5. If an encryption function ek is identical to the decryption function dk, then the key k is said to be involutory key. (a) Suppose k = (a,) is a key in an Affine Cipher over Zn. Prove that k is an involutory key if and only if a = 1 and B.(a + 1) = 0) in Zn. (b) Use part(a) to determine all the involutory keys in the Affine Cipher over Z40. Avoid brute force search