Let the plaintext probability distribution be P(A) 1/4, P(B) = 3/4 and the key distribution be P(k₁) = 1/4, P(k₂) = 1/2, P(ks) = 1/4. (a) Find the ciphertext probability distribution. (b) Find entropy of the plaintext variable, the key variable, and the ciphertext variable. (e) Find the key equivocation. (d) Find a different key distribution that will make the key equivocation less than 0.5. (e) Find a different key distribution that will make the key equivocation greater than you found in question le above.

If an encryption function er is identical to the decryption function dg, then the key K is said to be an involutory key. (a) Let K = (a, b) be a key in an affine cipher over Z/nZ. Show that K is an involutory key if and only if a- = a (mod n) and b(a+1) = 0 (mod n).

Alice and Bod have decided to use a symmetric encryption algorithm. They have some assumptions about their messages:- Messages only contain capital letters (i.e. A to Z)- The length of their shared key must be greater than or equal to the length of the plaintext- They assign each letter a number as follows: (A,0), (B,1), (C,2), (D,3),…, (Z,25)Their algorithm combines the key and the message using modular addition. The numerical values of corresponding message and key letters are added together, modulo 26. For example, if the plain text is “HELLO” and the key is “SECRET” then the encrypted message is calculated as following:Since the length of the plaintext is 5, we just need the first 5 letters of the key (i.e. “SECRE”), then for each letter, we should add corresponding letters in both the plaintext and the key modulo 26.Plaintext: H (7) E (4) L (11) L (11) O (14)Key: S (18) E (4) C (2) R (17) E(4)Cipher: Z (25) I (8) N(13) C(2) S (18) Write a program in Python, C/C++ or JavaScript to…