Please solve both parts A and B. I need a second opinion on this one so I would appreciate if you didn't guess, and only answer if you know the solution. (It doesn't need more information. If you are going to comment that, you NEED to specify what.)

(a) Prove that the Affine Cipher achieves perfect secrecy if every key is used with equal probability 1/312 (b) More generally, suppose we are given a probability distribution on the set 26 gcd(a, 26 Suppose that every key (a, b for the Affine Cipher is used with probability Pr[a]/26. Prove that the Affine Cipher achieves perfect secrecy when this probability distribution is defined on the keyspace