An affine cipher is encryption using simple mathematical function. Suggest the affine cipher c = ax+b (mod 26) where x is the plaintext, the function applied to each letter of plaintext separately, where each letter is represented such as A is 0, B is 1, ... , Z is 25 and so on, a and b are numbers modulo 26 and c is the ciphertext for the corresponding letter of the plaintext.
A. In modulo 26 how many possible choices are there for the parameter a, in order to be able to uniquely decrypt an encrypted message?
B. A key pair for c=ax+b is (a,b). Now without caring about unique decryption, how many key pairs are there for the affine cipher modulo 26? That is, determine the size of the key space.
C. Consider applying two different affine ciphers successively in two rounds such as c1=a1x+b1 first and c2=a2 c1+b2 afterwards and the ciphertext is c2 given plaintext x. Again without caring about unique decryption, what would be the key space for this new double affine cipher? Compare the difficulty (time complexity) of an exhaustive search of all possible keys by an adversary of the double affine cipher and single affine cipher.