4. One special class of substitution ciphers consists of the affine ciphers, which encode letters using a linear function of the form f(x) = mx +b (mod 26), where we take the convention that a corresponds to the residue class 0 (mod 26), b corresponds to 1 (mod 26),..., and z corresponds to 25 (mod 26). (a) Encrypt the message doitnow using the affine cipher f(x) = 3x + 11 (mod 26). If the function f(x) = ax + b (mod 26) is used to encrypt a message, then the function f(x) = a(x-b) (mod 26) will decrypt the message. (b) Find the decryption function for the encryption function f(x) = 3r+11 (mod 26) and use it to decrypt the message QGLQNLAAJYX. (c) In order for an affine cipher to be decryptable, the function f(x) = ar + b (mod 26) must have a valid inverse function. Using this information, determine the total number of possible affine encryption functions (include the functions with a = 1 in your count). (d) Is affine encryption difficult to break or easy to break? Explain briefly.