A generalization of the Caesar cipher, known as the affine Caesar cipher, has the following form: For each plaintext letter , substitute the ciphertext letter :

C = E([a, b], p) = (ap + b) mod 26

A basic requirement of any encryption algorithm is that it be one-to-one. That is, if p q, then E(k, p) E(k, q) . Otherwise, decryption is impossible, because more than one plaintext character maps into the same ciphertext character. The affine Caesar cipher is not one-to-one for all values of a. For example, for a = 2 b = 3, then E([a, b], 0) = E([a, b], 13) = 3. a. Are there any limitations on the value of ? Explain why or why not. b. Determine which values of are not allowed. c. Provide a general statement of which values of are and are not allowed. Justify your statement.