Hong Kong Baptist University, Hong Kong

• COMP 7200

• Problem 1. (10 points (3,3,4)) A generalization of the Caesar cipher, known as the affine Caesar cipher, has the following form: For each plaintext letter p, substitute the ciphertext letter C: 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 and b = 3, then E([a, b], 0) = E([a, b], 13) = 3. a). Are there any limitations on the value of b? Explain why or why not. b). Determine which values of a are not allowed. c). Provide a general statement of which values of a are and are not allowed. Justify your statement.