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)mod26

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.

1. Are there any limitations on the value of b? Explain why or why not.

2. Determine which values of a are not allowed.

3. Provide a general statement of which values of a are and are not allowed. Justify your statement.