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1.     A generalization of the Caesar cipher, known as the affine Caesar cipher, has the following form: For

each plaintext letter p, the corresponding ciphertext letter c is computed as:

 c = (ap + b) mod 26 for some integer values a and b.

As mentioned in lecture, a basic requirement of an encryption algorithm is that it be one to one; that is, no two different values of p may map to the same ciphertext value c (otherwise, decryption is impossible.

a)     Is the affine Caesar cipher one-to-one for all values of b? Explain why or why not.

b)     For which values of a is the affine Caesar cipher not one-to-one? Explain why this is the case.

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