(4) (5 points) Let T be the plaintext space given by the set of strings on the alphabet A = {1, 2, ..., 28} and let a E A be a secret key. Let f:T + T be the mapping that takes a plaintext p = P1P2 Pn to the output f(p) = C1C2 . -. Cn where c = api (mod 29) and for i > 2 we have c; = apjPj-1 (mod 29). Explain why f defines a valid encryption algorithm and explain how to break the cryptosystem without knowing the secret key a. (4) (5 points) Let T be the plaintext space given by the set of strings on the alphabet A = {1, 2, ..., 28} and let a E A be a secret key. Let f:T + T be the mapping that takes a plaintext p = P1P2 Pn to the output f(p) = C1C2 . -. Cn where c = api (mod 29) and for i > 2 we have c; = apjPj-1 (mod 29). Explain why f defines a valid encryption algorithm and explain how to break the cryptosystem without knowing the secret key a