Problem 3 [Shift, Affine, and Hill Ciphers, 33 pts.): Alice is sending a message to Bob using one of the three cryptosystems shown below. In fact, Alice is bored and her plaintext consists of the letter a repeated a few hundred times. Eve knows what cryptosystem is being used, but not the key, and intercepts the ciphertext. For each of those three cryptosystems: Cryptosystem 1: Shift cipher Cryptosystem 2: Affine cipher Cryptosystem 3: Hill cipher (using a 2x2 matrix) 1. State how Eve will recognize that the plaintext is one repeated letter. 2. Decide whether or not Eve can deduce the letter and the key. Show your work step by step