Problem 1 (Affine Cipher): Alice read about the affine cipher. She liked that it had a bigger key space than the Caesar cipher. But, she thought it should be bigger still. Thus, she invented the double affine cipher. Here is how it works. Pick two affine cipher key pairs k1 = (1, 1) and k2 = (2, 2). Alices key is defined by the pair (k1, k2). Encrypt a plaintext letter m as Ek2(Ek1(m)), where Eki is the affine encryption function with key pair ki = (i, i), for i = 1, 2. 1. How large is Alices key space? 2. Suppose k1 = (7, 12) and k2 = (3, 8). What is Alices encryption of the letter D? Show your work. 3. Let c be a ciphertext letter (i.e., any letter of the English alphabet). Describe how to decrypt c, and show why one recovers the original plaintext letter. Work through the decryption for the ciphertext you found as your answer to the above question. 4. Bob told Alice that her scheme was no better than the original affine cipher because the substitution specified by Alices double key ((1, 1), (2, 2)) was the same as the affine substitution E(,) specified by a single key pair (, ). Alice could not understand how that can be. Help Alice by finding an affine key pair (, ) that defines the same substitution as the one specified by Alices double key ((7, 12), (3, 8)). Show your work