2. Modulo arithmetic and affine cipher (a.) (3 points) Construct the multiplication table modulo 8. Then find all the integers k, 0 k s 7 that are invertible under modulo 8 and give their inverses. (b.) (5 points) Suppose I want to send the note SEND MONEY to my parents, but I don't want my brother to read it. Encrypt my message using an affine cipher (mod 26) with a = 11 and b 4. (c.) Suppose the ciphertext has been encrypted using an affine cipher. However, we do not know the key (a, b) that was used. Fortunately, we know that the plaintext letter T becomes ciphertext H and the plaintext letter O becomes E. Find (c.1.) (4 points) The encryption formula E(x) and the decryption formula D(y). (c.2.) (3 points) Decrypt the message (d.) (Bonus - 2 points) Suppose we use the affine cipher on an alphabet with 143 letters. Find |K], the size of the key space for this cipher