5. In the text, we mentioned that the Enigma cipher is its own inverse. a. Prove that the Enigma is its own inverse. Hint: Suppose that the i th plaintext letter is x, and that the corresponding ith ciphertext letter is y. This implies that when the i th letter typed into the keyboard is x, the letter y is illuminated on the lightboard. Show that for the same key settings, if the i th letter typed into the keyboard is y, then the letter x is illuminated on the lightboard. b. What is the advantage of a cipher machine that is its own inverse (such as the Enigma), as compared to a cipher that is not (such as Purple and Sigaba)