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 ith plaintext letter is x, and that the corresponding ith ciphertext letter is y. This implies that when the ith letter typed into the keyboard is x, the letter y is illuminated on the lightboard. Show that for the same key settings, if the ith letter typed into the keyboard is y, then the letter x is illuminated on the lightboard.

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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)?

In the discussion of the attack on RC4 keystream byte K_{3} we showed that IVs of the form (3,255, V) are useful to the attacker. We also showed that IVs that are not of this form are sometimes useful to the attacker, and we gave the specific example of the (2,253,0).

Find an IV of yet another form that is useful in the attack on K_{3}.

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