Develop a ciphertext-only attack on the Enigma, assuming that all you know about the plaintext is that it is English. Analyze the work factor of your proposed attack and also estimate the minimum amount of ciphertext necessary for your attack to succeed. Assume that Enigma rotors, the rotor order, the movable ring positions, and the reflector are all known. Then you need to solve for the initial settings of the three rotors and the Stecker. Hint: Since E is the most common letter in English, guess that the plaintext is EEEEEE… and use this “noisy” plaintext to solve for the rotor and stecker settings.

Consider a rotor with a hardwired permutation of {0,1,2,…, n — 1}. Denote this permutation as P = (ρο,ρι,… ,p_{n-i}), where P permutes i to pi. Let d_{i} be the displacement of pi, that is, d_{i} = pi — i (mod n). Find a formula for the elements of the fcth rotor shift of P, which we denote P_{k}, where the shift is in the same direction as the rotors described in Section 6.2.3. Your formula must be in terms of pt and d_{i}.

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