Re: Super duper encrpytion device brought down by simple mistake
Four-rotor Enigma was reconstructed because in 1938, when the German military shifted to four/five rotor use, the Nazi Party's own internal security service remained on three-rotor machines, which created an abundance of messages that had been encoded in both algorithms. The work of reconstructing the four-rotor Enigma was done in Poland at the very start of the war.
At no point did Enigma rely on "obscurity" in the sense that cryptographers use that word. The mechanics of the device (i.e., the algorithm itself) were known from the 1930s, and while the addition of a fourth rotor made life very difficult, that job wasn't made much easier when the 4-rotor Enigma machine was fully described.
The Germans knew that Enigma could be cracked, and they knew that four-rotor Enigma could be cracked too. However, their predictions of how long any such crack would take were based on an assumption that proved to be untrue: that the Allies would not invest huge resources into cryptanalysis, and instead rely on brute-force attacks and traditional espionage techniques to obtain information. By 1945, the use of clever search-space reduction techniques developed by Alan Turing and Peter Twinn, brute-forced by the high-speed "bombe" machines commissioned from NCR by the US Navy (but deployed at Bletchley) allowed a 48 hour decryption of all Enigma traffic.
(The Colossus computer was built to decode a completely different German cipher, the electromechanical Lorenz SZ)
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