I know that that was why the codebreakers could break Enigma, but why?
In: Mathematics
The Engima machine is one giant, very complicated circuit, which “ticks” around in complicated ways. However, its one crucial flaw was in its *Umkehrwalze,* “reversing rotor,” aka “reflector” in English. This device, at the “end” of the Enigma machine, simplified the process of using the machine: it meant that (for example) if E maps to Q, then *Q also maps to E* for the same settings on the rotors. As a result of it being a complete circuit, however, it physically *couldn’t* map the same letter to itself–that would mean sending the signal back along the exact same wire, and that’s not how circuits work, you have to have a *loop,* not a single line of wire.
(The reason this simplifies the decoding process is that it means you just have to type out the enciphered message, with the right rotor settings, and you’ll instantly get the original message back out.)
The reason that this key weakness helped the UK’s Government Code & Cipher School crack the Enigma code is that it gave them a key weapon for testing any given plaintext against a given cipher text. That is, let’s say you have a guess about a phrase that might appear in the original German message. If you write out that phrase, and run it along the bottom, you can know with 100% certainty that that is NOT the message if even a *single* letter is the same in both the cipher text and your guess. With a LOT of very hard work and experts on German language and other such things, you can use this to slowly whittle down the possible combinations. GC&CS were enormously helped by also having received the original cipher work done by the Polish cryptographers, which they managed to send to the United Kingdom before Germany could stop them.
Alan Turing’s brilliant idea to help crack the settings was to use an electromechanical device, the Bombe machine (a reference to the smaller, purely-mechanical “Bomba” machines the Poles had designed for weaker versions of Enigma), which could check for errors in the chosen wheel settings at (for the time) lightning speed. A few hundred of these machines were built, both in the UK and the US, and collectively, they were able to crack *just* enough Nazi transmissions to be one step ahead.
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