The History and Mathematics of Codes and Code Breaking

German Cryptography is still Human Cryptography

During WWII, Germans sent out thousands of messages encrypted using the supposedly unbreakable Enigma machine. It was discovered after the war that German intelligence knew that these messages could be captured by the Allies, but they could not think anyone would have the time or resources to possibly decipher them. This strongly held idea that Enigma was unbreakable was perhaps the greatest mistake of Germany.

Another factor, besides German overconfidence, that allowed the Allies to decipher German messages were the patterns discovered when Enigma was used. These patterns were precisely the result of non-randomness that describes human nature. Some keys were easily guessed because the letters on the Enigma keyboard were next to each other. Other keys may have been similarly predictable because they resembled German names, or they were used repeatedly. These were called “cillies.” Ironically, an effort to consciously combat human un-randomness was also a mistake on Germany’s part. By avoiding “obvious” plugboard settings and arranging rotors to avoid repeated positions, the amount of possible settings were drastically reduced.

Human nature in and of itself is never truly random; this is a basic fact we learn in our statistics classes. If you asked a population to randomly choose a number between 1 and 4, would a fourth of the people choose each of the numbers? Polls have shown that, instead, a clear majority would choose the number 3. In the same manner, cipher keys are not always a random garble of letters. They are often derived from meaningful words or phrases that may be pertinent to the message or the receiver/sender of the message.


Rejewski and Turing


The Power Of The Individual

1 Comment

  1. Emily Struttmann

    You bring up a really good question as to how much the mechanization of the cipher actually benefitted German forces. I think that the essence of the enigma machine made it possible to break because it could be (and was) approached with an equally logical crypt-analytic mindset. The Allies, on the other hand, uses enciphering methods like the Navajo code talkers that relied less on methodical and logical approaches. So the question remains: does an “advance” in technology always make it better or more useful, or does obscurity play a larger role than complexity when it comes to cryptography? In this case, I agree with you that the patterns in Enigma were a disadvantage for German forces and made it more easily broken by British cryptanalysts.

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