Turing and the Enigma Code
During World War II, the Allied powers were at war with the Axis powers. Germany, a member of the Axis powers, transmitted encrypted messages to its troops and allies to relay information relevant to the war. These messages were encrypted with an Enigma machine with a code that was extremely difficult to crack. Since these messages contained information about Axis war strategies, the Allied powers wanted to intercept and decode these messages to gain an upper hand in the war. Alan Turing, a British mathematician, and his fellow codebreakers at Bletchley Park were tasked with decoding the encrypted messages. However, the encryption key changed every night at midnight, thus cracking the Enigma code and obtaining the correct decryption key proved to be a Herculean task.
However, Turing and the codebreakers at Bletchley Park used Bayesian insight to narrow down the number of possible decryption keys from a vast amount of different possibilities. The codebreakers concluded that certain words and phrases must be more common than other ones. They assumed that each message must contain a “crib”, or a known German word that would appear at around the same place in the message consistently. For instance, messages to U-boats were likely to contain messages about Allied shipping boats or the weather forecast, which was written in the same format each day.
As more and more information was gathered by the code breakers, the more and more decryption codes they could rule out. This is a direct application of Bayes’ Rule as we discussed in class. Gaining more knowledge changed the conditional probability of getting the correct decryption key given all the clues and information gathered. The conditional probability kept increasing since gaining more information shrinks the sample space of possible decryption keys. Using Bombe machines that quickly ruled out impossible decryption keys, Turing and the codebreakers could eventually decrypt all the German messages, vastly aiding the Allied forces and decreasing the duration of the war.
Source: https://www.archives.gov/files/publications/prologue/1997/fall/turing.pdf