Cryptography

The History and Mathematics of Codes and Code Breaking

The Value of Mathematicians as Cryptanalysts

A variety of factors contributed to the Allied cryptanalysts’ success over German cryptographers, including espionage, determination, and cooperation. One main element that contributed to the Allied success was the employment of mathematicians and scientists in their cryptanalyst units. The Polish breakthroughs in cracking Enigma demonstrated the value of mathematicians as codebreakers. Marian Rejewski, the main Polish cryptographer working on cracking Enigma, was a mathematician. Enigma was a highly complex machine requiring much logical and mathematical thinking in order to break it. In Britain, linguists and classicists had always dominated Room 40. The addition of mathematicians and scientists to the team greatly strengthened the unit and brought in a new perspective on how to break the ciphers. Analyzing the ciphers from a mathematical lens provided valuable new insight that was necessary to break the Enigma code.

Alan Turing is known for identifying Enigma’s greatest weakness, which made it possible to crack the Enigma cipher in tough circumstances. He was a master of math, science, and logic. His advanced skills in these areas helped him think through the different layers of Enigma and figure out how to approach and tackle the haunting task of cracking the code. Turing’s unique background in mathematical machines allowed him to create his bombes. These bombes tested Enigma settings much faster than they could be tested by hand. Without mathematicians like Turing, who could conceptualize and build such machines, it’s possible that Allied cryptanalyst units would never have broken the Enigma machine ciphers.

Nowadays, when I think of a modern cryptographer, the first thing that pops into my mind is a mathematician. However, a cryptographer has to be fluent in a variety of subjects, including mathematics, science, logic, and linguistics. The ability to integrate knowledge from diverse fields when attacking a cipher is what makes an exceptional cryptographer. Although the Germans’ overconfidence in the strength of Enigma played a significant role in the success of the Allied cryptanalyst efforts, many other factors were instrumental in the cryptanalysis as well. The realization that mathematicians could be important additions to cryptanalytic staffs was vital to the Allied cryptanalysts’ successes over German cryptographers.

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1 Comment

  1. yanrong

    In the passage, Julia suggests that the value of mathematicians as codebreakers was demonstrated in the process of cracking the Enigma machine.
    Would you agree that the mathematical skills probably have also played an important role in developing the enigma machine for Germany? If so, I’m wondering when both sides (the cryptanalysts and the code makers) are both mathematicians, would the difference in their mathematician essentially determine which side would eventually win the battle?

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