The Effect of Cryptanalysis in World War II and Beyond

James Sanborn once made the statement, “What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant.” Sanborn’s comment couldn’t be more true; during World War II cryptography was used by both the Allies and the Germans for sending secret messages back and forth. This is when the elegant science created not very elegant machines, such as: Enigma, Lorenz Cipher, and Japanese “Purple”. This drastic advancement in cryptanalysis changed the way that mathematicians and scientists viewed cryptosystems.

During World War II, the German Nazis set off a boom in cryptanalysis by creating a revolutionary invention, known as, Enigma. The Enigma machine operated by having someone enter a message and then (using permutations) scramble it around with the use of three to five rotors. To encrypt a message for an Enigma with three-rotors, they used the following equation: ; with P being the plugboard transformation, U being the reflector, and L,M, and R being the left, middle, and right rotors. This scrambled message was then sent to a receiver who had to decipher the message by recreating the exact setting of the rotors from the sender's machine. However, the code, which has 158 quintillion different settings, was eventually broken by the Allies and used against the German Nazis as an advantage. And to show how confident the Germans were with this machine, until recently they still had no idea that the Allies had even cracked their code.

Another encryption machine that was popular during WWII was the the Japanese 97 - shiki O-bun In-ji-ki known by the United States as “Purple.” The machine ...

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...ce and from that you could get small sections of the encrypted messages, and it was only a matter of time until the Allies could decrypt complete messages.

In conclusion, we’ve gone through three machines that helped shape cryptography not only during World War II, but helped shape the science as a whole for future years. We’ve seen advancements, in mathematics, from both encryption and decryption, plaintexts and ciphertexts. Enigma, although it started as a three rotor device advanced to eight rotors, “Purple” was a finished product of years of experimental cipher machines, and the Lorenz Cipher, got it’s start from Vernam. Technology builds on each other and failures turn into successes, and although World War II was a dark time for our planet, the advances that we achieved from that period are things that we still use and can continue to learn from to this day.