ABSTRACT
As we have noted, Germany’s “unbreakable” Enigma ciphers were in fact broken. Early versions of the Enigma were broken by a team of Polish mathematicians led by Marian Rejewski using a machine designed by Rejewski called a bomba. More complex versions of the Enigma were later broken at Bletchley Park by a team of Allied mathematicians that included Alan Turing using a machine designed by Turing called a bombe. Books that describe some of the technical details regarding the cryptanalysis of the Enigma tend to focus more on Rejewski’s bomba; for example, see [2], a comprehensive history of cryptology written by a colleague whose interest in the subject was inspired in part by the same person who inspired ours. In this chapter, we will describe some of the technical details regarding the cryptanalysis of the Enigma, however our focus will be on Turing’s bombe. This will be a challenge, but one well worth the effort, as the cryptanalysis of the Enigma at Bletchley Park is not only one of the supreme achievements of the human intellect, but it also saved many lives on both sides during World War II by directly contributing to a swifter end to the war. To make this discussion as accessible as possible, we will limit our focus to the cryptanalysis of the three-rotor Wehrmacht Enigma at Bletchley Park.
Turing had no interest in replicating or extending Rejewski’s methods for breaking early versions of the Enigma, because he believed that the Germans would make improvements to the security of the machine that would render Rejewski’s methods obsolete. This is indeed exactly what happened in December 1938, when the Germans made modifications to the Enigma,
