The Mathematics of the Enigma Machine

The Enigma machine used rotors and plugboards to encrypt German messages. Its key space was enormous (approx 10¹¹⁴ possibilities). Alan Turing and the team at Bletchley Park used mathematical cryptanalysis, including the Bombe (a machine implementing an algorithm based on known plaintext ‘cribs’). The mathematics included combinatorics, permutation groups, and the principle of contradiction (Turing’s ‘Banburismus’ used Bayes’ theorem). Breaking Enigma shortened the war by years. The work was classified until the 1970s, but it laid the foundation for modern computer science.