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This paper will examine the mathematics used to decode the Enigma machine. The enigma was a machine that was used by the Germans to send secure, encrypted messages amongst each other during World War II. This paper will discuss the workings of the machine and how it was continually adapted to increase security. Polish mathematicians, in particular Marian Rejewski applied theories of permutations of disjoint cycles in order to crack the enigma cipher. The work done by Rejewski and his colleagues was used by the British at Bletchley Park in order to continue breaking ciphers throughout the war. Being able to read the message sent amongst the German military played a significant role in insuring Ally victory in World War II.