 This Month's Feature Column
Marian Rejewski and the First Break into Enigma
The settings of an Enigma machine were exactly the same for writing and reading messages, which simplified its practical use enormously. It also simplified the task of the Allies enormously...
Introduction
During World War II the British read German military communications regularly, because they were able to decipher messages encoded on the Enigma machines used by the Germans. As the war developed and the German networks became larger and more complicated, the methods used by the British became correspondingly more and more sophisticated, depending on a huge effort with thousands of people involved in interception, decipherment, and interpretation of the German signals.
But the process started long before the war, in 1932, with a tiny group of Polish mathematicians. They made the first breaks into the Germans' code by relatively simple techniques that were fortunately able to deal with the relatively simple German encoding techniques of those early days.
One of the very first steps, and one of the most intriguing, was made by Marian Rejewski, who applied the theory of permutations in an interesting way to figure out `message keys' used by German operators as well as the structure of the German Enigma machines. I hope to explain here the mathematics behind Rejewski's accomplishment.
A simplified Enigma machine
Bill Casselman
University of British Columbia, Vancouver, Canada
cass at math.ubc.ca
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