Rejewski's Catalog

When attacking the German Enigma cipher machine during the 1930s, the Polish mathematician Marian Rejewski developed a catalog of disjoint cycles of permutations generated by Enigma indicators. By comparing patterns that resulted from message indicators with his catalog, Rejewski was able to determine the ground settings. Well, not quite—the mapping from the disjoint cycles to the ground settings is not one-to-one. Rejewski’s catalog no longer exists. This article reports on the output of a program that ‘‘recreates’’ the catalog and answers the question ‘‘How far from being one-to-one is the mapping?’’