The Cryptographic Mathematics of Enigma

20 pages. Illustrations. References. Dr. A. Ray Miller received a B. S. in computer science from the University of Central Florida in 1979. He received an M. S. and a Ph.D. in computer science from the University of Illinois in 1984 and 1987, respectively. While in school, he worked at the Naval Experimental Computer Simulation Laboratory, and the Center for Supercomputing Research and Development. Dr. Miller has been employed at the National Security Agency since 1987 and has taken a tour at the Supercomputing Research Center. He has received the 1991 Computer and Information Sciences Institute Award for Excellence, NSA's highest award in computer science. The Enigma cipher machine had the confidence of German forces who depended upon its security. This misplaced confidence was due in part to the large key space the machine provided. This paper derives for the first time the exact number of theoretical cryptography key settings and machine configuration for the Enigma cipher machine. It also calculates the number of practical key settings Allied cryptanalysts were faced with daily throughout World War II. Finally, it shows the relative contribution each component of the Enigma added to the overall strength of the machine. …