Components and Mathematics of the Enigma Electromechanical Rotor Ciphers

Author:  Kristi Short and Aharon Dagan
Date:  May, 2013



This paper describes the mathematics of the Enigma electromechanical rotor ciphers used by Germany during WWII. The research is focused on the contributions made by the Polish Cipher Bureau and presents their incentives for breaking Enigma encryptions. German operational procedure is included to show how redundancy measures allowed frequency analysis to be enabled, easing Polish efforts. Also included are the calculations for the strength of encryption granted by each component. Research focuses on the three-rotor configuration of the Wehrmacht Enigma variant used by the German Army in 1932. Also presented are examinations of the mathematical solutions of Marian Rejewski in order to show the method of decoding as well as the significance of contributions from the Polish Cipher Bureau prior to the beginning of World War II.  This paper shows why it is important to calculate the practical as well as theoretical encryption strength of a cipher method. Also, that it is important to eliminate redundancy methods whenever possible.