Cryptology-I: § 2.3: Vigenere-Based Systems.

Instructors: R.E. Newman-Wolfe and M.S. Schmalz

The production of ciphertext by the one-time pad and other such manual devices, while intuitively attractive and efficient in the field, does not lend itself to mechanization with the technologies that were available shortly after World War I. For example, consider what one could construct with components such as relays, electromagnets, primitive switching equipment, and sophisticated gearing and mechanical transmission devices (similar to miniature automobile transmissions). To mechanize the production of ciphertext, a family of devices called rotor machines was invented, which implement Vigenere ciphers with long periods. Two of the best-known instances of rotor machines are the Hagelin Machine, a commercial device, and the series of rotor machines generically called the Enigma Machine, which were employed by the German military in World War II. It is interesting to note that a similar predecessor of Enigma was invented in Germany by Arthur Scherbius and Arvid Damm in the 1920s, then later patented in the United States in 1928 [-].

The cracking of the Enigma code is has been said to be the most important historical contribution of cryptanalysis [-]. It is well known that the efforts of the Bletchley Park cryptanalysis team (also called "crippies", who were led in part by Alan Turing), directly resulted in the saving of at least tens of thousands of lives and the shortening of World War II by perhaps several years. An excellent review of this period in cryptology is given in Reference [-], with supplemental material in References [-], [-], and [-].

2.3.1. General Concepts of Rotor Machines.

2.3.2. The ENIGMA Machine.

The German Enigma apparently began as a more-or-less standard rotor machine [-] with three rotors. However, requirements of increased security brought on by early phases of the war in Europe (1939-1942) dictated an increased number of rotors. In order to increase the effective number of rotors without drastically increasing weight and power consumption (important considerations for field operations), the developers of Enigma added a reflector, which routed the rotor machine's output back through the rotors, but by a different path than that shown in Figure 1. When the rotor gearing was chosen properly, this effected a doubling of the number of rotors and a squaring of the size of the search space associated with cryptanalysis. That is, instead of a maximal period |F|n, it was possible in certain circumstances to achieve a maximal effective period of |F|2n+1.

A further addition was the Steckerboard, a manual plugboard not unlike a small telephone switchboard of the time. The Steckerboard first implemented a substitution, which Enigma's developers thought would render Enigma secure. Near the end of the war, there was an attempt to implement a transpostion using the Steckerboard, which was a difficult goal due to the requirement of buffer memory (then available using only relays or mercury delay lines). The Enigma machine developers thought this would render the machine resistant to all cryptanalytic attacks. In the more usual Enigma machine configuration, with the reflector in place, not only were the number of rotors effectively doubled, but the Steckerboard transposition was inverted at the end of the encryption sequence. An Enigma-like rotor machine is shown in Figure 2.

2.3.3. Cryptanalysis of Rotor Machines.

The preceding discussion could lead one to surmise that cryptanalysis of the GRM or Enigma machine may not be as difficult as the mechanical complexity of the machine may indicate. In order to understand the associated techniques, let us recall some concepts from group theory.