Enigma Cipher Research Articles

Turing’s anticipation of empirical bayes in connection with the cryptanalysis of the naval enigma*

The Enigma was a cryptographic (enciphering) machine used by the German military during WWII. The German navy changed part of the Enigma keys every other day. One of the important cryptanalytic attacks against the naval usage was called Banburismus, a sequentiai Bayesian procedure (anticipating sequential analysis) which was used from the sorine of 1941 until the middle of 1943. It was invented mainlv bv A. M. Turina and was perhaps the first important sequential Bayesian IE is unnecessab to describe it here. Before Banburismus could be started on a given day it was necessary to identifv which of nine ‘biaram’ (or ‘diaraph’) tables was in use on that day. In Turing’s approach to this identification hk had io istimate the probabilities of certain ‘trigraphs’. rrhese trigraphs were used. as described below. for determinine the initial wheel settings of messages). For estimatidg the probabilities, Turing inventedin important special case o the nonparametric (nonhypermetric) Empirid Bayes method independently of Herbert Robbins. The techniaue is the sumxisine form of Emdrical Baves in which a physical prior is assumed to eist but no apbroxiGate functional fonn is assumed for it.

WHAT DID THE SINKOV MISSION RECEIVE FROM BLETCHLEY PARK?

ABSTRACT Lists what the Sinkov Mission received during their visit to Bletchley Park in early 1941, and the information subsequently given by Bletchley to US Navy codebreakers in OP-20-G about naval Enigma. Also considers how far OP-20-G progressed in its attack on Enigma using that information.

APPLYING STATISTICAL LANGUAGE RECOGNITION TECHNIQUES IN THE CIPHERTEXT-ONLY CRYPTANALYSIS OF ENIGMA

A 1995 article in this journal presented a study by James Gillogly entitled “Ciphertext-Only Cryptanalysis of Enigma” [7, p. 405]. In this paper I will make improvements on Gillogly's techniques by choosing a more effective statistical test and an improved algorithm which allow me to decipher a 500-letter message encrypted by an Enigma machine with 10 plugs.

RECOVERING THE WIRING OF ENIGMA'S UMKEHRWALZE A

Umkehrwalze A was the original reflector used in the version of the Enigma machine employed by the German armed services. Its wiring was originally deduced by the Polish cryptanalyst Marian Rejewski in December 1932 or January 1933, but details of the wiring have not previously been published. Sufficient information to recover the wiring analytically is provided in a wartime document by Alan Turing, and other sources have been found to confirm the solution. This paper presents the wiring, along with alternative methods of recovering it from Turing's data.

Specifying and simulating rotor machines using Maple

The symbolic computation language, Maple, is used tospecify and simulate the performance of time-varying substitution cipher systems known as rotor machines, the most famous examples of which are the ENIGMA machines used by Germany during World War II. A mathematical model is presented, initially for a one-rotor machine. The direct implementation of this model in Maple provides a prototype system from which more efficient implementations are derived via a process of program transformation. The one-rotor system is then generalized to an N -rotor system. The paper provides a tutorial on the application of symbolic computation to a problem of interest to students of mathematics and of computer science.

AN ERROR IN THE HISTORY OF ROTOR ENCRYPTION DEVICES

Many historians have erred in giving credit for the Enigma cipher machine of World War II famed to Hugo Koch and not to the rightful inventor, Arthur Scherbius. This is corrected here.

EFFECTIVENESS OF THE DIAGONAL BOARD

The bombe was an electromechanical machine devised by Alan Turing and Gordon Welchman for breaking the German Enigma cipher in World War II. Welchman's contribution was the ‘diagonal board’ and it was vital to its success. The device reduced the number of times that the bombe stopped for an apparent solution which was not valid. The ratio by which the false stops were reduced is calculated in this paper. The work showed that there remained a class of false stops which had not been eliminated and further investigation showed that an attachment called the ‘machine gun’ helped to reduce the time lost for this reason. While this work was in progress, numerical results derived by Turing became available, but he did not give the theory and these are consistent (apart from apparent numerical errors) with our results.

THE BOMBE A REMARKABLE LOGIC MACHINE

The bombe was an electromechanical machine devised by Alan Turing and Gordon Welchman for breaking the. German Enigma cipher in World War II. The way in which it used a reductio ad absurdum logic to reduce 263 possibilities to a few is a unique example of ingenious circuit design, which is described in detail. Its relationship to the Polish version of the ‘bombe’ is explored. The importance of the diagonal board is shown as is the threat that this device faced from the German's use of the ‘Enigma-Uhr’.

KRIEGSMARINE SHORT SIGNAL SYSTEMS - AND HOW BLETCHLEY PARK EXPLOITED THEM

The principal Kriegsmarine short signal systems, and the way in which Bletch-ley Park used them to break the main naval Enigma ciphers, are described.

ENIGMA VARIATIONS: AN EXTENDED FAMILY OF MACHINES

Several previously unknown models of the Enigma machine have recently been discovered through archive research and inspection of machines in museum collections. The present knowledge about these machines, including both use and technical details, is presented. The paper shows that the Enigma was not one machine, but rather a family of machines built upon the principle of wired rotors with a fixed or rotatable reflector. It also describes simulations In software for some of these machines.

SOVIET COMINT IN THE COLD WAR

Soviet communications intelligence came more from bugs and traitors than from cryptanalysis. Successes seem to have helped the USSR's leaders only modestly during the Cold War. During World War II, the Soviets solved what Americans called the Japanese PURPLE machine and captured enough German Enigma machines and key lists to read many German messages. The KGB comint organization consisted of its 16th Directorate, created and headed for years by KGB General Andrei Nicolayevich Andreyev.

THE FIRST NAVAL ENIGMA DECRYPTS OF WORLD WAR II

Comments on, and text of, the first naval Enigma decrypts of World War II.

Naval enigma: An astonishing blunder

(1996). Naval enigma: An astonishing blunder. Intelligence and National Security: Vol. 11, No. 3, pp. 468-473.

WERFTSCHLÜSSEL A GERMAN NAVY HAND CIPHER SYSTEM PART II

During World War II the German Navy employed not only the Cipher Machine ENIGMA but also a number of hand cipher systems. The peculiar hand system in question here, the “Werftschlüssel”, though quite unknown to the public provided valuable intelligence for the British and supported the cryptanalysis of naval enigma traffic.

CIPHERTEXT-ONLY CRYPTANALYSIS OF ENIGMA

Enigma messages can be solved by recovering the message key settings, the ring settings, and the plug settings individually. Recovery of the message key setting is sensitive enough to distinguish the correct rotor order. The method is demonstrated on a 647-letter message, and its performance is estimated for different message lengths and numbers of plugs used.

WERFTSCHLÜSSEL A GERMAN NAVY HAND CIPHER SYSTEM PART I

During World War II the German Navy employed not only the Cipher Machine ENIGMA but also a number of hand cipher systems. The peculiar hand system in question here, the “Werftschlssel” though quite unknown to the public provided valuable intelligence for the British and supported the cryptanalysis of naval enigma traffic.

THE CRYPTOGRAPHIC MATHEMATICS OF ENIGMA

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 cryptographic key settings and machine configurations for the Enigma cipher machine. It also calculates the number of practical key settings Allied cryptanalysts were faced with on a daily basis throughout World War II. Finally, it shows the relative contribution each component of the Enigma added to the overall strength of the machine.

Impact of technology on the defeat of the U-boat September 1939-May 1943

From the 3rd September 1939 to 31st May 1943 the Allies lost 11576000 tonnes of shipping. Although the great destructive power of U-boats had been demonstrated during the First World War the essential lesson to be learnt (the need for huge air and sea escort forces) was incapable of being implemented at the outbreak of the Second World War. The expectation that ASDIC (a submarine location system developed by the Admiralty during the interwar years) would prove immediately effective and prevent a repetition of the (1915-1918) U-boat offensive was not realised. There was an urgent need for technology to aid the air and sea forces in their searches for submarines. Notwithstanding the development of airborne and shipborne radars, the breaking of the German naval enigma cyphers, the utilisation of land-based and ship-based HF direction finders, HF radio telephony, Leigh lights, improved ASDICs, operational research and many other innovations the threat to the security of the United Kingdom in March 1943 was, according to the Admiralty, greater than at any other rime of the war. But in May 1943 the U-boats were withdrawn temporarily from the North Atlantic following the introduction of a new radar, ASV Mark III. The paper is based on material held in the Public Record Office and highlights the application of technology in the Battle of the Atlantic.

THE POSTAL SERVICE FAILS TO DELIVER THE GOODS

In the album for its 1992 stamp set issued to commemorate the 50th anniversary of WW II, the US Postal Service labels a German Enigma cipher machine as a Japanese Purple machine.

AN ENIGMA CHRONOLOGY

A list of important events in the making and breaking of the German Enigma cipher machine of World War II is given in the order of their occurrences.