German Enigma Research Articles

Engineering Places: Bletchley Park [engineering research

The introduction of electro-mechanical encoding machines with billions of permutations at the end of the First World War brought a new challenge to code-breakers. Perhaps the greatest threat was the German Enigma machine and its far more complex big brother, the Lorenz machine. Not that this seemed to bother the British government, who were aware Polish intelligence had managed to `break' an Enigma during its testing with the German army. It did, however, bother Admiral Sir Hugh Sinclair, head of the Secret Intelligence Service (SIS/MI6) and all cryptanalysts who realised that the Polish Enigma was only `broken' until the Germans changed the machine's rotor settings, which at the time they rarely did. With some prescience, Admiral Sinclair decided to set up a joint physical base for SIS and the Government Code and Cipher School (GC&CS), settling on Bletchley Park as their new home.

A Half-Rotor Cipher for the Classroom

Ciphers based on rotor machines were the state-of-the-art in the mid-1900s, with arguably the most famous being the German Enigma. We have found that students have great interest in the Enigma and its cryptanalysis, so we created our own rotor cipher that is simulated with shifting tables and can be cryptanalyzed. Ours and the historic rotor ciphers are based on rotating wheels that change the encryption with each character encrypted. Our cipher is easily programmed or can be simulated in Excel for students with less experience, and its cryptanalysis leads to interesting structure and the re-creation of the rotors.

An Algorithm for a Matrix-Based Enigma Encoder from a Variation of the Hill Cipher as an Application of 2 × 2 Matrices

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The ideal assumed background is a rudimentary familiarity of matrix multiplication and vector addition, but students who have successfully completed introductory linear algebra, number theory, and discrete mathematics will find this example accessible. Making this connection between these two systems provides a rich field for the introduction of the concepts mentioned above.

‘Mother says I’m just an odd duck’: Alan Turing, The Imitation Game and the ‘gay boffin’

The legacy of mathematician Alan Turing comprises both his contribution to the British war effort decrypting the German Enigma code at Bletchley Park and his treatment after the war, when he was convicted of gross indecency, underwent hormonal therapy and committed suicide. The Imitation Game (Tyldum, 2014), a ‘prestige’ biopic about his life, negotiates Turing’s problematic legacy as both war hero and gay martyr by modelling him through the ‘boffin’ stereotype present in British films about scientists. The boffin’s key characteristic is his ‘outsider’ status and the biopic reworks this to construct Turing as an outsider in different communities – at Sherborne School, within the code-breaking team at Bletchley but also, due to contemporary homophobic legislation, in wider British society. This article examines The Imitation Game’s depiction of Turing as ‘gay boffin’, how it negotiates the different histories that Turing’s life embodies and how film reviewers criticized The Imitation Game for its lack of scenes depicting gay relationships. Unlike other contemporary efforts that challenged the suppression of Turing’s homosexuality in public memory, The Imitation Game’s gay boffin instead exemplifies a continued anxiety with Turing’s legacy as a homosexual war hero.

Mathematics at the universities of Poznań, Vilnius and Kaunas in the interwar period – a comparative study

The three universities – Poznan and Vilnius in Poland, Kaunas in Lithuania – had much in common: all three were founded in 1919, each promised studies in mathematics, and none possessed a native mathematician of its own. Mathematicians had to be taken from a far. Poznan relied on Zdzislaw Krygowski (1872-1955), a newcomer from the Lvov polytechnic, who in the next twenty years laboriously worked up programs of studies and collected academic staff. Teaching was satisfactory (there was a course in cryptography, students of which have later broken the German Enigma) but research rather modest. In Vilnius there happened to be Wiktor Staniewicz (1866-1932), a refugee from the polytechnic in Petersburg. Being rather old and ill, he required support and that came in persons of Juliusz Rudnicki (1881-1948) and Stefan Kempisty (1892-1940), both from the Warsaw polytechnic. The three men secured satisfactory level of studies but only the arrival of Antoni Zygmund (1900-1992) in 1930 and his briliant student Jozef Marcinkiewicz (1910-1940) changed the picture by adding a high level research. Kaunas offered a chair to a German mathematician Otto Volk (1881-1989) who worked there 1923-1930, offered good teaching and secured further development. Although following different roots, all three universities succeeded and the article offers some insight into their specific stories.

The value of planning and the values in planning

In July 2015, I took part in a well-attended roundtable debate organised by the Royal Town Planning Institute (RTPI) in the AESOP Annual Congress which was spearheaded by a provocative Discussion Paper by the RTPI Deputy Head of Policy and Research (Harris, 2015). This viewpoint is based on my response to two issues raised in the paper: the interface between research and practice and the value of planning. As regards the first one, the Discussion Paper criticises the planning academics' research for not focusing on 'those issues that are of direct relevance to potential research users in ways which provide practical, actionable evidence' (Harris, 2015, 1). This statement reminds me of a story, which, although has been told elsewhere (see Davoudi, 2015a), is worth retelling here. The story is about a scene in Hugh Whitemore's play, Breaking the code (1986), which should be recounted every time academics are asked to demonstrate the practical worth of their research. The scene is a job interview when a civil servant asks a young academic about his research and receives this enthusiastic, yet confused answer:'Hilbert thought there should be a single clearly defined method for deciding whether or not mathematical assertions were provable ... I wanted to show that there can be no one method that will work for all questions ... Eventually I conceived the idea of a machine ...' (Whitemore, 1986, 33-34)The baffled civil servant then asks: 'You actually built a machine?' (Whitemore, 1986, 34), to which the young academic replies: 'No, no. It was a machine of the imagination' (Whitemore, 1986, 34). The civil servant's next question is emblematic of the dominant, albeit stereotypical, perception of academics as people who live in their ivory towers and use taxpayers' money to do 'blue sky' research of no use to anyone. He asks:'What is the point of devising a machine that cannot be built, in order to prove that there are certain mathematical statements that cannot be proved?' 'Is there any practical value in all this?' (Whitemore, 1986, 34)By now you have probably guessed that the play is based on a true story; that the young academic was Alan Turing, who was interviewed for the post of the leading cryptanalyst at Bletchley Park; that he went on to break the German's Enigma code which influenced the date of the Normandy landings, shortened the Second World War and saved countless lives. And, if that was not enough for the practical relevance of his research, he also built, almost by accident, the first electronic computer (Davoudi, 20:5a).The story is worth repeating because it brilliantly shows the non-linear, unpredictable and contingent nature of both the process and the outcome of research. It shows that 'researchers' flights of fancy can pay off (Reisz, 2008, 37) even if they may not have an immediate, practical utility or a quantified economic value. History is full of examples of scientific breakthroughs that have happened as a result of intellectual curiosity and speculative research. They have often come from a desire for knowledge rather than for filling a gap in the market or responding to immediate, practical questions. These examples tell us that academic research should not be judged through the limited lens of instrumentalism; that researchers should not always be expected to be 'on tap' to provide the right answer to what is often the wrong question and that there are other ways of framing the entwined relationship between research and policy (see Davoudi, 2006) or knowledge and action (see Davoudi, 2015b). For example, a conceptual model defines such a relationship as iterative and long-term whereby the findings from research creep into policy deliberations and illuminate the landscape within which decisions are made. I am not suggesting that planning academics should stop being concerned about the impact of their research and its relevance to the society. I do, however, suggest that they should resist the instrumental model of policy-research interface and its obsession with quantification; that they should resist the erosion of respect for learning. …

The Turing Bombe Victory and the first naval Enigma decrypts

ABSTRACTVictory was the name of the first prototype Bombe that was developed for breaking the German Enigma messages of World War II. It lacked the diagonal board and simultaneous scanning that was provided for all the later models, but these disadvantages were overcome by the ingenious use of a column menu (a special Bombe menu where the Enigma fast rotors are all in the same position) to break six days of naval traffic, 22–27 April 1940, following the pinch of material from an armed trawler Schiff 26 (Polares). These were the first naval decrypts of the War, and their solution took several months to complete. No further naval breaks occurred until November. This article examines the decryption process in some detail in order to explain the difficulties, highlight the role of Victory in this process, and provide detailed workings of the processes. It also sheds some light on the early development of the British Bombe.

A recursive solution for Turing’s H-M factor

ABSTRACTTuring devised an electromechanical device, called a Bombe, to decipher German Enigma messages. His original design was considerably improved by the addition of Welchman’s diagonal board, allowing the use of much weaker menus and even menus without closures. Turing then made some extensive calculations to predict the performance of the improved Bombe. He provided a table, called the H-M factor, which allowed the expected number of stops to be predicted for menus containing a given number of letters and closures, but he gave no indication of how he constructed the table. This article is of technical interest and sheds some light on the H-M factor, including its variability with the tree-arrangement of the menu. It derives the H-M factor using a recursive technique for both the standard Bombe and the Jumbo Bombe, a later version incorporating the machine gun mechanism. These results may be of interest to those that code or run Bombe emulators.

Revelation for Cilli's

In the early stages of the Second World War, the Bletchley Park codebreakers (really cipherbreakers) used a variety of methods to break into German Enigma messages. One of these schemes was known as via Cilli's. This article presents an origin for this unusual designation.

Alan Turing, Marshall Hall, and the Alignment of WW2 Japanese Naval Intercepts

M arshall Hall Jr. (1910–1990) is deservedly well remembered for his role in constructing the simple group of order 604800 = 27 × 33 × 52 × 7 as well as numerous advances in combinatorics. A brief autobiography is on pages 367–374 of Duran, Askey, and Merzbach [5]. Hall notes that Howard Engstrom (1902–1962) gave him much help with his Ph.D. thesis at Yale in 1934–1936 and later urged him to work in Naval Intelligence (actually in the foreign communications unit Op-20-G). I was in a research division and got to see work in all areas, from the Japanese codes to the German Enigma machine which Alan Turing had begun to attack in England. I made significant results on both of these areas. During 1944 I spent six months at the British Headquarters in Bletchley. Here there was a galaxy of mathematical talent including Hugh Alexander the chess champion and Henry Whitehead the eminent topologist... Burroughs, Lieberman, and Reeds [2] clarified the work of Op-20-G on the Enigma in a contribution to the obituary of Andrew Gleason (1921–2008). Unfortunately the surviving records scarcely allocate credit to individuals. Hall was one of about ten core members of a team of about thirty not far from being another galaxy of mathematical talent. See Christenson [3].

Uncrackable codes: The second world war's last Enigma

The second world war Allies captured a German Enigma code machine 70 years ago – but one message has never been decoded, says MacGregor Campbell

Lovesong of the Electric Bear

Lovesong of the Electric Bear Snoo Wilson (bio) The play by Snoo Wilson presented here is an imaginative recreation of the intricate interior life of Alan Turing (1912–54), the English mathematician whose idea of the Universal Turing Machine figures significantly in the conception and development of the modern computer, an embodiment of artificial intelligence that can be programmed to perform a sequence of operations leading to the solution of complex and challenging problems. Turing's early education took place at Sherborne School in Dorset. After securing First-Class Honors in Mathematics and a graduate fellowship at King's College, Cambridge, and a Ph.D. at Princeton University, he first came to prominence as one of the most brilliant of the codebreakers assembled to work together at Bletchley Park during the Second World War to out-think the German Enigma machine used to generate codes for strategic military communications, and he was for a time the head of the section assigned responsibility for deciphering the particular codes involved in German naval operations (including U-boat attacks). He ultimately became chief consultant for the overall program of codebreaking operations. During this period, among his colleagues Turing became as well-known for his various forms of eccentricity and unpredictability as for his evident genius. For his numerous significant accomplishments, in the late stages of the war he was awarded the Order of the British Empire. When the war ended, he was offered a position at the National Physical Laboratory in London, where he focused his attention on an ambitious plan for the design and production of an electronic computer. In 1951 his distinguished work as a scientist was recognized when he had the honor of being elected a Fellow of the Royal Society. Arrested and prosecuted in 1952 for homosexuality (which was at that time illegal under English law), he was subsequently denied security clearance by the British government. In order to avoid imprisonment, he submitted to a year of estrogen treatments meant to produce a form of chemical castration. He died of cyanide poisoning in the spring of 1954. In the fall of 2009, Prime Minister Gordon Brown issued a formal public apology to Turing for his treatment after the war. Readers interested in more detailed information about Turing's life and achievements may wish to begin by consulting Andrew Hodges's account in the Oxford Dictionary of National Biography, as well as the Turing website that Hodges maintains at www.turing.org.uk. Cast of Characters (doubling as needed): • Alan Turing • Porgy Bear • Blackwood, Turing Sr [Julius], Cornish, Sergeant • Winston Churchill, Davis, Barman, Greenbaum, Dilly Knox [End Page 8] • Clemmie Churchill, Mother, Judge • Christopher Morcom, Joan Clarke • Kjell Christiansen, Undergrad 1, Marian Rejewski, Arnold Murray • Nurse, Fortune Teller, Undergrad 2, Ylena • Bronwyn, Varia • Old Southern Woman, Hallam, Man Act 1 (Churchill at his easel, an old man, in sunhat, painting outdoors. Dappled light. Birdsong.) Clemmie: (Off) Winston! Winston! (Enter Clemmie, his ancient wife. Churchill oblivious.) Clemmie: (Accusatory) Where's your hearing aid? (Clemmie goes to Churchill's jacket, looks in the pockets. Failure. She has to speak louder.) Clemmie: (Loud) Moran called, with bad news—for you, he said. Lord Moran. Your physician, Winston. Churchill: Bad news is always the same from my doctor: "You drink too much." Clemmie: He said you would want to know. Alan Turing's dead. Churchill: Come off it, woman—Hermann Goering's been dead for years! Clemmie: No, Alan Turing. (Precise) A-LAN TU-RING. Churchill: (Shocked) Turing … How? Clemmie: By his own hand. Churchill: Oh, Christ. Clemmie: Who was he? I never heard his name before. Churchill: He was a Bletchley backroom boy. A genius. Clemmie: Why would he kill himself? (Turing becomes visible, wrapped only in a sheet, peacefully dead. He is holding an apple with a bite out of it. He could be Christ taken down recently from the cross. Churchill shakes his head and turns away.) Churchill: He can't have been more than forty. Clemmie: Will you come in now? If I call you when it's lunchtime, you won't hear. I'm not coming out again. I'm too old to be running around. Churchill: I'll...

Enigma Message Procedures Used by the Heer, Luftwaffe and Kriegsmarine

This paper is an effort to merge existing information about the message procedures, the enciphering methods and the required documents used with the German Enigma cipher machine by the German Heer (Army), Luftwaffe (Air Force) and Kriegsmarine (Wartime Navy) during the Second World War.

From the Archives: The Last Bombe Run, 1955

A declassified document confirms that the United States' 1943/4 Bombes continued to be used against the German's Enigma encryption device until at least 1955.

Dilly Knox—A Reminiscence of this Pioneer Enigma Cryptanalyst

This article describes the importance of the Knox contribution to the breaking of the plugboard German Enigma through his early work on the commercial machine; as well as his invention of “rodding” and exploitation of the Saga method of “boxing.” It also covers the multi-turnover Abwehr machine through observation of the phenomenon of ‘crabs and lobsters’ in message indicators.

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?”

The German Enigma cipher machine

The German Enigma cipher machine

Stealing secrets, telling lies: how spies and codebreakers helped shape the twentieth century

How important is it to know your enemy's secrets? The German victory at the Battle of Tannenberg in 1914, the entrance of the United States into World War I, the defeat of Nazi Germany, and the Soviet Union's faster-than-anticipated development of the atomic bomb were all facilitated by stealing enemy secrets. Espionage and codebreaking have, throughout history, been instrumental in the rise, fall, and preservation of world powers. In Stealing Secrets, Telling Lies, James Gannon provides the full story behind the critical intelligence breakthroughs that helped alter the course of history in the twentieth century. The interception of the Zimmerman Telegram, the deciphering of the German Enigma machine, the Soviet's damaging penetration of the British Foreign Service through the Cambridge Five spy ring, and the U.S. counter-intelligence coup known as Operation Venona (still secret until 1995) are just some of the episodes detailed here.

Rebuilding the Bombe [Enigma code breaking machine

Film makers who wanted to recreate the machines that played a vital part in breaking the German Enigma code were able to turn for advice to a group of engineers who are building their own working replica. Both film and book take their name from the coding device used by the German military to communicate battle plans. The machine was almost unbreakable in its sophistication, but procedural flaws such as reusing code book settings, made it vulnerable, and as early as 1932 Polish experts had broken the Enigma cipher and constructed a machine, the Bomba, that led to the cyphers being broken for the first time. Just before the war, they handed their work over to the British and French, and it was at Bletchley Park that mathematician Alan Turing and his colleague Gordon Welchman laid the foundations for the Bombe, electro-mechanical machine that speeded up the codebreaking process. When it came to creating several replica Bombes they commissioned South London based Asylum Models and Effects to make six machines. Asylum in turn went to a group of people who have learned the hard way the complexity of these early computing devices-a team which with support from the Bletchley Park Trust and Computer Conservation Society is rebuilding its own working Bombe. The 'Target Machine' that is under construction is based on a parts list from October 1943 for one of 68 devices built to a similar specification to decode messages from three-wheel Enigmas. This article describes the project and the history behind the building of the first Bombe machines.

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.