Hans Rohrbach

Hans Rohrbach
Born (1903-02-27)27 February 1903
Berlin
Died 19 December 1993(1993-12-19) (aged 90)
Bischofsheim an der Rhön
Theses
  • Eine Axiomatisierung der allgemeinen Mechanik (1938)
  • Die Charaktere der binären Kongruenzgruppen mod p2 (1937)
Doctoral advisor Issai Schur, Erhard Schmidt (1932)
Known for Breaking the American diplomatic O-2 cypher which was a variant of the M-138-A strip cipher during World War II.
Influences Ludwig Bieberbach, Eugen Blasius, Max Dessoir, Georg Feigl, Heinz Hopf, Wolfgang Köhler, Max von Laue, Karl Löwner, Richard von Mises, Max Planck, Hans Rademacher, Heinrich Rubens, Wilhelm Schlenk, Erhard Schmidt, Issai Schur, Gabor Szegö, Arthur Wehnelt, and Wilhelm Westphal[1]
Notable awards Order of Merit, Federal Cross of Merit, Order of Merit of Rhineland-Palatinate

Hans Rohrbach was a German mathematician.[1] He worked both as an algebraist and a number theorist and later worked as cryptanalyst at Pers Z S, the German Foreign Office cipher bureau, during World War II. He was latterly known as the person who broke the American diplomatic O-2 cypher, a variant of the M-138-A strip cipher during 1943.[2] Rohrbach wrote a report on the breaking of the strip cypher when he was captured by TICOM, the allied effort to roundup and seize captured German intelligence people and material.[3]

Personal life

Hans Rohrbach was a son of journalist Paul Rohrbach and his wife Clara born Müller who were married in Berlin in 1897. There was always confusion around Rohrbachs' name, one source gives his full name as Hans Joachim Albert Rohrbach, while the mathematician Bernhard Neumann believed this full name to be Hans Wolfgang Rohrbach, and was sure his middle initial was a 'W'.

Rohrbach entered the Gymnasium (school) at Berlin-Friedenau in the Autumn of 1909 and studied there until Autumn 1917. He then entered the Fichte Gymnasium in Berlin-Wilmersdorf. After having successfully passed the school leaving exam in 1921, he entered the Friedrich-Wilhelm University in Berlin, where he studied mathematics, physics, and philosophy for two years. In 1923, as a head of the Berlin student organization Mathematisch-Physikalische Arbeitsgemeinschaft (Mathematics and Physics Working Group), he went with a his father to the United States. The visit, which Rohrbach called his propaganda visit, was a tour of American universities to raise money for impoverished Berlin students. Germany's economy, which was undergoing a period of hyperinflation, was making life extremely difficult for students, who had to take employment to supplement their income.

In the autumn of 1924 Rohrbach resumed his studies at the University of Berlin and studied there until 1929. In the late 1920s he started work on his PhD thesis, titled Die Charaktere der binären Kongruenzgruppen mod p2 (The characters of the binary congruence groups mod p2), advised by Issai Schur. He submitted it and was awarded his doctorate on 25 July 1932.[1]

While studying at Berlin University, Rohrbach met fellow student Rose Gadebusch (born 1905),[1] who studied mathematics starting in 1925. Gadebusch took a major role in the Mathematisch-Physikalische Arbeitsgemeinschaft. After graduation she took a position at the Women's Gymnasium. Rohrbach married her sometime around 1932.[1]

In 1936, Rohrbach was appointed senior assistant at the University of Göttingen. In 1937, he undertook his habilitation there with a paper titled Ein Beitrag zur additiven Zahlentheorie nebst einer Anwendung auf eine Gruppentheoretische Frage (English: A contribution to additive number theory together with an application on a group theoretical question).[4]

On 1 April 1938 he was appointed as a senior assistant at the Mathematical Institute of the German University of Prague. In 1941 he was promoted to extraordinary professor and in 1942 he became an ordinary professor. He also served as Director of the Mathematical Institute there.[1][5]

Rohrbach was a member of the Nazi Party and the Sturmabteilung (the party's original paramilitary wing, later superseded by the SS), but was considered not fully reliable due to his friendship with Jewish colleagues.[6]

After the war ended, Rohrbach was not allowed to teach for a number of reasons. However, he held an appointment as Visiting Professor in the Department of Mathematics in the Faculty of Science at the University of Mainz, 1946–1951. From 1951 to 1957 he was Extraordinary Professor in the Faculty of Science at Mainz, and was later dean of the Faculty of Natural Sciences, 1954–1958. He was then Associate Professor in the Department of Mathematics between 1957 and 1969. While undertaking all these roles, he was appointed Director of the Department of Mathematics at Mainz, a position he held from 1958 until 1970.[4]

Between 24 November 1966 and 1967 he was Rector of the University of Mainz.[4] Between July 1967 – 1977, he was a director of advisory center for student life issues at the University of Mainz. He was also an editor of Crelle's Journal, 1952–1977, assisting Helmut Hasse.[1] He held this chair until he retired as professor emeritus in 1977.

Work

Hans Rohrbachs time was split between work with an academic focus, and work involving the military. During his time of doctorate in the very early 1930s, he published several solutions to mathematical problems that were set by the Jahresbericht (Annual Report) of the German Mathematical Society.[1] In 1931, he published a solution to Problem 66, in 1932 a solution followed to Problem 84 and Problem 89 was also solved in 1932.[1]

In 1937, Rohrbach introduced a mathematical puzzle, which was a variation of James Joseph Sylvester's stamp puzzle:

I have a large number of stamps to the value of 5d and 17d only. What is the largest denomination which I cannot make up with a combination of these two different values.

In 1937, he formulated in his paper Ein Beitrag zur additiven Zahlentheorie (A contribution to the additive number theory) a related problem, which he considered much more difficult:

An envelope may carry no more than h stamps, and one has available k integer-valued stamp denominations. Given h and k, find the maximal integer n = n(h, k) such that all integer postage values from 1 to n can be made up. In addition, find all sets of k stamp denominations satisfying this condition. The problem statement is usually modified by augmenting the solution sets with a stamp of value zero, and requiring that a letter carry exactly h stamps.

Here are some examples from Mactutor, which have been copied verbatim to ensure mathematical accuracy:

  • n(2, 3) = 8 with the unique solution set {0, 1, 3, 4}.
  • n(2, 6) = 20 with five solution sets {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 3, 4, 9, 11, 16}, {0, 1, 3, 5, 6, 13, 14}, and {0, 1, 3, 5, 7, 9, 10}.
  • n(3, 4) = 24 with one solution set being {0, 1, 4, 7, 8}.

Within the paper, Rohrbach find asymptotic bounds for n with h fixed and k large. This is a problem many mathematicians have looked at but have not been solved yet.

It was while Rohrbach was at the Mathematical Institute of the German University of Prague, starting in 1933 as a senior assistant. In 1944, he wrote a report, of which this is an exert:

I am taking the move of the Mathematical Institute into the recently completed new rooms as an opportunity to give a short report on the development of the Institute in the last year. Up to the end of 1943 no research work was carried out in the Institute. The two established professors had been assigned to war work but, in addition, continued to carry out their teaching duties. The assistant had been drafted into the army, and no additional mathematicians were available. However, since I arrived here, I have made efforts to have the Institute itself to be involved in war related research. To achieve this I required more space and more collaborators. Once my requests to enlarge the Institute were granted in a satisfactory way by the curator, the work of setting up began a year ago.[1]

The work undertaken by Rohrbach was related to the computational problems associated with the manufacture and flight of V-weapons. The research and prototyping experimental work was undertaken at the village of Peenemünde. The scientists detailed in Rohrbach report above were Dr Gerhard Gentzen, Dr Franz Krammer and Dr Paul Armsen.

The other major area that Hans Rohrbach contributed to the German war effort was as working as Cryptanalyst (Cryptography) in the Mathematical and Cryptological Section of the special section of unit Z (The cryptanalysts) in the Reich Foreign Office (German: Auswärtiges Amt) (Pers Z S).[7][8][9]

He was awarded the War Service Cross 2nd Class (KVK II) in September 1944, for his work on the solution of the U.S. Diplomatic Strip System O-2.

Rohrbach had originally broken the cipher in 1943 after working on it for more than a year. The cipher was used by the US state department for diplomatic traffic, and the US Navy from 1940 to 1944. Rohrbach and his team used Hollerith punched card machinery and also built a special decoding machine called Automaton to aid cryptanalysis of the cipher. The Americans who made up the TICOM Team that investigated Pers Z S, ordered Rohrbach to write a report on 6 August 1945, in the form of homework to describe the process. The report was formulated as TICOM document I-89.[10]

This is the introduction to the report:

In this report we are dealing with a field of applied mathematics which has been foreign to most mathematicians and on which practically nothing has been published up to now. Methods and results have generally been left in secrecy, existing largely in the minds of the people involved. For these reasons we must go into the basic concepts and principles of this field rather thoroughly. Further, we cannot expect this report, as a first approach, to be exhaustive. The written materials needed for a foundation, including in particular the only publication to my knowledge of the character of a scientific journal (Scientific papers of the Dahlem Special Service, published by the Foreign Office, Berlin, 1940–45), either have been destroyed or have been retained by the Allies; the workers concerned are known to me only in small part or cannot be contacted. Accordingly, I can bring only scattered examples to the best of my memory. They come largely from the work of the Foreign Office, the Department of Defense (OKW), and the Department of the Army (OKH). By agreement with those workers that I have been able to contact, I will not give any names – it's a chance selection at best. Naturally much more work in this field has been done in Germany than I am able to take into consideration here, for the reasons already given. It seems to me at least, as will be brought out sufficiently in the material that follows, that mathematical cryptology is a very attractive field of applied mathematics. With good reason have all larger nations selected mathematicians for special use, particularly for use in cryptanalysis.

Here is how Hans Rohrbach split his work between academia and the military:[1]

I had concluded my activity there [Prague] for the winter semester 1944–45 [at the end of February] and was in Berlin, where during the war I was busy full time at the Foreign Office. I looked after the work in Prague for only two days in the week during the semester, traveling there at night in a sleeper coach, two night later back in a sleeper coach, thus working four days a week in Berlin, two days in Prague. During the vacations I was busy only in Berlin. I intended to return to Prague for the summer semester 1945 [at the end of April]. I had as always left everything personal behind in the Institute, in particular books, lecture manuscripts, etc. But at the beginning of April 1945 I was already in the store of the Foreign Office in Thuringia.

Honours

Publications

References

  1. 1 2 3 4 5 6 7 8 9 10 11 O'Connor, J. J.; Robertson, E. F. (10 April 1016). "Hans Rohrbach". Mactutor Archive – School of Mathematics and Statistics University of St Andrews, Scotland. JOC/EFR. Retrieved 20 July 2016.
  2. ↑ "Volume 6- Foreign Office Cryptanalytic Section" (PDF). NSA. p. 55. Retrieved 5 July 2016.
  3. ↑ "I-89 Report by Dr H. Rohrbach on Pers. ZS on American Strip Cypher [0–2 Cypher](PDF)". Google Drive. 6 August 1945. p. 1. Retrieved 24 July 2016.
  4. 1 2 3 4 "Hans Rohrbach". Verzeichnis der Professorinnen und Professoren der Universität Mainz 1946 – 1973 (English: Directory of Professors of the University of Mainz 1946 – 1973). Gutenberg Biographics, Johannes Gutenberg-Universität Mainz. Retrieved 12 November 2016.
  5. ↑ Sanford L. Segal (23 November 2014). Mathematicians under the Nazis. Princeton University Press. p. 470. ISBN 978-1-4008-6538-3.
  6. ↑ Brüning, Jochen; Ferus, Dirk; Siegmund-Schultze, Reinhard (1998), Terror and exile: persecution and expulsion of mathematicians from Berlin between 1933 and 1945 (An Exhibition on the Occasion of the International Congress of Mathematicians, Technische Universität Berlin, August 19 to 27, 1998), Berlin: Deutsche Mathematiker-Vereinigung, p. 45
  7. ↑ "Foreign Office Cryptanalytic Section" (PDF). NSA. p. 2. Retrieved 5 July 2016.
  8. ↑ Peter F Matthews (1 May 2013). SIGINT: The Secret History of Signals Intelligence in the World Wars. History Press. pp. 145–. ISBN 978-0-7524-9301-5.
  9. ↑ R. A. Ratcliff (14 August 2006). Delusions of Intelligence: Enigma, Ultra, and the End of Secure Ciphers. Cambridge University Press. pp. 67–. ISBN 978-0-521-85522-8.
  10. ↑ Ticom I-89
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