Cyclometer (cryptology)

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The cyclometer (1934) was designed by Rejewski to catalog the characteristics of the Enigma permutations, namely the number and length of the cycles. Above you can see the two sets of Enigma rollers (on the left with the lid closed and on the right with the lid open). On the right of the front panel there are 26 alphabet switches and 26 indicator lamps that signaled the characteristics sought. The “ rheostat ” for dimming the lamps is arranged on the left.
The Polish code breaker Marian Rejewski (1932)
Plug board of the Enigma
(in the picture A is plugged into J and S is plugged into O)
The reversing roller was replaced on November 2nd, 1937 with a new one with completely changed wiring

The cyclometer (from Greek : κύκλος (cyclos) "loop" and μέτρον (metron) "knife" (in the sense of: measuring device ), literally in German: loop knife ; in the Polish original: " cyclometry ") was a cryptanalytic device that was developed in 1934 by the Polish mathematician and cryptanalyst Marian Rejewski during his work in the BS4 department responsible for Germany in the Biuro Szyfrów (German: "Chiffrenbüro") in Warsaw. It served to decipher the radio messages that the German military encrypted with the help of their rotor key machine Enigma .

An important task that the Poles had to solve in order to decipher an Enigma radio message was to find the “ Tagesschüssel ” that the German encryptors used. This included finding the correct roller position and starting position of the key machine. Due to the use of three rollers with 26 letters each, the Enigma had 26³ = 17,576 different starting positions and 3! ( Faculty ), i.e. 6 different roller positions.

For deciphering, Marian Rejewski, together with his colleagues Jerzy Różycki and Henryk Zygalski, who joined them in 1932 (photo of the three see under web links ) , exploited a serious procedural error which the Germans made and which offered the decisive starting point for deciphering: a secure transmission To ensure this, the initial position of the rollers was placed at the beginning of a message twice in a row and transmitted in encrypted form as a message key ( " message key duplication" ). Thus the first and fourth, the second and fifth as well as the third and sixth ciphertext letters were each assigned to the same plain text letter. This resulted in “characteristic permutations ” that were independent of the number and selection of plugs that the Germans had plugged into the Enigma's plug board, and that only depended on the roller position and the initial position.

Instead of the astronomically large number of possibilities caused by the plug board (more than 100 billion when using six cables), the Polish code breakers only had to use the comparatively small number of 6 roller positions and 17,576 initial positions, ie "only" 6 · 17,576 = 105,456 possibilities examine.

With the help of the cyclometer, which embodied two Enigma machines connected one behind the other and offset by three rotational positions, the Polish code breakers were able to determine for each of the six possible roller positions which characteristic permutations occurred in the various roller positions. The cyclometer helped simplify this very tedious and time-consuming work of cataloging the characteristic permutations. The “characteristics” determined were recorded in a catalog. The work on this catalog was completed by the Poles in 1937. They had thus created ideal conditions for deciphering the German Enigma radio messages.

The creation of this catalog of characteristics , Rejewski said, "was laborious and took more than a year, but after it was finished [...] day keys could [be determined] within about 15 minutes".

For this purpose, the assignment of the letter pairs observed in a radio message to be deciphered was compared with the catalog with regard to their characteristics. In this way, it was possible to rule out the vast majority of possible roller positions and initial positions, since these had unsuitable characteristics. After analyzing several spell keys, there was ultimately only one option left. This was the desired roll position and the correct starting position.

After this was found, the Polish cryptanalysts had little trouble finding the six correct connector pairs and the ring position using a replica Enigma . Then the complete key was revealed and they could read the ciphertext just like the authorized recipient using the now known key.

After the Germans replaced the Enigma's reverse cylinder (VHF) on November 2, 1937 - the VHF A was replaced by the new VHF B - the Polish code breakers were forced to start the laborious catalog creation from scratch a second time. Even before they could complete this work, the Germans changed their process engineering on September 15, 1938 by introducing a new indicator method with a freely selectable basic position for the spell key encryption. Again three months later, on December 15, 1938, there was a further complication with the introduction of the new rollers IV and V. The number of possible roller layers increased from six to sixty.

The catalog and the cyclometer became useless as a result of the new German procedure for agreeing on the key words and the Polish Biuro Szyfrów was forced to come up with new methods of attack. This led to the invention of the punch card method by Henryk Zygalski and to the construction of the bomba by Marian Rejewski.

literature

  • Rudolf Kippenhahn : Encrypted messages, secret writing, Enigma and chip card . Rowohlt, Reinbek near Hamburg 1999. ISBN 3-499-60807-3
  • Władysław Kozaczuk : Secret Operation Wicher . Bernard et al. Graefe, Koblenz 1989, Karl Müller, Erlangen 1999. ISBN 3-7637-5868-2 , ISBN 3-86070-803-1
  • Władysław Kozaczuk: Under the spell of Enigma . Military publishing house of the German Democratic Republic , 1987, ISBN 3-327-00423-4
  • Władysław Kozaczuk & Jerzy Straszak: Enigma - How the Poles Broke the Nazi Code . Hyppocrene Books, New York 2004. ISBN 0-7818-0941-X
  • Alex Kuhl: Rejewski's Catalog . Cryptologia , Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 31.2007,4, pp. 326-331. Accessed: December 18, 2015. PDF; 0.1 MB
  • Tadeusz Lisicki : The performance of the Polish deciphering service in solving the method of the German "Enigma" radio key machine in J. Rohwer and E. Jäkel: The radio clearing up and its role in the Second World War , Motorbuch Verlag, Stuttgart, 1979, pp. 66-81 . PDF; 1.7 MB . Retrieved May 16, 2017.
  • Marian Rejewski: An Application of the Theory of Permutations in Breaking the Enigma Cipher . Applicationes Mathematicae, 16 (4), 1980, pp. 543 - 559. Accessed: December 18, 2015. PDF; 1.6 MB .
  • Gordon Welchman : From Polish Bomba to British Bombe: The Birth of Ultra . Intelligence and National Security, 1986.

Web links