Zygalski perforated sheets

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Zygalski perforated sheets were used to determine the Enigma key

The Zygalski-Lochblätter (also: Zygalski-Lochkarten or Zygalski-Blätter ; in English: Zygalski sheets , perforated sheets or with the German foreign word as "Netz" for short ; in the Polish original: Płachta Zygalskiego ) were a by the Polish cryptanalyst Henryk Zygalski cryptanalytic tool devised in 1938 . From 1938 to 1940, they were used to decipher German radio messages that were encrypted using the Rotor Enigma key machine . The prerequisite for their functioning was the German procedural error of the duplication of the slogan key , which the Polish code breakers were able to use with the Zygalski sheets to open up the roll position and the slogan key of the Enigma.

Background and history

→ Main article: Cyclometer
Ten years after the invention of the Enigma in 1918 by Arthur Scherbius , the German Reichswehr decided to use the Scherbius machine on a trial basis. The most modern commercial version at the time, the Enigma D , was supplemented with a secret additional device, the plug board , exclusively for military use . This strengthened the cryptographic security of the Enigma (see also: cryptographic strengths of the Enigma ). The Reichswehr machine, known as Enigma I (read: "Enigma Eins"), embodied one of the most modern and secure encryption methods in the world at the time. While it failed French and the British, in the encryption break and they classified the Enigma as "unbreakable", succeeded Polish cryptanalysts in charge of Germany Unit BS4 of Biuro Szyfrów (abbreviation BS ; German: "Cipher Bureau") in the year 1932 first break-in (see also: deciphering the Enigma ). To do this, they took advantage of a serious procedural error that the Germans had made, namely the duplication of the key to the slogan .

Saying key duplication

→ Main article: Slogan key duplication
An essential part of the Enigma's key was the so-called "Slogan key" . This was selected individually for each radio message, for example "WIK" and secretly communicated to the authorized recipient. From September 15, 1938 to April 30, 1940, the following procedural regulation applied : The key to the verdict is placed twice in a row, i.e. doubled in the example for "WIKWIK". This duplicated spell key obtained in this way is then encrypted. To do this, enter the six letters one after the other via the Enigma's keyboard and read the lights that light up, for example "BPLBKM". This is the duplicated and encrypted spell key. It is placed in front of the actual ciphertext and, like this, transmitted in Morse code by radio .

method

Two Zygalski sheets on top of each other on a light table in the Bletchley Park Museum

The concept of the Zygalski perforated sheets is based on the German procedural error of the duplication of the spell key. The Poles recognized this mistake and identified the six letters of the duplicated and encrypted spell key. They concluded that the first and fourth, second and fifth as well as the third and sixth ciphertext letter of the encrypted slogan key (in the example "BPLBKM") each had to be assigned to the same plain text letter . This important finding enabled them to search for a pattern using the letter pattern “123123”.

In addition, one day the Poles sifted through the encrypted message keys for the many dozen, sometimes more than a hundred, intercepted German radio messages. They looked for special ones in which the first and fourth, the second and fifth or the third and sixth letters of the encrypted spell key were "coincidentally" identical. In the example "BPLBKM" above, this is the case for the first and fourth letters. They called such highly welcome cases “females” (Polish samica or colloquially samiczkami ), in this case more precisely a “(1,4) female”. The code breakers recognized that such a female was only possible with very specific roller positions and roller positions, but impossible with most of the others.

Henryk Zygalski had the idea in autumn 1938 to systematize and simplify this pattern search for females using perforated leaves. On the German side, three rollers were in use at this time (I, II and III), which were inserted into the machine in daily changing sequences according to the secret daily key . So there were six (= 3 · 2 · 1) different possibilities for the roller position, which the poles had to check individually and of which one was the correct one. In addition, the roller position, i.e. the starting position of the three rollers, was unknown to the Poles. Each of the three reels has 26 possible positions. With three rollers there are 26³, i.e. 17,576 different roller positions. Zygalski decided to use a perforated sheet for each of the 26 positions of the left roller. Together with the six roller layers, 6 · 26 or 156 perforated sheets had to be produced.

Each of these perforated sheets consisted of a 26 × 26 matrix in which the 26 letters of the alphabet were lined up horizontally and vertically for the middle and right rollers. This resulted in 26 x 26 or 676 coordinate intersections, which for a certain perforated sheet exactly represented a certain position and position of the Enigma rollers. If a female appeared, it was marked with a hole. All other positions where it did not appear remained unperforated. The work to produce the perforated sheets was laborious and time-consuming, as each individual hole was manually cut into the cards with the help of razor blades.

To check several radio messages, for which, as in the example, additional (1,4) females had been determined, additional perforated sheets were now placed over the first and shifted horizontally and vertically according to the letters of the encrypted message key. For practical reasons, the 26 × 26 matrix of each perforated sheet was duplicated horizontally and vertically in order to enable the stacked perforated sheets to be shifted and at the same time to obtain a central 26 × 26 area for all perforated sheets lying one above the other. It was sufficient to restrict yourself to the 25 letters A to Y (without Z) for the duplicated matrices on the right and below the original matrix. A Zygalski perforated sheet therefore actually had 26 + 25 or 51 letters each horizontally and vertically and a total of 51 * 51 or 2601 coordinate intersections.

If one investigated a wrong of the 156 possible cases as the assumed roller position and roller position of the left roller, then gradually all the holes disappeared as several sheets were superimposed and none remained free. The cryptanalysts use a light table to make their work easier. In the event that exactly the right one of the 156 cases was available, one hole remained light, regardless of how many more radio messages they evaluated and further perforated sheets were placed on top of each other, shifted accordingly. This was the solution they were looking for and indicated the roller position and roller position selected by the Germans.

The End

With the commissioning of rolls IV and V on December 15, 1938, the number of possible roll layers increased from six to sixty (= 5 · 4 · 3). This meant that instead of 156 perforated sheets, ten times the number was suddenly required to unlock the German keys. This exceeded the Polish production capacities and the Enigma was safe again (with the exception of days when neither of the two new rollers was used).

In the summer of 1939, in view of the situation and the impending danger, the Polish leadership decided to hand over all of their cryptanalytic knowledge to their French and British allies in order to successfully decipher the Enigma. On July 26th and 27th, 1939, shortly before the German invasion of Poland , the legendary Pyry secret meeting of French, British and Polish code breakers took place in the Kabaty Forest of Pyry , just under 20 km south of Warsaw, at which the Poles took part The British and the French were amazed by their cryptanalytic methodologies and devices, especially the Zygalski perforated sheets, and they were left with them.

The Zygalski perforated sheets were not only used by the Polish cryptanalysts of the BS against the German machine during their time in Poland, but also after the beginning of the Second World War in their new location “PC Bruno” in exile in France. At the end of 1939, the British Codebreakers from Bletchley Park , under the direction of John Jeffreys, produced two complete sets of Zygalski sheets , as they called them in English, for all 60 roller layers . It was also common to refer to them as perforated sheets (German: "Lochblätter") or for short with the German word "Netz" (from "Netzverfahren"). The British also translated the cryptanalytic Polish term samiczkami (German "Weibchen") into English and called it females . The production of the Zygalski sheets continued into the new year and was finally completed on January 7, 1940. According to Gordon Welchman , Alan Turing took a set of these sheets to France on January 17, 1940 and handed them over to the Polish cryptanalysts. When asked by Zygalski, who was surprised at the strange hole size of around 8.5  mm and therefore almost didn't recognize “his” blades, Turing replied with a laugh: “That's perfectly obvious. It's simply one third of an inch. " (German:" That's very clear. It's just a third of an inch . ")

With the change in the German procedural rules and the dropping of the doubling of the spell key on May 1, 1940, the Zygalski perforated sheets suddenly became useless.

literature

Web links

Individual evidence

  1. ^ Rudolf Kippenhahn: Encrypted messages, secret writing, Enigma and chip card . Rowohlt, Reinbek bei Hamburg 1999, p. 211. ISBN 3-499-60807-3
  2. ↑ Simon Singh: Secret Messages . Carl Hanser Verlag, Munich 2000, p. 178. ISBN 3-446-19873-3
  3. ↑ Simon Singh: Secret Messages . Carl Hanser Verlag, Munich 2000, p. 199. ISBN 3-446-19873-3
  4. ^ Marian Rejewski: An Application of the Theory of Permutations in Breaking the Enigma Cipher . Applicationes Mathematicae, 16 (4), 1980, pp. 543–559, cryptocellar.org (PDF; 1.6 MB), accessed on May 27, 2019.
  5. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 355. ISBN 0-304-36662-5 .
  6. ^ Gordon Welchman: The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, p. 16. ISBN 0-947712-34-8 .
  7. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 49. ISBN 0-304-36662-5 .
  8. ↑ a b Ralph Erskine: The Poles Reveal their Secrets - Alastair Dennistons's Account of the July 1939 Meeting at Pyry . Cryptologia. Rose-Hulman Institute of Technology. Taylor & Francis, Philadelphia PA 30.2006,4, p. 294.
  9. ↑ The Bletchley Park 1944 Cryptographic Dictionary formatted by Tony Sale . Bletchley Park, 2001, p. 37. Retrieved December 9, 2015. PDF; 0.4 MB
  10. ^ Gordon Welchman: The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, p. 220. ISBN 0-947712-34-8 .
  11. ^ Hugh Sebag-Montefiore: Enigma - The battle for the code . Cassell Military Paperbacks, London 2004, p. 357. ISBN 0-304-36662-5 .
  12. ^ Friedrich L. Bauer: Decrypted Secrets, Methods and Maxims of Cryptology . Springer, Berlin 2007 (4th edition), p. 123, ISBN 3-540-24502-2 .