Bomba (cryptography)

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Cryptologic bomb. Diagram from Marian Rejewski's papers.
1: Rotors (for clarity, only one 3-rotor set is shown).
2: Electric motor.
3: Switches.

The Bomba, or Bomba kryptologiczna (Polish for "Bomb" or "Cryptologic bomb") was a special-purpose machine designed about October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma machine ciphers.

The German Enigma used a combination key to control the operation of the machine: rotor order, which rotors to install, which ring setting for each rotor, which initial setting for each rotor, and the settings of the stecker plugboard. The rotor settings were trigrams (for example, "NJR") to indicate the way the operator was to set the machine. German Enigma operators were issued lists of these keys, one key for each day. For added security, however, each individual message was encrypted using an additional key modification. The operator randomly selected a trigram rotor setting for each message (for example, "PDN"). This message key would be typed twice ("PDNPDN") and encrypted, using the daily key (all the rest of those settings). At this point each operator would reset his machine to the message key, which would then be used for the rest of the message. Because the configuration of the Enigma's rotor set changed with each depression of a key, the repetition would not be obvious in the ciphertext since the same plaintext letters would encrypt to different ciphertext letters. (For example, "PDNPDN" might become "ZRSJVL.")

This procedure, which seemed secure to the Germans, was nonetheless a cryptographic error. Using the knowledge that the first three letters of a message were the same as the second three, Polish mathematician Marian Rejewski was able to determine the internal wirings of the Enigma machine and thus to reconstruct the logical structure of the device. Only general traits of the machine were suspected, from the example of the commercial Enigma variant, which the Germans were known to have been using diplomatically. The military versions were sufficiently different that they presented an entirely new problem. Having done that much, it was still necessary to check each of the potential daily keys to break an encrypted message (ie, a "ciphertext"). With many thousands of such possible keys, and with the growing complexity of the Enigma machine and its keying procedures, this was becoming an increasingly daunting task.

In order to mechanize and speed up the process, Rejewski, a civilian mathematician working at the Polish General Staff's Cipher Bureau in Warsaw, invented the "bomba" (bomb), probably in October 1938. It was an electro-mechanical device — essentially an electrically powered aggregate of six Enigmas. The bomba method was based, like the Poles' earlier "grill" method, on the fact that the plug connections in the commutator did not change all the letters. But while the grill method required unchanged pairs of letters, the method of the bombs required only unchanged letters. Hence it could be applied even though the number of plug connections in this period was between five and eight. In mid-November 1938 the bombs were ready, and the reconstructing of daily keys now took about two hours.^[1]

The German Enigma plugboard greatly improved the security of the machine.

Just how the machine came to be called a "bomb" has been an object of considerable fascination and speculation. One, most likely apocryphal, version originated with the Polish engineer and army officer Tadeusz Lisicki (who knew Rejewski and his colleague Henryk Zygalski in wartime Britain but who had himself never been associated with the Cipher Bureau). He claimed that it was Jerzy Różycki—the youngest of the three Enigma cryptologists, who had perished in the sinking of a passenger ship in the Mediterranean Sea in January 1942—who had named the "bomb," after an ice cream dessert of the name. This story seems implausible, as Lisicki never met Różycki and it is unlikely that Rejewski and Zygalski, who had been sworn to secrecy about their work on Enigma, would have discussed Enigma decryption, much less the naming of the bomb, with an unauthorized person in wartime. Lisicki received information from Rejewski after Enigma decryption had become public knowledge and Lisicki — who after the war had remained in Britain — offered to advocate for Polish priority. Rejewski himself, in a posthumous paper published in the Polish Wiadomości matematyczne (Mathematical News) in 1980 and appearing as appendix D to Kozaczuk's Enigma 1984, stated that the device had been named "bomb" "for lack of a better idea."^[2] Perhaps the closest we will get to the name's actual origin is the version given by a Cipher Bureau technician, Czesław Betlewski: workers at B.S.-4, the Cipher Bureau's German section, dubbed the machine a "bomb" (also, alternatively, a "washing machine" or "mangle") on account of the characteristic muffled noise it produced when operating.^[3] According to a top secret US Army report dated 15 June 1945,^[4]

A machine called the "bombe" is used to expedite the solution. The first machine was built by the Poles and was a hand operated multiple enigma machine. When a possible solution was reached a part would fall off the machine onto the floor with a loud noise. Hence the name "bombe".

Up to July 25, 1939, the Poles had been breaking Enigma messages for over six and a half years without telling their French and British allies. On December 15, 1938, two new rotors, IV and V, had been introduced (three of the now five rotors being selected for use in the machine at a time). As Rejewski wrote in a 1979 critique of appendix 1, volume 1 (1979), of the official history of British Intelligence in the Second World War, "we quickly found the [wirings] within the [new rotors], but [their] introduction [...] raised the number of possible sequences of drums from 6 to 60 [...] and hence also raised ten-fold the work of finding the keys. Thus the change was not qualitative but quantitative. We would have had to markedly increase the personnel to operate the bombs, to produce the perforated sheets (60 series of 26 sheets each were now needed, whereas up to the meeting on July 25, 1939, we had only two such series ready) and to manipulate the sheets."^[5]

Some suggestions have been made that the Poles decided to share their Enigma-breaking equipment and techniques with the French and British in July 1939 because they had encountered insuperable technical difficulties. Rejewski explains, in the same critique: "No, it was not [cryptologic] difficulties [...] that prompted us to work with the British and French, but only the deteriorating political situation. If we had had no difficulties at all we would still, or even the more so, have shared our achievements with our allies as our contribution to the struggle against Germany."^[5]

[edit] See also

• Biuro Szyfrów: Cipher Bureau.
• Bombe: a machine, inspired by Rejewski's "Bomba", that was used by British and American cryptologists during World War II.
• Cryptanalysis of the Enigma.
• Zygalski sheets: invented about October 1938 by Henryk Zygalski and called "perforated sheets" by the Poles, they made possible the recovery of the Enigma's entire cipher key.

[edit] References

1. ^ Rejewski, in Kozaczuk's Enigma 1984, pp. 242, 290.
2. ^ Kozaczuk, p. 267
3. ^ Kozaczuk, Enigma 1984, p. 63, note 1.
4. ^ http://www.codesandciphers.org.uk/documents/bmbrpt/bmbpg010.HTM
5. ^ ^{a b} Rejewski, 1979

• Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, edited and translated by Christopher Kasparek, Frederick, MD, University Publications of America, 1984.
• Marian Rejewski, "Remarks on Appendix 1 to British Intelligence in the Second World War by F.H. Hinsley," translated by Christopher Kasparek, Cryptologia: a Quarterly Journal Devoted to All Aspects of Cryptology, vol. 6, no. 1 (January 1982), pp. 75-83.
• The US 6812 Division Bombe Report Eastcote 1944

[edit] External links

• Codebreaking and Secret Weapons in World War II By Bill Momsen
• A Brief History of Computing Technology, 1930 to 1939