词条 | Card catalog (cryptology) |
释义 |
The card catalog, or "catalog of characteristics," in cryptography, was a system designed by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski, and first completed about 1935 or 1936, to facilitate decrypting German Enigma ciphers.[1] HistoryThe Polish Cipher Bureau used the theory of permutations to start breaking the Enigma cipher in late 1932. The Bureau recognized that the Enigma machine's doubled-key (see Grill (cryptology)) permutations formed cycles, and those cycles could be used to break the cipher. With German cipher keys provided by a French spy, the Bureau was able to reverse engineer the Enigma and start reading German messages. At the time, the Germans were using only 6 steckers, and the Polish grill method was feasible. On 1 August 1936, the Germans started using 8 steckers, and that change made the grill method less feasible. The Bureau needed an improved method to break the German cipher. Although the steckers would change which letters were in a doubled-key's cycle, the steckers would not change the number of cycles or the length of those cycles. Steckers could be ignored. Ignoring the mid-key turnovers, the Enigma machine had only {{math|263}} distinct settings of the three rotors, and the three rotors could only be arranged in the machine {{math|1=3!=6}} ways. That meant there were only {{#expr:26*26*26*6}} likely doubled-key permutations. The Bureau set about determining and cataloging the characteristic of each of those likely permutations. Each letter of the key could be one of partition number 13 = 101 possible values, and the 3 letters of the key meant there were {{#expr:101*101*101}} possible keys. On average, a key would find one setting of the rotors, but it might find several possible settings. The Polish cryptanalyst could then collect enough traffic to determine all the cycles in a daily key. That usually took about 60 messages. The result might be: He would use the lengths of the cycles (132;102-32;102-22-12) to look up the wheel order (II I III) and starting rotor positions in the card catalog. He would then use an Enigma to compute the un-steckered cycles: By comparing the steckered cycles from the German traffic and the un-steckered cycles, the cryptanalyst can determine the steckers. In the example, the CF permutation has
Where Repetition produces the steckers A-M, F-I, N-V, P-S, T-U, W-Z. Preparation of the card catalog, using the cyclometer that Rejewski had invented about 1934 or 1935, was a laborious task that took over a year's time. But once the catalog was complete, obtaining Enigma daily keys was a matter of some fifteen minutes.[2][3] When the Germans changed the Enigma machine's "reflector," or "reversing drum," on 1 November 1937, the Cipher Bureau was forced to start over again with a new card catalog: "a task," writes Rejewski, "which consumed, on account of our greater experience, probably somewhat less than a year's time."[2] On 15 September 1938 the Germans completely changed the procedure for enciphering message keys, rendering the card-catalog method useless. This spurred the invention of Rejewski's cryptologic bomb and Henryk Zygalski's "perforated sheets."[4] Notes1. ^Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," pp. 284–87. 2. ^1 Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys...", p. 242. 3. ^Marian Rejewski, "How the Polish Mathematicians Broke Enigma," p. 264. 4. ^Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys...", pp. 242–43. References{{Cipher Bureau}}{{EnigmaSeries}}
3 : History of cryptography|Science and technology in Poland|Biuro Szyfrów |
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