Циклометр Марианa Реевского: Устройство для взлома шифра Энигма.

Cryptologic device
the cryptologic device

The cyclometer was a cryptologic device designed, "probably in 1934 or 1935," by Marian Rejewski of the Polish Cipher Bureau's German section (BS 4), to catalog the cycle structure of Enigma permutations, thereby facilitating the decryption of German Enigma ciphertext. With Rejewski's later cryptologic bomb, it can be viewed as a predecessor to the Bombe that was to help break Enigma ciphers later in the war at Bletchley Park in England. Using drawings made by Rejewski, Hal Evans and Tim Flack at the Department of Engineering, University of Cambridge, in 2019 constructed a working version of the cyclometer.

During Marian Rejewski's mathematics studies at Poznań University, the Polish Cipher Bureau recruited him and some other mathematics students, including Jerzy Różycki and Henryk Zygalski, to take a Bureau sponsored course on cryptology. The Bureau later hired some of the students to work part time at a temporary local Bureau office. After graduating from Poznań University, at the University of Göttingen Rejewski completed the first year of a two year actuarial statistics course, then returned to Poznań. In September 1932 he, Różycki, and Zygalski went to Warsaw to work full time for the Cipher Bureau. In December 1932 Rejewski was tasked by the Cipher Bureau to work on the German Enigma cipher machine. The Bureau had attempted, but had failed, to break it. Within a few weeks, Rejewski managed to reconstruct the machine. The German Enigma message procedures used common, secret daily machine settings, but also required a cipher clerk to choose an individual three letter message key. Thus, a clerk might choose "ABL" as the message key. The message key was used to set the initial position of the rotors when enciphering or deciphering the message. Choosing an individual message key was a security measure: it avoided having all the day's messages sent using the same polyalphabetic key, which would have made the messages vulnerable to a polyalphabetic attack. However, the sender needed to communicate the message key to the recipient in order for the latter to decipher the message. The message key was first encrypted using the day's Grundstellung (a secret initial position of the Enigma's rotors, e. g., "FOL"). Communications were sometimes garbled, and if the message key were garbled, the recipient would be unable to decrypt the message. Consequently the Germans took the precaution of sending the message key twice; if there was a garble, the recipient should be able to find the message key. Here the Germans committed a crucial error. Instead of sending the encrypted message key (e. g., "PKP") twice to get "PKP PKP", they doubled the message key (e. g., "ABL ABL"), encrypted the doubled key to get ("PKP JXI"), and sent the encrypted doubled key. That mistake allowed Rejewski to identify six sequential permutations of the Enigma and exploit the knowledge that they encrypted the same message key. With the help of a commercial Enigma machine, German materials obtained by French spy Hans Thilo Schmidt, and German cipher clerks who chose weak keys, Rejewski was able to reverse engineer the wiring of the Enigma's rotors and reflector. The Cipher Bureau then built several Polish Enigma doubles that could be used to decrypt German messages.

Rejewski could use this cycle information and some sloppy habits of code clerks to figure out the individual permutations A B C D E F using the grill method, but that method was tedious. After using the grill, the Poles would know the rightmost rotor and its position, the plugboard connections, and Q (the permutation of the reflector and other two rotors). In order to get the daily key, the Poles would still have a lot of work to do, and that work could entail trying all possible orders and positions for the two left rotors to find the position for the Grundstellung. The Poles started using a Q catalog to make part of the grill method easier; that catalog had 4,056 entries (26 × 26 × 6). To find the ring settings, the grill method could require trying 17,576 possibilities. The grill method worked well until 1 October 1936, the day the Germans stopped using six steckers (plugboard connections) and started using five to eight steckers. More steckers could frustrate the grill method.

Instead of indexing the catalog by the actual cycles, the Poles hit upon indexing the catalog by the length of the cycles. Although the plugboard changed the identity of the letters in the permutation, the plugboard did not change the lengths of the cycles. It turns out there are 101 possible patterns for the cycle lengths of an indicator permutation. With the three permutations in the characteristic, there are about one million possible cycle length combinations Consequently, the cycle lengths could be used as a hash function into a hash table of the 105,456 possible combinations. The Poles would look at the day's traffic, recover the characteristic of the indicator, and then look in the card catalog. The odds would be good that only one (or maybe a few) cards had those cycle lengths. The result would be the appropriate rotor order and the positions of all the rotors without much work. The method was simpler than the grill method and would work when there were many steckers.

The cyclometer was used to prepare a catalog of the length and number of cycles in the "characteristics" for all 17,576 positions of the rotors for a given sequence of rotors. Since there were six such possible sequences, the resulting "catalog of characteristics," or "card catalog," comprised a total of (6) (17,576) = 105,456 entries. The utility of the card catalog, writes Rejewski, was independent of the number of plug connections being used by the Germans on their Enigma machines (and of the reconstruction of message keys). Preparation of the catalog "was laborious and took over a year, but when it was ready daily keys [could be obtained] within about fifteen minutes." On November 1, 1937, however, the Germans changed the "reversing drum," or "reflector." This forced the Cipher Bureau to start anew 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." But then, on September 15, 1938, the Germans changed entirely the procedure for enciphering message keys, and as a result the card catalog method became completely useless.