Cyclometer

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.

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.

[2] Fede Weierud provides the procedure, secret settings, and results that were used in a 1950 German technical manual.

In September 1932 he, Różycki, and Zygalski went to Warsaw to work full-time for the Cipher Bureau.

The message key was first encrypted using the day's Grundstellung (a secret initial position of the Enigma's rotors, e.g., "FOL").

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.

The German procedure that sent an encrypted doubled key was the mistake that gave Rejewski a way in.

The Poles started using a Q-catalog to make part of the grill method easier; that catalog had 4,056 entries (26 × 26 × 6).

In the grill method, the above characteristic would be solved for the individual permutations A B C D E F and then a laborious search would be done.

The cryptanalyst can determine each of the individual permutations A* B* C* D* E* F* by setting an Enigma to the given wheel order and initial positions.

At this point, the potential steckers can be read from the differences in the first two lines; they can also be checked for interchange consistency.

[11] 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.

"[13] 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.

"[14] 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.

[14] This spurred the invention of Rejewski's cryptologic bomb and Zygalski's perforated sheets.