Cryptanalysis of the Engima carried out by the allies

• Rejewski's Catalog
• Cyclometer
• Rejewski's Bombe
• Zygalski's Sheets
• Turing's Bombe
• Turing / Welchman Bombe

The breaking of the commercial Enigma by the British

In 1927, Foss examined a commercial Enigma bought by GC&CS. He wrote a paper entitled "The Reciprocal Enigma" in which he showed how, if the wiring was known, a crib of fifteen letters would give away the identity and setting of the right-hand rotor and how, if the wiring was unknown, a crib of 180 letters would give away the wiring of the right-hand and middle rotors.

In April 1937, Knox realizes the feat of reading the traffic of the Italian Navy encrypted by the commercial Enigma but whose rotors have been rewired. Thanks to twenty or so "in depth" encrypted messages, it can, at first, reconstruct the plaintexts and thus obtain several elementary permutations. Then, thanks to the method "Buttoning-Up" that he invents, he reconstructs the wiring of the rotors. Finally, he can read the messages through cribs by another method, "Rods" which he also invents. He can then read messages from Franco's Spain which use the same machine and the same rotors.

Note: in fact, the Poles broke in 1933 (?) the first version of the German Navy Enigma. This machine was actually a modified commercial Enigma (it had 29 keys because it used umlauts). But the technique used by Rejewski was not based on the use of a crib but on the weakness of the indicator system (throw-on) in which the message key was encrypted twice.

The breaking of the military Enigma by the Polish

In 1930, the spy Hans-Thilo Schmidt sold to the French intelligence service (SR) documents concerning the Enigma. The French cipher service does not know how to use them. Captain Bertrand of the SR decides to transmit these documents to the French allies: the English and the Poles.

The Polish cryptologist Rejewski, thanks to Enigma traffic and the notices and key tables provided by Bertrand, managed to find the rotor wiring at the end of 1932. A replicas of the Enigma could then be built. From the beginning of 1933, the daily traffic could be deciphered.

Rejewski's catalog and the cyclometer

At first, the Poles read Enigma messages thanks to errors from the cipher clerks. Then, Rejewski finds a method to find the key of the day. His method is still based on the message headers where the message key was encrypted twice.

He develops a theory: the theory of cycles. This one (based on Group theory) highlights motives dependent only on the order of rotors, ringstellung and grundstellung but not steckers! Subsequently, based on this theory, he develops a method (called "Catalog") to find the daily key.

To manufacture the catalog intended to identify the key of the day, Rejewski imagined a device called Cyclometer. This machine is made up of two sets of 3 connected rotors. The two sets of rotors are offset by 3 positions, in order to emulate the simultaneous encryption of the letters of the indicator.

Rejewski’s Bombe

The catalog method was possible because the message key encryption method used in 1930 required that all message keys were encrypted at the same position of the rotors (Grundstellung) and that this was part of the key of the day.

After the Grundstellung was abandoned on September 15, 1938, the catalog method was no longer usable. In November 1938, Rejewski invented a machine, the Bombe, composed of six Enigmas functioning automatically and testing all possible positions of the rotors to find the one compatible with the indicators of the day

Zygalski’s sheets

One big flaw with Rejewski’s Bombe is that the letters used to make up a menu must not belong to a stecker. Conversely, Zygalski, invented a method using perforated sheets in October 1938. This method does not involve the use of self-steckered letters. So this method is more general.

English manual methods

Once again, the change in German procedures in May 1940 made the Allied methods obsolete. Rejewski's Bombe and Zygalski’s sheets are no longer usable.

Sheets can no longer be used to crack Enigma keys, but several German errors will allow English cryptologists to continue their decryption, primarily through the use of Knox's Cillies and the Herivel method.

The discovery of the existence of rules in the elaboration of Enigma keys is also of great utility and complements the above-mentioned methods.

The Turing / Welchman Bombe

At the end of July 1939, in Pyry, near Warsaw, the Poles transmitted to the French and English not only the wiring of the Enigma rotors but also their methods for breaking the keys of the day (Rejeswki's Bombe and Zygalski's sheets).

As soon as Knox returned from Pyry, he signaled to Denniston the main flaw of the Polish methods (Bombes and Zygalski’s sheets): they depended on the indicator method. If, unfortunately, the Germans were to change it, their methods would become useless overnight.

Based on the theory of Rejewski’s cycles that he generalizes, Turing invents a machine (the Turing Bombe) which, like the Polish one, scans all the configurations of the rotors, but which is independent of the indicator method, because it is based on the presence of a Crib.

Welchman, in the fall of 1939, had the brilliant idea of using the impossibility of a letter being coded by itself to improve the Bombe. To materialize the corresponding test, a "diagonal board" had to be added to it.