Cryptography - Enigma

December 2016
"Never blindly trust a cryptography system" - Gilles Dubertret

The history of Enigma

The need to encrypt messages appeared at the end of World War I (although encryption techniques had already existed for a long time).

It was a Dutchman living in Germany, Dr. Arthur Scherbius, who developed the Enigma machine for commercial purposes; this machine was used to encode messages.

The machine's model A (Chieffrienmaschinen Aktien Gesellschaft) was presented in 1923 at the Bern Universal Postal Congress. The machine's price at the time (equivalent to 30,000 euros today) made it a miserable failure. But the idea caught on and the German Navy took up the project in 1925, entrusting its development to the encryption division (Chiffrierstelle) of the German war ministry. The Enigma M3 model was adopted by the Wehrmacht (German army) on 12 January 1937.

What the Germans didn't know is that the French and Polish counter-intelligence services had also been working on a decryption method since 1930. To that end, Captain Gustave Bertrand of the French secret services recruited Hans Thilo Schmidt (codenamed Asche), who worked for the Chiffrierstelle at the time.

When World War II broke out in 1939, the allies were able to decrypt Enigma's messages. On 24 July 1939, Marian Rejewski (manager of the Biuro Szyfrow - the most advanced European service involved in research on German encryption) gave a model of the Enigma machine to Captain Bertrand and Alistair Denniston, head of the British Intelligence Service's decryption division.

The war then intensified and decryption efforts picked up speed. Between the months of October and June 1939, over 4,000 encrypted messages were decoded by the French secret servivces. These operations had a name: Operation Z for the French and Ultra Secret for the English.

In August 1939, the English set up their Code and Cipher services in Bletchley Park (50 miles from London). No less than 12,000 English, Polish and French scientists and mathematicians worked to break the Enigma code. Among these mathematicians was one of the inventors of modern computer science: Alan Turing, who oversaw all this work.

The messages that were decrypted at Bletchley Park arrived at Hut 6 by conveyor belt and were then sent to the station for translation (2 stations per team):

  • one for late messages
  • one for urgent material

Messages that were translated from the Luftwaffe were sent to 3A and those from the army were sent to 3M (A=aviation; M=military). Zs were then assigned according to the messages' importance (1Z: not very important; 5Z: extremely urgent). Their information was then summarized and sent in 3 copies:

  • one to the Broadway SIS;
  • one to the appropriate ministry division or to Whitehall;
  • one to the general concerned in the field.

The English were therefore able to decrypt these coded messages. However, since the Kriegsmarine (German war navy) used different encryption measures, decryption proved to be more difficult. An important breakthrough was made with the capture of an Enigma and especially of its instructions on the U-110. This made it possible to find out the positions of sub-marines and reduce the tonnage sunk by U-Boots (See: The film U-571).

On 1 February 1942, the Enigma M4 model was commissioned. For eleven months, the allies were unable to decrypt its messages.

Throughout the war, over 18,000 messages were decrypted per day, making it possible for the allied forces to find out Germany's intentions. The last encrypted message was found in Norway, signed by Admiral Doenitz: "The Führer is dead. The battle continues". The Germans never suspected their precious machine could be decrypted.

Source:

How Enigma worked

Enigma's functioning was particularly simple: the object was equipped with a keyboard for inputting messages, different rotors for encoding, and a lamp panel for results.

Whenever a key was pressed on the keyboard, a letter on the lamp panel lit up. There were 3 encoding wheels, called "Scrambler-Rotors", which connected the keyboard to the lamp panel.

For example, with just one rotor, when B was pressed, current passed through the rotor and A lit up on the lamp panel:

Enigma rotor

To make the machine more complex, whenever a key was pressed, the rotor turned one notch. After one press the following was obtained:

Enigma rotor turned one notch

Depending on the model (M3 or M4), the system had either 3 or 4 rotors. The second and third rotors moved forward a notch when the previous went full circle. There was also a plugboard that mixed up the letters of the alphabet and a reflector that sent current back through the rotors before results were displayed.

In total, for Enigma machines equipped for 26 letters, there were 17,576 combinations (26 x 26 x 26) related to the orientation of each of the three rotors, 6 possible combinations related to the order of the rotors and therefore 100,391,791,500 possible connections when the six pairs of letters in the plugboard were connected: 12 letters chosen out of 26 (26! /(12!14!)), then 6 letters out of 12 (12!/6!), and since certain pairs were the same (A/D and D/A), it was necessary to divide by 26.

Enigma machines could therefore encrypt a text using 1016 (17,576 * 6 * 100,391,791,500) different combinations!

Cracking of the Enigma code

The Polish invented "the Bombe" (later renamed "Ultra"), which made it possible to find out Enigma's settings. However, as of 1938, it was the operator himself who established the settings. To fix this problem, the Polish found the solution: each message contained either repeated words or recurring words (called "females").

This was a clue as to the core (basic rotor setting). To discover this setting, the Polish then used the "Grill" (perforated sheets corresponding to all core permutations). These sheets were stacked one on top of the other according to the position of the "females".

The next step was to find the point where a series of holes lined up from the top to bottom of the stack.

Article written by Jean-François PILLOU and Sébastien DELSIRIE


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