The work of Bletchley Park

Thus far we’ve looked at how mathematics helped break the Enigma machine before the Second World War started. In the lead-up to the War, security improvements were made to Enigma, making Rejewski’s methods less practical. We shall now discover how the men and women of Bletchley Park enabled the Enigma secrets to be read throughout the War.

In July 1939, when it became clear that the world was heading towards war, the Polish mathematicians who had had such success against Enigma shared their knowledge with British and French mathematicians in a meeting in Pyry Forest near Warsaw. On the British side was Alastair Denniston (head of Bletchley Park, where the UK’s code breaking activities were centred) and Dilly Knox (Bletchley’s expert on Enigma).

The insights gained from this meeting and a later meeting in January 1940 in Paris, where Alan Turing was also present, helped immensely in the design of Turing’s bombe, a device for breaking the daily Enigma keys.

The Germans knew the double encryption of the message indicator (which Rejewski’s method relied upon) was a security risk, and after 10th May 1940 they stopped repeating the message indicators. (This was when Nazi Germany successfully invaded Belgium, the Netherlands, and France, leading to the Dunkirk evacuation at the end of that month.)

However, by then enough was known about the bad habits of some German operators (such as reusing the same message indicator repeatedly) that the Allies still could read certain messages. Gordon Welchman, another mathematician who worked at Bletchley Park wrote in his book The Hut Six Story

Unbelievable! Yet it actually happened, and it went on happening until the bombes came, many months later.

This piece of information was a strategic plum.

This was because Churchill, confident that the invasion was off, approved tanks to be sent from the UK to Africa to fight there.

However, to read more messages, it was clear a new idea was needed. Turing started working on his bombe in 1939, when he joined Bletchley Park. It was designed to logically rule settings out of consideration, thus making the codebreakers’ work vastly more manageable.

It simulated the effect of a number of Enigma machines wired together (not dissimilar to the Double Enigma Machine used in the cyclometer). It relied on a crib, which was a guess for the plaintext that would appear in the message. The crib and the ciphertext message were then encoded into the bombe, which ran through various rotor settings and checked the logical implications of the plaintext-ciphertext pairs to see if they forced the plugboard to pair a letter with two different letters. Since that’s impossible, it would rule out that rotor setting for any plugboard.

If a contradiction was detected, and those rotor settings ruled out, the bombe would then mechanically move its simulated Enigma machines to another rotor position and try again.

If the setting did not lead to a contradiction, the bombe would stop and that potential setting could be tested further to see if it yielded something that looked like a real German message.

The longer the crib was, the more logical connections between the various plaintext-ciphertext letters, and thus the more false settings that could be ruled out. Turing’s original design needed impractically long cribs. However, Gordon Welchman invented a diagonal board that utilised further symmetries inherent in the Enigma’s plugboard, and reduced the required length of a crib to a more manageable length.

Two common cribs were wettervorhersage (weather report) and Keine besonderen Ereignisse (which simply means “nothing to report”!).

The first bombe came to Bletchley Park in March 1940. The second bombe came in August 1940 and implemented Welchman’s diagonal board, making it much more powerful. The number of bombes steadily increased to over 150 by the end of the War.

When the Americans joined the Allies, following the attack at Pearl Harbor, they built their own version of the bombe. These were particularly useful in attacking the four-rotor Enigma machines used in U-boats.

Remark: The bombe should not be confused with the world’s first programmable electronic computer, Colossus, created by Tommy Flowers for use at Bletchley Park. This was to attack a completely different cipher (the Lorenz cipher).