Cracking The Enigma(I)

Continuing from my first blog in this blog I’ll introduce the initial minds that attempted to break the Enigma and laid the foundation for others to finally crack the seemingly impossible task.Here’s the link to my first blog for an introduction to the working of the Enigma:

After the arrival of the Enigma the British cryptoanalysts in Room 40(the headquaters for cryptography in Britain) were completely baffled.The Americans and the French also tried but their attempt were equally dismal.It appeared codebreakers had lost the earlier zeal they had during the First World War,probably the fear was the main driving force earlier.They thought that Germany was crippled by deafeat.But it’s mostly when one is defeated is one dangerous.However ,one nation could not relax Poland reestablished itself as an independent state after the war and was in constant threat from the Allies and German forces.Sandwiched between these two enemies, the Poles were desperate for intelligence information, and they formed a new cipher bureau, ‘The Biuro Szyfrów’.

‘If necessity is the mother of invention, then perhaps adversity is the mother of cryptanalysis’

The first blow towards breaking the Enigma came from the own lands of the Germans.Hans-Thilo Schmidt a soldier of the German army who was left in destitute after the First war by the German forces was humiliated by this behaviour.He secretly got held of some documents containing the Enigma’s secret and sold them to the French. As a sense of overconfidence and lack of motivation the French didn’t care to examine the documents thinking that cracking Enigma was impossible and sold the documents to the Poles through military cooperation.The documents revealed important secrets of several structures of the scrambler wirings and the layout of a typical code book.The Poles convinced themselves that there must be a shortcut to finding the key to an Enigma-encrypted message, and that if they applied sufficient effort, ingenuity and wit, they could find that shortcut.

Rise of Marian Rejewski


Marian Rejewski was a statistician who was given this task by the Poles. As a Mathematician he would try to analyse every aspect of the machine’s operation.Rejewski’s strategy for attacking Enigma focused on the fact that repetition is the enemy of security: repetition leads to patterns, and cryptanalysts thrive on patterns. The most obvious repetition in the Enigma encryption was the message key, which was enciphered twice at the beginning of every message as a measure for security.The Germans demanded to change the key settings each day for a new message being sent as this would stop several billion messages to be encrypted by the same scrambler settings the same day.Thus they would let the reciever know on radio by typing the scrambler setting for the message by repeating it twice at the start of the message(As the scrambler settings are easy to alter than the rest ones it just involves changing the dial to a new letter among the 26).If the operator chose the message key ULJ, then he would encrypt it twice so that ULJULJ might be enciphered as PEFNWZ, which he would then send at the start before the actual message. The Germans had demanded this repetition in order to avoid mistakes caused by radio interference or operator error. But they did not foresee that this would jeopardize the security of the machine.

The Attack

Rejewski argued that for any repeated message key the 1st and the 4th letter in the ciphertext enocoded the same letter.Thus the 1st and 4th letter were somehow related.If he had access to many messages in a day he could develop all relations.He tabulated such relation for particular day key as shown:

2ndHe next wanted to find the link between the letters.Eventually, he began to study one particular type of pattern, which featured chains of letters. For example, in the table, A on the top row is linked to F on the bottom row, so next he would look up F on the top row. It turns out that F is linked to W, and so he would look up W on the top row. And it turns out that W is linked to A, which is where we started. The chain has been completed.He numbered the links.


He did the same process with the 2nd and 5th and the 3rd and 6th letters.Rejewski noticed that the chains changed each day. Sometimes there were lots of short chains, sometimes just a few long chains. And, of course, the letters within the chains changed. The characteristics of the chains were clearly a result of the day key setting-a complex consequence of the plugboard settings, the scrambler arrangement and the scrambler orientations. However, there remained the question of how Rejewski could determine the day key from these chains. Which of 10,000,000,000,000,000 possible day keys was related to a particular pattern of chains? The number of possibilities was simply too great!

With one step closer in cracking Enigma.How Rejewski dealt with this problem will  be coming up in my next blog.Stay tuned!

Thank you,

Shoubhik Banerjee

IISER Bhopal


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