Allied Crytographic Success


The Enigma machine was a sophisticated mechanical cipher invented in around 1918 by a German engineering firm. It was intended to replace the easily cracked ciphers used during the First World War with something more difficult to decode, and to this end, the company produced a more complicated military version.

Many cryptographists would agree that the inter-allied intelligence operation Enigma was the greatest success of World War II after the atom bomb. The breaking of this sophisticated German machine cipher was probably the most spectacular event, in terms of its difficulty and far-reaching consequences, in the entire history of cryptography. Operation Enigma was one of powerful weapons of the anti-Nazi war coalition but in contrast to that of nuclear weapons, which itself had come to light in the terrific holocaust of Hiroshima and Nagasaki in August, 1945, the secrets of the Enigma remained hidden and unknown to the public for the next almost three decades. Its details have started to emerge only recently after the Official Secrets Act has ceased to apply.

Encrypting Messages in Enigma

Each day, a new three letter key was chosen and distributed to the German Enigma operators. This told them how to set up their machines in order to send and receive messages on that day. As an added security measure, the operators would often only use the day key in order to encrypt and send a new message key to another receiver. This key would then be used to encrypt messages sent between the pair as normal. In order to avoid transmission errors, each message key was sent twice.

Why were Enigma Messages so difficult to decipher?

Although the design of the Enigma machine was simple, it exploited the rapidly increasing complexity which arose from only a few operations. For instance, the plug board consisted of six cables each of which swapped a pair of letters around. Due to the fact that there are about ten million ways in which six pairs of letters can be chosen from twenty-six it became impossible to decipher Enigma messages by brute force.

How was the Plugboard Bipassed?

In order to successfully decipher the messages it was necessary for Turing's team to find messages which, while being different for each scrambler setting, would not be affected the exchange of the plugboard leads. The point that could be most easily exploited was the fact that the message key would be repeated twice at the beginning of each transmission. As a result of this it it was clear that the 1st and the 4th letters of each message, before encryption, would be the same, as would the 2nd and the 5th and the 3rd and the 6th. From this it could be seen that a particular letter which might be encrypted as an F initially would be encrypted as an M three letters later. If enough messages were intercepted then tables such as that shown underneath could be built up.

A B C D E F G H I J K L M O N P Q R S T U V W X Y Z 

S V N G Y P Q T E B L Z J R U D F C M O I X H K W A 

From such a table chains of letters could be created with varying numbers of links. For the example above there are three chains.

ASMJBVXKLZA (10 letters)

CNUIEYWHTORC (11 letters)

DGQFPD (5 letters)

For each scrambler setting, the number and length of the chains would be different but unaffected by the plugboard settings. Hence, all that had to be done was to compile a file of all the scrambler settings and the corresponding chains. Each day, the scrambler settings could be looked up and the day key determined.

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Ed. note: The Enigma simulator has been moved to