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How messages were sent in practice

Before we can understand how Enigma was broken, we need to appreciate the details of how messages were sent in practice.
An old radio room
© University of York

Before we can understand how Enigma was broken, we need to appreciate the details of how messages were sent in practice.

Before 15 Sept 1938 the operator set the machine according to the settings given in the keybook for that day. He then chose three random letters (called the message indicator) which he encoded twice, yielding six ciphertext letters. He then reset the machine (by turning the rotors) so his message indicator were the letters that appeared on the top of the rotors. (Essentially, this is like the operator making a random choice for the Ground Setting for each message.) With this setting, he encrypted the actual message he wished to send. Finally he sent, via Morse code, first the six letters followed by the enciphered message.

Example

Suppose that the settings for the day are as follows:

  • Rotors: III (slow) I (middle) II (fast)
  • Plugboard: CD GI HZ OX PT RY
  • Ground setting: YRK (this is the position of the rotors for the first key press)

The machine is set up, and the operator randomly chooses the message indicator QQQ. He typed this into the machine, and obtained MFK FXT. He then reset the rotors to show QQQ, and types in the plaintext HELLO THERE obtaining UPGFSMERGZ.

He broadcasts MFK FXT UPGFSMERGZ. (Technically, it would be sent as MFKFX TUPGF SMERG Z as everything was broadcast in five-letter bursts).

To decode the message, the receiver would have his Enigma machine set up to the daily settings, including the rotors in the Ground Setting position. He types in the first six letters of the ciphertext, and notes down the repeated three letters that come out (this will be the decrypted message indicator). He then resets the rotors to those three letters, and then types in the rest of the ciphertext, yielding the plaintext.

In the example above, the receiver has his Enigma set up using the same global setting for the day that the first operator used (in particular the rotor settings are in position YRK). He types in the first six letters MFK FXT and obtains QQQ QQQ. He then resets the machine so the rotors show QQQ, and types in the rest of the message, obtaining the correct plaintext.

This repetition of the message indicator turned out to be a major flaw, which we will discuss later.

Note also that the message indicator, which was meant to be random, in this example is QQQ – not very random! Some operators were very bad at choosing random letters, some using repeated letters (like QQQ), some using keyboard-based patterns of letters (like QWE), and some repeatedly using the same letters (for example, their girlfriend’s initials – this actually happened!).

Although not important at this point, since mathematics doesn’t care about poor choices of message indicators, it’s worth noting that there were times in the War where exploiting known poor practices helped the Allies continue to read messages even when they would otherwise have been locked out.

© University of York
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The Mathematics of Cryptography: From Ancient Rome to a Quantum Future

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