This explains how the Enigma was used in German military practice,
and outlining the problem facing anyone trying to break the system.
The Message Key and Setting Sheets
The message key which was the complete and exact configuration of the
machine in its starting position, had to be conveyed to the intended recipient
of the message.
The Germans, following Scherbius's original suggestions, decided to specify
exactly everything except the rotor start position for each 24-hour period. This
was achieved by pre-printing setting sheets — a month's settings on one sheet,
which was distributed by courier.
| Geheim! Secret indeed! This is an example
of the setting sheets used:
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The sheet shows a line of entries for each day in the month.
On the top line, the day 31 is followed by the rotor order for assembling the
rotors on their shaft, in this case: I V III.
The next three numbers are the ring settings. The setting sheets says that
the ring on the left hand rotor should be turned until 6 (letter F) is by the
catch, 20 (letter T) on the middle rotor and 24 (letter X) on the right hand
rotor.
Next come the Steckerverbindungen or plug connections. There are ten
pairs of letters and the two-pin plugs at each end of a piece of wire are
plugged into the letter sockets given, i.e. U to A, and so on.
For the moment we can ignore the last section (the Kenngruppe) which
was used in various different ways at different times by the German armed
forces.
Both sender and intended receiver have identical copies of the setting sheet
and so both can put their machines into exactly the same 'base position' for a
given 24-hour period.
Now what remains is for the sender to choose, and then
convey to the recipient, a rotor start position. The principle was that this
should be a different start position for every message sent.
The method for
this was to use the Enigma machine itself to encipher this crucial part of the
message key.
There were different systems used by different forces at
different times, but we will describe the simple system used before the war by
the German Army and Air Force.
First, with the machine in the base configuration, the rotors were turned to
a start position selected by the operator but sent in clear in the message
preamble. Then the operator keyed in one after another the three letters
actually to be used for the start of the message.
The lamps that lit (the
encipherment) were then also sent in the message preamble.
But the Germans made a bad mistake in devising this system. They required the
operator to key in the message key letters twice in succession and
transmit the six letters that resulted. This was a primitive form of
error-correcting code, ensuring that this vital message key arrived correctly,
despite possibly bad radio connections.
But it meant transmitting redundant information, and this mistake gave the
Polish analysts their great success in the period just before the outbreak of
war.
Sending and receiving a message using the simple Enigma indicator
system
To send a message:
- Set the Enigma machine into the base configuration for the day as
given in the setting sheet for the month.
- Select a three letter start position, (the indicator), from which to
encipher the selected three letter message key.
- Turn the rotors to the indicator position, key in the message key,
twice, and note down the lamps that light.
- Turn the rotors to the message key letters and key in the message to
be sent, noting down the lamps as they light.
- Give the enciphered message plus its preamble to the radio operator
for it to be transmitted by Morse code.
On receiving a message:
- Set the Enigma machine into the same base configuration for the day
from the setting sheet.
- Turn the rotors to the indicator letters received in the preamble to
the message.
- Key in the next six letters to reveal the repeated message key as
the lamps light.
- Turn the rotors to the message key letters. Key in and decrypt the
cipher text.
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The complexity of the Enigma machine
As mentioned at the start, it
is assumed that the interceptor has an Enigma machine. The protection against
decryption then depends on the number of setting combinations that have to be
tried in order to decipher a message.
The basic 3-rotor Enigma has 26x26x26 = 17,576 possible rotor states for each
of 6 wheel orders giving 6x17,576 = 105,456 machine states.
For each of these the plugboard (with ten pairs of letters connected) can be
in 150,738,274,937,250 possible states.
The total number of combinations is thus (even for the simplest military
Enigma) of the order of 15,000,000,000,000,000,000, and then there is the
ring-setting complication on top of this.
The task facing anyone trying to decipher a particular message is to find
which one of these 15 billion billion settings has been used.
The Germans considered the task to be impossible, and certainly even a modern
computer might take a year to work through this number of machine settings, if
it simply tried them out in turn.
However we have already noticed how there are a colossal number of alphabetic
substitutions but nevertheless you can solve simple cryptograms by using such
facts as that E is the most common letter, which eliminate huge numbers of
possibilities at once.
So the size of the possible message-key space is not the only consideration.
We shall continue in future pages to show how first the Polish
mathematicians and then the codebreakers in Bletchley Park achieved the
apparently impossible. To be continued.......
REFERENCES