Welcome to Anoraks Corner, a quick revision of the Enigma machine, its
physical and operational characteristics.
1. The physical characteristics.
The Enigma machine is an electro/mechanical way of achieving a seven, or nine,
layer substitution cipher. The individual substitutions are fixed by wiring
within wheels which can be rotated by the operator but which also index
round, like a car miles indicator, as letters to be enciphered or deciphered
The Enigma was patented in 1918 by Arthur Scherbius in Berlin, developed
by him as a commercial product and shown to the public in 1922.
Because the machine could be bought by anyone, the security of the cipher
depended not on the machine itself but on the vast number of ways in which it
could be configured before the start of an encipherment.
To increase the complexity of this setting up, each wheel has a tyre, or ring,
round the core containing the cross wiring. Letters or numbers on the surface
of this ring appear in the windows above each wheel. The ring can
be rotated around the core and set by the operator before encipherement
begins. It remains set throughout the message input.
The action of pressing a key causes the right hand wheel to index one position,
(one of 26). At some point this rotation is transfered to the next wheel on the left.
This is known as a carry and is caused by a slot, the carry slot, coming
into line with the indexing pawls. This carry slot was initially on the wheels,
later it was moved to the ring and in fact was there for most of WW II.
An electrical current is used to sense the substitutions. When a key is
pressed a connection is made from the battery to a point on the fixed entry disc
on the right hand side of the wheels, AFTER the right hand wheel has
indexed and any carry has caused other wheels to turn..
The electrical current flows through the internal wiring in the wheels
from right to left, is turned round in the reflector and comes back through
the wheels to exit at a different point on the entry disc which is connected to a
lamp on the lamp panel. The lamp that lights is the encipherement of the key
Thus the variable elements of the Enigma are; the wheels and their order
from left to right in the machine, the ring setting for each wheel, the
wheel rotational position, the start position, before encipherment starts.
The first Enigma machines, the glow lamp machines of the 1920's had three
wheels which could be removed and replaced in any order. (6 combinations).
The relector was rotatable by the operator (26 positions). The wheel
start positions gave 26x26x26 positions. The ring settings gave a 26
position rotational translation of each wheel start position.
Total number of different configurations, 2,741,856.
From 1930 the plug board (stecker) was added to the Enigma used by the
German Army and Air Force. At the same time the reflector became fixed.
This machine was then also adopted by the German Navy.
The plug board enabled pairs of letters to be completly transposed.
Initially 6 pairs were transposed, later this was increased to 10, the
nearly optimum number.
For this Enigma the wheels give 6x26x26x26 = 105,456. Six plug pairs
gives 100,391,791,500 possibilities;
total approximately one thousand, million, million. (10^17)
ten plug pairs gives 15, million, million, million. (1.5x10^19)
In 1938 two more wheels were introduced giving 60 for the three wheel
selection, raising the ten plug pairs total to 150, million, million,
Then the German Navy first added wheels 6,7 and 8 giving 336 wheel
combinations then introduced the fourth wheel, rotatable but not indexed.
So the Naval 4 wheeler (M4) had 123,543,936 combinations on the wheels plus
the ten plug pairs giving 1.8 thousand, million, million, million. (1.8x10^22).
These are very big search spaces, even with modern computers, so exhaustive
search was definitely not an attack option in the 1940s.
The Enigma machine is also reciprocal. From any configuration a key
pressed lights a lamp. From precisely the same configuration, if the key
corresponding to the lamp is pressed, then the lamp corresponding to
the first key pressed, lights up. This also means that the Enigma machine
can be used both for enciphering and deciphering from the same start
configuration without having to have a changeover switch between the two
modes of working, a big operational advantage. The downside of this is that
no letter can encipher to itself, a cryptographic weakness.
2. Operational characteristics.
In order to encipher a message, send the enciphered text by Morse code,
recieve the text and then decipher it on another Enigma machine, both
Enigmas had to be configured to exactly the same start points. Problem;
how to tell the intended recipient this setting without it being discovered
by an interceptor of the cipher text, in modern cryptography the key
Arthur Scherbius, the inventor of Enigma, suggested that most parts of
the configuration be written down and passed as a document between the
He proposed that the written document, the setting sheet, should
contain; the wheel order, the ring settings and later the plug pairs.
These were to form the core settings and remain in force for 24 hours.
That left the actual wheel positions from which encipherment or decipherment
would start. This would be chosen by the operator and would be different for
each message. Problem; how to tell the intended recipient this without
it being discovered by an interceptor.
Scherbius suggested enciphering
this start position, the message key, on the Enigma machine itself, but for
this to work both ends had to have a known wheel start position from
which this encipherment and decipherment of the message key could proceed.
Initially this position, known as the indicator, was printed onto the
setting sheet and remained in force for 24 hours like the core settings.
Later, in 1938, the indicator triplet of letters, was, like the message key, chosen by
the operator, different for each message. Now the indicator was sent in
clear in the message header.