Anoraks Corner
by Tony Sale

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 are entered.

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 just pressed.

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 reflector 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, million. (1.5x10^20).

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 exchange problem.

Arthur Scherbius, the inventor of Enigma, suggested that most parts of the configuration be written down and passed as a document between the communicating parties.

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.

This page was originally created by the late Tony Sale, the original curator of the Bletchley Park Museum,

Anoraks Corner by Tony Sale

Welcome to Anoraks Corner, a quick revision of the Enigma machine, its physical and operational characteristics.

1. The physical characteristics.

2. Operational characteristics.

Anoraks Corner
by Tony Sale