Thursday, May 13, 2010

The Enigma Machine

The Enigma Machine

Invented by Arthur Scherbius in 1918 the Enigma machine is a very ingenious way of achieving seven alphabet substitutions between a text input letter and a ciphered output letter. The alphabetic substitutions are implemented via wiring inside rotors.

Enigma rotors (or wheels)

Before seeing how the Enigma machine was constructed you should see the rotors or wheels which embodied the alphabetic substitutions.

Figure 4: details of an Enigma rotor:
(1) The finger notches used to turn the rotors to a start position.
(2) The alphabet RING or tyre round the circumference of the rotor (see below for an explanation of its significance).
(3) The shaft upon which the rotors turn.
(4) The catch which locks the alphabet ring to the core (5).
(5) The CORE containing the cross-wiring between contacts (6) and discs (7). It is the core which effects the essential alphabetic substitution.
(6) The spring loaded contacts to make contact with the next rotor.
(7) The discs embedded into the core to make contact with the spring-loaded contacts in the next rotor.
(8) The CARRY notch attached to the alphabet ring (see below for explanation).

These rotors were manufactured with their wirings buried inside and they could not be modified in use.
In the 1930s, the Enigma had only three different kinds of rotor, I II and III. These rotors could be assembled on the shaft in any order giving 6 (i.e. 3x2x1) possible configurations.
In 1938 the Germans added rotors IV and V to the repertoire, thus giving 60 (i.e. 5x4x3) configurations by choosing a set of three rotors from the five. Some further wheels were brought into use during the course of the war but basically the rotors remained unchanged throughout.

The Military Enigma Machines

We are now ready to see the machine actually used by the German armed forces, and to go on to the further complications introduced through the ring-setting and the plugboard or Steckerverbindung.

You can readily see three rotors in place. In operation, a current flowed from right to left then back left to right, so the reflector is at the left and the entry disc is at the right.
The entry disc is a fixed disc of 26 contacts. The keyboard contacts are connected to the right hand side. The left hand side of the entry disc has metal contact discs just like the wheel discs. A curious aspect of the Enigma design was that the keyboard was connected to the entry disc in the simple order ABCDEF... and did not take advantage of the opportunity for introducing a further scrambling.
As explained above, it is important that the rotors are interchangeable. Mechanically, this is effected as follows. When the release lever is pulled forward, the reflector slides to the left and the group of three rotors can be taken out on their shaft. Then the operator can assemble a new sequence of rotors on the shaft, and put this back into the machine.
The lamp panel shows the enciphered output letter for the keyboard key pressed. This was rather a primitive aspect of the Enigma as it relied on the operator to observe and write down the lit-up letter at each stage of encipherment and decipherment.

The plugboard

The plugboard or 'Stecker', visible on the front of the machine, was the most important addition made to the basic Enigma when turning it into a machine for military use. The operator simply inserted plugs so as to connect pairs of letters (generally 10 pairs, in wartime use) and this had the effect of hard-wiring such a swapping.Because the plugboard affected both the incoming current from the keyboard and the outgoing current to the lamps. it left unchanged the reciprocal property of the Enigma. It also meant that the military Enigma still had the property that no letter could ever be enciphered to itself. This was a very grave mistake in the design.
To see how this worked in more detail, it is best to forget the physical picture of the Enigma and concentrate on a logical diagram of how the electrical current effected substitutions:

Circuit Diagram of the Enigma with Plugboard

The keyboard was laid out as follows:

The same arrangement was used for the lamp panel and the plugboard.

In this illustration, when key W is pressed on the keyboard (5) current from the battery (4) flows to the plugboard panel socket W, but socket W has been plugged to socket X so current flows up to the entry disc (E) at point X.
The current then flows through the internal wiring in the rotors (2) to the reflector (1). Here it is turned round and flows back through the rotors in the reverse direction emerging from the entry disc at terminal H. Terminal H on the Entry disc is connected to socket H on the plugboard (6) but this socket is plugged to socket I so finally the current flows to lamp I which lights up.
Thus in this instance, the letter W is enciphered to I.

You can now also see that if the key I had been pressed, the lamp W would have lit up. This is because the path from W to I through the steckers and rotors remains the same, though with the current flowing in the opposite direction.
When the W key is pressed the connection to the W lamp is broken and the I lamp lights. If the I key is now pressed down the connection to the I lamp is broken and the W lamp lights.

The motion of the rotors

Now you will recall from our introduction that the whole point of the rotors is that they must rotate, so that every time a letter is enciphered, the machine is in a different configuration. So, when a key on the keyboard is pressed down, a mechanical linkage causes the right hand rotor to turn by 1/26 of a revolution, i.e. by one letter on the alphabet ring.This means that the next time a key is pressed, the substitution effected by the rotors is quite different.
At certain points on the rotation of the right hand rotor, the motion is 'carried' to the middle rotor, M which then moves on one letter. Carry will also occur from the middle to the left hand rotor when the carry notch engages, but obviously this will happen much less often.

The Enigma sent the current through the wires AFTER the mechanical linkage had moved the right-hand wheel and any other wheels knocked on by the carry mechanism. The principle is just the same as the 'carry' on an adding machine knocking on to tens, hundreds and thousands, but there is a subtlety in the design affecting the point at which the knocking-on occurred.
To appreciate this we must first describe the alphabet RING settings.

The ring setting

Referring again to figure 4, not that on each rotor there is a spring loaded catch (4). When this is pulled to the right the ring (or tyre) can be turned with respect to the core of the rotor. In fact the ring for each rotor can be set by the operator in any one of 26 possible settings.The effect of this is that the core which contains the wiring, is turned in relation to the letter showing in the window of the Enigma machine.
At first sight this extra complication might seem rather pointless because it did not change anything to do with the essential scrambling going on inside the system. However the indicator systems, to which we will come later, depended on describing the 'window position' of the rotor, and the ring-setting determined the relationship between the window letters and the actual scramblings. Furthermore, the carry mechanism is affected by the ring setting. The 'carry' point is in fact determined by the position of the carry notch (8) in figure 4, and the crucial point is that this notch is attached to the alphabet RING, and not to the core of the rotor.
The carry notch was arranged to be in a different position for each of the rotors I, II, III, IV, V. This turned out to be a bad cryptographic mistake; it helped first the Poles and then the British analysts at Bletchley Park to identify the right hand rotor in use.


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