The Enigma Machine, one of several cryptographic devices employed by the Axis powers during World War II, sounds like it aught to be an immensely complicated device - especially when one considers the effort to which the Allied powers (Britain especially) went to crack the code.

In reality the Enigma machine was fairly simple. The central active encryption element of the machine was a collection of rotors, situated in a row. These are essentially wheels which have letters inscribed on their outside edge (think of the writing on the edge of a coin). Before use, the rotors were turned to a certain position. As an example, they might be turned to X-Z-P: The first rotor would be set to X, the second to Z, the third to P. Generally these settings were changed once or more per day, meaning anyone who was trying to guess the combination would have less messages to work with.

Around the edges of the two faces of each rotor were arranged a set of pins or contacts: If the device was designed to encrypt only letters (no numbers, punctuation, etc.) then there would be 26 of these pins, one for each of A-Z.

Inside the rotor was a certain pattern of electrical wiring, which connected a pin on one side of the rotor to a contact on the other. The most simple form would be to connect pin 1 on one side to pin 1 on the other side - the effect of this is to pass electrical current straight through the rotor as if it was not there, regardless of which pin was used. In reality, each pin was connected to an entirely different pin, so that if you passed an electrical current into the A pin, it might come out at T, for example.

To type the message into the machine, the operator used a keyboard. Each key on the keyboard was connected to a pin on a non-rotating disc, next to which the rotor was positioned - thus each pin on the non-rotating disc connects to a pin on the rotor. When a key was pressed, electrical current from that key was sent into the relevant pin on the first rotor. The current would then come out of the other side of the rotor, albeit on a different pin. The effect of this is to replace, for example, all As with Ts, Bs with Ws, Cs with Es, and so on - every letter becomes something else. Each of the output pins is connected to a lamp, so that when you press A, the T lamp would light - this is how you would know what the encrypted letter was. The operator would then write down the encrypted sequence before transmitting it via radio, or on paper. Any third party who intercepts the message cannot decrypt it unless they know the wiring pattern of the rotor.

This is enigma at its most basic, however it is not very secure as you get the same letters every time you press the same key - A always comes out as T, for example. With simple logic (such as "E is the most commonly used letter") it is not difficult to figure out the pin-mappings and crack the code.

Therefore to add additional complexity the rotor was set to rotate after every key press. This means that pressing the same key would give you a different letter every time (until the rotor had completed one entire rotation), as the current from pressing the key would be sent into a different pin.

This is now more secure, however it is still not the complete picture. To get the full enigma security, there must be multiple rotors. Initially three were used, but later on more rotors were added. By placing rotors in series, the pins and contacts on the sides of the rotors can be aligned so that electrical current passes into rotor one, comes out, goes into rotor two, and so on, until it comes out of the chain on an arbitrary pin.

Which pin it comes out of is defined entirely by what the rotors were set to when you started typing in the message. The effect of this is for the A you typed in to be translated into a T (by rotor one) then, for example from T into P by rotor two, then from P into C by rotor three.

The advantages of multiple rotors is a vastly increased number of possible combinations: With only one rotor, there is only one possible combination; A always maps to T. With two rotors (of 26 pins) A could map to one of 26^1 = 26 possible values, depending on the second rotor position. With two rotors, it can map to 26^2 = 676 possible outcomes, and so on.

Finally, to further raise the complexity of the code there is a fixed wheel at the far end of the row which serves like a reflector - it sends the signal back through the three rotors, on a different pin. The final current path is thus rotors 1, 2, 3, reflector, 3, 2, 1, and the letter may go through transformations such as

A => T, T => P, P =>C (first pass)

C => O (reflector; mapping depends on reflector internal arrangement)

O => Q, Q => L, L => J (return pass)

Thus, our initial A is encoded as a J. The first rotor (A => T) then rotates by one position, which means the entire transformation chain is updated; A no longer maps to T. After a pre-defined number of key presses (or after a full rotation of one rotor) the rotor next to it also advances, again changing the entire sequence.

It was thus almost impossibly complex to try and determine the initial settings of the machine, or the configuration of the rotors, given the state of computer technology in the 1930s-40s. Doing it by hand would have meant calculating millions of possibilities - by which time the message and cracked rotor settings would have been far out of date. By changing the rotor settings every day, or more than once a day, it was possible for the user of the Enigma to be assured that if the enemy did crack the code, they would have only been able to read messages from one 24-hour or less period.

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