Enigma variations

The basic principle was of schoolboy simplicity. But the code machine had a permutation of 17,576 alphabets. The turn of a knob could create a further 17,576 and variable wiring brought the total available to five followed by 92 noughts
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It could be mistaken for an outsize laptop computer but is actually a battery-driven Enigma, the most famous military code machine. The Germans used it during the Second World War to transmit orders and strategic information, but the Poles and British cracked its secrets. Forewarned was forearmed, and the Allies not only gained invaluable day-to-day military intelligence, but were untimately able to shorten the War by two years. Their greatest coup came in 1940, when they discovered Goering and Hitler's plans for invasion.

Almost all of the 40,000 machines made have been destroyed, but their rarity makes them highly valued. Recent London auction prices have ranged from pounds 6,820 to pounds 22,000 - the one pictured was bought for pounds 12,075 at Sotheby's in September. Another was recently offered for a fiver in Brick Lane street market, east London, to a spy radio collector, who, much to his chagrin, didn't realise what it was.

As easy as ABC

Enigma was pioneered as early as 1923 by Dr Arthur Scherbius, a German engineer, and used by businesses to transmit trade secrets. The London Patent Office granted a patent in 1927, but there was little interest until the outbreak of war, when the British were given two replicas made by the Poles. Its basic principle - substituting letters of the alphabet - was of schoolboy simplicity. The machine would encode or decode letters typed on its keyboard, flashing up substitute ones on a parallel "lampboard". But the Enigma used not one alphabet but permutations of literally billions, changing with each coded letter. Between the two keyboards are three rotors each with 26 starting positions. They geared with one another, giving 26 x 26 x 26 possible settings - a permutation of 17,576 alphabets. The turn of a knob could create a further 17,576 and variable wiring brought the total available to five followed by 92 noughts.

How did the codebreakers crack it?

The weak point of the Enigma was the radio transmission of simple six- letter instructions for the daily rotor settings, such as HSB ZAH. Marian Rejewski, a Polish mathematical genius, calculated that, although there were billions of possibile alphabets, a set of just six equations enabled a codebreaker to work out which one was being used. He was unwittingly aided by lazy operators choosing banal keys such as ABC SSS, and by the idiosyncrasies of the German language. A 17-letter German word with the same letter in eighth and ninth positions and another the same in third, tenth and z16th positions was obviously Obergruppenfuhrer.

Some of Britain's finest minds were deployed around the clock as codebreakers in a collection of wooden huts in Bletchley Park, Buckinghamshire, and the site, once threatened with demolition, is now a museum.

Today's computer-coded military airwave traffic is much harder to detect, let alone decode. Messages hop from frequency to frequency, needing sophisticated beat frequency oscillators (BFOs) to capture them intact. Careless military operators have given decoders some trivial successes. Most notably, the American Air Force frequency once broadcast on 6.761 MHz a 19-letter code key including the letters HPMS. What did they mean? Clue: the date was 22 December