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Police said the thief is thought to have carried the cipher machine, which looks like a large typewriter, out of the museum in broad daylight, on a day when the building was open to the public.
It is one of only three such machines in the world, and its value is estimated at more than £100,000.
Christine Large, the director of the Bletchley Park Trust, said, "This particular one was extra special because it was used by the German SS and was made to a higher standard than the ones which were used in the field. We can only hope we get it back."
Stolen to order
It's thought the machine may have been stolen to order. It is thought more than one person may have been involved in a carefully-planned operation.
The machine was secured in a glass cabinet which had not been broken. There was an alarm system in operation as well as volunteers watching over the collections.
The theft comes just a week before a new security system was to be installed.
Bletchley Park, a stately home in 50 acres of grounds, was known as Station X during the war. There, British agents succeeded in cracking the Enigma code - a cipher with 150 million million million possible combinations which the Germans thought was unbreakable.
By 1945 there were 10,000 mathematicians, linguists and chess champions working there, decoding up to 18,000 messages a day.
The methods they used - inventing machines which ran through large numbers of possible positions in a short period of time - meant the work at Bletchley Park paved the way for the invention of the modern computer.
Their work is said to have shortened the war by several years. Winston Churchill referred to the staff as "the geese that laid the golden eggs, and never cackled".
Station X was a secret until 1967, but is now a popular tourist attraction.
The machine's whereabouts remained a mystery until in September 2000, police began receiving letters from a man saying he was acting on behalf of someone who had bought it. The letter writer demanded £25,000 for its safe return.
The museum agreed to pay the money, but a 6 October deadline was not met.
Two weeks later, BBC television presenter Jeremy Paxman opened a parcel at his office at Television Centre, London. It contained the missing Enigma machine.
No ransom was paid. The machine was missing three of its four encryption rotor wheels, but they were later also returned safely.
Police arrested antiques dealer Dennis Yates in November 2000. The 58-year-old from Derbyshire admitted sending the letters to the police, and sending the Enigma machine to Jeremy Paxman. He was jailed for 10 months.
During his trial the court heard he had become involved in events which spiralled out of his control.
He had received death threats from those he was working for, and has never named the mystery buyer to police.
Those who carried out the theft have never been caught.
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