It is a riddle wrapped in a mystery inside an Enigma. Who stole a rare version of the machine that the Germans used to encrypt military secrets during the Second World War? And does an anonymous note contain a coded clue to the thief's identity?

The ‘Enigma machine’ was stolen in April from Bletchley Park Museum in Buckinghamshire. During the war, Bletchley Park was home to a team of mathematicians and cryptographers who worked on cracking coded German military communications.

In the past weeks the museum has received two strangely worded, anonymous letters offering to return the machine for a five-figure sum. The first starts: “I have been asked by the current owner the above Enigma machine, who purchased it in good faith (in good faith being the operative words) to say and tell you now today, the unwitting person have no desire of depraving [ sic] your august self or any one the pleasure to see it again.” It was sent from the Midlands of England, and appears to have been written on a typewriter dating from the Second World War.

The museum's chief executive, Christine Large, says the episode has “an element of mystique which is completely in keeping with the history of the park. It is an unusual letter but seems genuine. It doesn't surprise me that the author is a middleman. We really want to assure them that our priority remains getting [the machine] back in good condition.”

The museum is now waiting for the next contact. “We have made it very clear that, assuming there is no criminality involved, that police will not prosecute,” says Large. The machine was on long-term loan from the Government Communications Headquarters in Cheltenham, which acquired it after the war.

There are several hundred Enigma machines on the market. But the stolen one, which carries the serial code G 312, is a very rare four-rotor machine used by the Abwehr German military intelligence. The only other known example is owned by the US National Security Agency.

Bletchley Park became the home to the UK Government Code and Cypher School in 1939; the teams that worked to crack the Enigma machines were housed in wooden huts. The Germans updated the machines over the years, but a series of breakthroughs by cryptographers meant that German messages could be decoded for much of the war.

The Buckinghamshire police say the letters are their best lead so far. The first letter ends in a word — which is not being released by police — that some have suggested may be in code. But Large says that the word is recognizable, although not English. The machine featured in an Interpol ‘wanted’ poster in June, but the police say they have no evidence that it has left the country.