Three amateur code-breakers have almost proven a match for the country's top experts after winning the intelligence agency's Christmas card challenge.
GCHQ released a cryptographic festive brainteaser in December, challenging entrants to try to crack the code.
More than 600,000 people completed the first stage, but the winners, all men, worked their way through five rounds to come closest to success. Around 30,000 people reached the final stage, with 550 submitting answers.
David McBryan, 41, from Dublin, Wim Hulpia, 40, from Belgium and American-born Kelley Kirklin, 54, who lives in London, will each receive a GCHQ paperweight, pen and signed copy of the book Alan Turing Decoded, written by his nephew Dermot Turing.
Mr McBryan, who now lives in Edinburgh, said: "I thought I had solved it, but a news report came out a few days ago saying nobody had...so I went back and had another look and figured out what I missed, but I was too late at that point.
"It was challenging - a very well-constructed set of puzzles, I'd recommend it to anyone actually. It's enjoyable but it's tough."
Mr McBryan, a former Fifteen to One game show winner who now writes questions for the show, studied maths and artificial intelligence at university.
The compendium of word and number puzzles took a team of eight GCHQ cryptographers two months to compile, and included a mix of past and fresh challenges - with plenty of hidden material.
The initial grid-shading exercise revealed a scannable QR code to direct people to the next part. Puzzlers were then tested on their analytical prowess and knowledge of phonetics, semaphore, French, snooker and The Lord of the Rings, among other things.
"For a long time after I got all the solutions I was still looking for more because you've got no idea if you've got it all," said Mr McBryan.
Of the 550 answers to the final stage, six were considered "complete" by the team of cryptographers, who chose the final three winners based on the quality of their reasoning.
One of its cryptographers, whose identity cannot be revealed, said the team initially worried it would be too hard but added it was "very gratifying" that people had got so far.