'He was an amazing human being who is finally, rightfully, getting recognition for the great advances he made," Benedict Cumberbatch says about Alan Turing, the British mathematician, logician, cryptanalyst, and computer pioneer who led the team of code-breakers responsible for cracking Nazi Germany's daunting Enigma machine.

Cumberbatch, of course, is playing no small part in seeing to it that Turing gets his due: In The Imitation Game, opening Christmas Day at area theaters, the actor is Turing - a deeply complicated figure whose breakthroughs at Bletchley Park, the top-secret intelligence enclave set up in 1939 in Buckinghamshire, are credited with bringing World War II to a speedier end, thus saving hundreds of thousands of lives.

Turing's arrest and trial in 1952 for committing homosexual acts - a crime in Great Britain until the repeal of the law in 1967 - supply the sad coda to the film. A man who should have been a national hero was, instead, disgraced. Turing pleaded guilty, albeit defiantly, to the charges, and the court gave him the choice of prison or a hormonal treatment akin to chemical castration. He chose the latter.

Two years later, he was dead, a suicide.

"Poisoned, in his own bed, with a bite taken out of an apple dusted with cyanide," Cumberbatch says. "It's devastating. It really makes you ashamed of a country . . . to do that to a man who was so instrumental in shortening the war. . . . It wasn't just him, obviously. It was a massive team of brilliant men - and women - at Bletchley Park. But he was at the forefront. Alan came up with ideas that nobody could possibly have thought of. He linked mechanics with numbers with logic in a way that truly was revolutionary."

One of those brilliant women was Joan Clarke, a cryptanalyst whom Turing recruited and who worked with him in "Hut 8," Bletchley's code and cipher section. In The Imitation Game, she is portrayed by Keira Knightley.

Last week, Cumberbatch was nominated for a best actor Golden Globe and Knightley for supporting actress for their work in the film. Expect them to be similarly kudoed when Academy Award nominations are announced next month.

"They were both very much misfits," Knightley said of Clarke and Turing in an interview at the Toronto International Film Festival in September. "She figured out how to play the game better than he had. But actually, they were both coming at things from the same place."

That is, Clarke was confronted with deep-seated societal prejudices, too. She was a woman in a world of men, hired on at Bletchley at a secretary's salary despite her university degree and her genius for numbers. In The Imitation Game, and in life, Clarke and Turing became close friends. For a short time, they were even engaged to be married. The proposal scene begins, brilliantly, with Knightley's Clarke calling out Turing as a "fragile narcissist," and then, some storm-tossed minutes later, accepting his proposal.

"It's quite interesting to think that you are telling a story from the Second World War," Knightley mused, "and yet how relevant it feels, unfortunately, today. They were both facing sexism, prejudice - the feminist angle with her, gay rights for him. Both causes have made huge advances since the '40s, the '50s. But they are still an issue.

"It's always important to keep those conversations going. And really, I think, that's what this film is about. You have to embrace people's differences."

The Imitation Game screenplay covers three key periods of Turing's life: his adolescence, when he fell in love with a fellow schoolboy (Alex Lawther is the young Turing); the time at Bletchley Park, working feverishly to decipher the Enigma missives and bonding with Clarke; and the early 1950s in Manchester, where Turing was a math professor, his wartime accomplishments still classified, caught in an "indecent" act.

Graham Moore's script was one of the top titles on Hollywood's "Black List" of unproduced screenplays three years ago. The Weinstein Co. bought it in 2012 and found an unlikely candidate to direct: Morten Tyldum, a Norwegian whose crime thriller, Headhunters, a Nordic noir based on a book by Jo Nesbø, had caught Hollywood's notice.

Tyldum's attention was, in turn, drawn to Moore's script.

"It was a balancing act, this movie," said Tyldum, also on hand at the Toronto Film Fest. "You could make so many movies out of this material. You could make a pure war thriller: the race to breaking Enigma . . . . And then it's a spy thriller, because they had this [German] spy at Bletchley Park. . . . And then there are these two love stories: the young Alan Turing who meets [the classmate] Christopher, who means everything for him, and then meeting Joan Clarke. And then, in many ways, it's a gay rights movie."

So, to find his way in, Tyldum decided to view the story of Turing as a mystery.

"Who is this man?" he asked. "To find out, we started to put all the pieces together."