​Benedict Cumberbatch, Alan Turing and Enigma

Germany's top-secret World War II code was called "Enigma." The Englishman who played a key role in breaking that code was very much an enigma himself. Anthony Mason this morning helps decode the decoder.

In 1939, as Nazi troops were invading Poland and threatening Europe, British intelligence secretly moved its code-breaking operation to a country estate about an hour outside of London.

At Bletchley Park, the British covertly recruited a team of the country's top cryptographers to try to crack the Germans' "Enigma" code.

Among them: a young mathematician named Alan Turing.

In the new film, "The Imitation Game" (out next month), Benedict Cumberbatch plays the mathematics prodigy who would change the course of the Second World War.

Commander Denniston: "How old are you, Mr. Turing?"
Turing: "27."
Denniston: "And how old were you when you became a fellow at Cambridge?"
Turing: "24"
Denniston: "And how old were you when you published this paper that has a title I can barely understand?"
Turing: "Uh, 23."
Denniston: "And you don't think that qualifies you as a certified prodigy?"
Turing: "Well, Newton discovered binomial theorem aged 22. Einstein wrote four papers that changed the world by the age of 26. As far as I can tell, I've barely made par."

Mason asked Cumberbatch, "That must be sort of intimidating, to try to have to put all that on the screen." "Hell, yeah it is," he replied.

To better understand Turing's work, Cumberbatch familiarized himself with the Germans' encryption device, called the Enigma Machine, on display at London's Imperial War Museum.

It was the machine that Turing was warring against. "Exactly," said Cumberbatch. "This is the enemy. The 'crooked hand of death,' as it's called in the film."

"Turing viewed this as a mathematical problem, didn't he?" asked Mason.

"Absolutely. I mean, he really did. But he also understood that to beat a machine, you had to use a machine rather than humans, because there just wasn't enough time."

What was happening at Bletchley Park was absolutely top secret, said archivist Victoria Worpole. "And in fact, everybody who worked here kept the secret for 30 years after the war."

She said the code-breaking operation was headquartered in Hut 8. It's where Turing and his team worked with captured German machines.

The Nazis set their codes on the Enigma's alphabetic keyboard: "And each time you press it, the light lights up and tells you what to write down as your ciphered text," said Worpole.

The code was reset every day, so the cryptographers had only 24 hours to crack it. The odds: One in 159 million million million.

Turing conceived of a massive machine with rotating drums that would mathematically eliminate potential codes.

"You've got a column on three verticals," said engineer Tony Jarvis. "The drums actually replicated one Enigma machine. And so what you've got are actually 36 Enigmas all looking for an answer."

It took nine months for Turing and his team to design and build a prototype.

Cumberbatch said, "That moment in the film actually gave me goosebumps. To think what it must have been like the first time it worked and stopped to give the settings for the day. I mean, just literally the hairs stood on the back of my neck, as it must have been for them. I mean, this is a 'Eureka!' moment."

Cracking the cypher allowed British intelligence to decode messages to German U-boats that had preyed on Allied shipping. It's estimated Turing's work shortened the war by two years, saving millions of lives.

Jim Hendler, professor of Computer Science at Rensselaer Polytechnic Institute in New York, has taught a course on Turing. He called Turing's work in the 1940s "stunning."

"He revolutionized cryptography, the modern field of computer science, [and] the subfield of artificial intelligence," Hendler said. "A lot of the math with those things goes right back to Turing."

"And he did it all essentially in anonymity," said Mason.

"He did it very much in anonymity, because during wartime he was working under secrecy."

Even his family's wasn't fully aware of what he was doing. Sir Dermot Turing, Alan Turing's nephew, told Mason, "For the first part of the war, the family didn't even know where he was based. All those things were completely unknown until the mid-'70s."

"Even you didn't know what he'd been doing?"

"No, no. We crowded 'round this small black-and-white TV set that we had at home in the '70s to find out, when the BBC put out a little program on it. That's how we found out!"

But by then the man who created the blueprint for the modern computer had already taken his own life.

After the war, Turing had become a world-class marathon runner. He moved to the University of Manchester to do research. But in January 1952, he was arrested and charged with "gross indecency" for having sexual relations with another man.

"When he was prosecuted, he was not in denial about it," said Dermot Turing.

"He didn't try to hide it?"

"He didn't try to hide it at all."

Turing was sentenced to probation, and required to undergo estrogen treatments, then believed to suppress homosexual desires.

"I say it could have been worse," said Dermot. "But I still think what happened to him was pretty awful."

In 1954, Turing died after eating an apple dipped in cyanide. He was 41.

It would take nearly 60 years for his reputation to be fully rehabilitated. Only last year he was finally pardoned by Queen Elizabeth.

Today at Bletchley Park -- now a museum -- Alan Turing is celebrated for what he was: a war hero, with a story like something out of a movie.

His was, said Cumberbatch, "a really epic life. A too-short epic life. Forty-one years of it. We owed him at least double that, I'd say."

To watch a trailer for "The Imitation Game," click on the video player below.

For more info:

• Bletchley Park
• Imperial War Museums
• Alan Turing: The Enigma (turing.org.uk)
• Professor Jim Hendler, Rensselaer Polytechnic Institute
• "The Imitation Game" (Official site)
• Enigma machine courtesy of Christie's Auction House. Two Enigma machines will be among a selection of rare cipher machines available at auction - exclusively online - at www.christies.com/codebreakers beginning Nov. 19.