The British actor, who stars in Kathryn Bigelow's political thriller with Oscar nominee Jessica Chastain, admitted he had to keep logging on to read the screenplay because it would often time itself out after a few minutes.
"I didn't get the script until later. When I did get the script, it came to me via my computer. It was a special system whereby you had to apply for permission to read the script on the computer, and if the system didn't detect after two minutes that you were turning pages, it went blurry and you had to reapply," he deadpanned.
"I had to do it often," he added.
Mark - who has starred in Kick-Ass, Robin Hood and Tinker Tailor Soldier Spy - understood the huge amount of privacy surrounding the project.
"The secrecy was paramount with good reason. They wanted to make sure they were writing things that were accurate and all the furore that has blown up as a result recently just goes to show that they were right in keeping a lid on everything while they were making it," he explained.
The 49-year-old actor said he wishes co-star Jessica "all the best" for an Oscar win, but admitted it's not strange that Kathryn was snubbed for a best director nomination.
"I don't think it's as sinister as it seems because Tom Hooper, who directed Les Miserables, is also not nominated and yet the film is very good," he said. "I think what's probably happened there is that voters think, 'Well, they've just recently won best director'. I vote on Bafta myself so I'll sometimes juggle nominations."