Film explores moral and political repercussions of proving P equals NP

What would happen if one government learnt how to bypass the world's encryption systems? That's the all-too-timely question asked by Travelling Salesman, a movie that hands the starring role to a mathematical puzzle.

Its title refers to the "travelling salesman problem" -- given a list of cities and the distances between them all, what's the most efficient way that a salesman can visit them all and return home?

It's easy to check whether a given answer satisfies the criteria, but finding the best solution without trying every single possibility may be impossible. This puzzle, and others like it, are referred to as P vs NP.

In Travelling Salesman, a quartet of mathematicians solve this problem -- they find a way to shortcut the brute-force process of trying every approach, instantaneously negating the way the world's encryption systems operates. They've been hired to do their work by the United States, but they're confronted with the moral quandary of whether to hand over their research to the government or publish it publicly for the whole world's benefit. "We wanted to make a film that felt authentic to a niche group, but also ultimately would be accessible to a wide audience," said Tim Lanzone, one of the movie's creators. "The film is science fiction, but we wanted the science part to be as accurate as possible," his brother and co-writer, Andy Lanzone, added.

It's set almost entirely around a conference table in a sleek, modern, government facility. Initially the four argue over the implications of their research, before a representative of the government arrives and their argument escalates significantly. "I wanted to see if I could contain drama in one room," says Tim Lanzone. "Film school professors always warn that the hardest and most difficult scenes to shoot occur around kitchen tables."

Of course, that makes shooting it cheap, too. The film has a definite DIY aesthetic, but it's impressive what Lanzone has managed to achieve within those constraints. He opted deliberately for a cool colour temperature to make the atmosphere intense and unsettling. "Most of the drama takes place in one room, so we looked to use any sort of additional drama we could harness to our advantage."

That atmosphere is paired with fast-paced and complex dialogue -- it's not a movie that you can put on in the background. Attempts are made to explain the mathematical ideas behind the plot, but you will get more out of it if you've done a little research beforehand. The Lanzones admit this. "Understanding P vs NP directly isn't essential to enjoying the film -- especially if you have some grasp of the implications," says Tim. "We try to simplify it as well as we can during certain scenes but the pace of the dialogue is so fast that a lot of people are just along for the ride."

The movie isn't about the maths, though. Travelling Salesman is a film about power, and how it should be distributed. The government representative's job is to convince the four to sign off their parts of the solution, but it's an uphill struggle as they grapple with the repercussions of what the knowledge would mean for the world.

The bogeyman of China is brought up repeatedly, but it's fascinating to watch the film in light of recent revelations about the extent to which the US and UK's security agencies are already violating global encryption systems through back doors created in many of the world's communication networks.

The script was written long before Edward Snowden's revelations came to light, but Tim Lanzone says the topic had been on his mind for some time. "I wrote the first draft of the script back in early 2009, which in cyber-time is like an eternity. Back then, articles were really starting to come out more and more highlighting issues related to cyber-security and cyber-espionage -- particularly on important defence targets. It just seemed to be the next cold war-style battleground."

Andy Lanzone adds: "I don't know anyone that foresaw the scope of what the NSA is doing, so that was entirely coincidental. But the more general topic of cyber warfare was an interesting topic that we felt would only become more relevant over time."

The film firmly fails the Bechdel Test in that every one of the characters is white and male, limiting their perspectives considerably. The Lanzones blame this lack of diversity on budget: "We shot the film for under $25,000 and had a whirlwind casting session over two days in LA -- which was all the time we could afford," says Tim. "Knowing we only had about ten days to shoot Travelling Salesman, we were just trying to narrow it down to the five people who could most ably handle the complex language."

Ultimately, you'll get the same amount out of Travelling Salesman that you put into it. It's not a casual watch, but rewards concentration and occasionally pausing the movie and opening Wikipedia to check whether you've understood something right. If you were being cruel, you'd call it an argument for an hour and a half. But the themes and issues it addresses have never been more relevant -- the power of access to private communications, and whether it's right for that power to be concentrated under the auspices of one or a few governments. If you have strong feelings on the matter, on either side, Travelling Salesman is an essential watch.

This article was originally published by WIRED UK