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This is a new dawn for spies. Only last week the US filed a lawsuit against China for alleged corporate cyber espionage, accusing Beijing of trying to gather information on its energy and metal industries. But it’s the face-off between Russian and US influence in Ukraine that is sending nations scurrying back to their Cold War habits — perhaps partly in the nostalgic hope that a new East-West standoff might dissipate threats from other corners of the new geopolitical order.

As ever, London is at the heart of the game, and MI5 is looking to reacquire its expertise in all things Russian, recruiting analysts with relevant linguistic and cultural skills as a counter to the 40-odd Russian spies thought to be operating out of the embassy in Kensington Palace Gardens, a stone’s throw from Kate and William’s abode. The UK’s close relationship with America makes London a possible back door into US intelligence and is therefore a tempting target for Vladimir Putin’s energised Federal Security Service (FSB).

It’s London’s turn to be the backdrop for fictional spying, too; the big-screen Spooks adaptation starring Game of Thrones’ Kit Harington has just started filming, with scenes being shot on Waterloo Bridge and in the City. The fourth season of hit show Homeland is going to South Africa, and the second season of The Americans — created by former CIA officer Joe Weisberg and about two Russian sleeper agents in 1980s Washington DC — has just reached its conclusion. There are spies on television, spies in the movies and, of course, spies on the internet. GCHQ, the NSA and the US Navy are all trying to recruit codebreakers quite openly through puzzles on websites, while GCHQ has started certifying Masters degrees in cyber security.

But it’s not always easy to tell if something is espionage or not. Take this mystery. It could be one of the strangest and most exigent recruitment drives ever made. It’s either terrifying or hilarious. It might be both. One competing puzzle, which originally appeared on bulletin board 4chan and then spread across internet forums and Skype channels, is in alphanumerics on a depthless black background, a throwback to the early monochrome screens from the days of dial-up — a time when email was for most people an undiscovered country.

Still, the question marks and dashes make a clear image: a picture of an insect with wings spread open. It’s just a little bit creepy, especially if you’re old enough to remember the poster campaign for The Silence of the Lambs: the moth spread over Jodie Foster’s mouth. On closer examination, though, this isn’t a moth but a cicada, and it’s the emblem of some of the most convoluted and taxing puzzles ever created. The puzzles are set by a group called Cicada 3301, which resurfaced via a post on Twitter in January — to the delight and frustration of millions — to bamboozle the world for the third year in a row. The Cicada 3301 puzzle — more a chain of interlinked puzzles drawn from a wide variety of disciplines — purports to be a recruitment tool, though no one knows for what. It could be the CIA, MI6 or the NSA (or none of these). Past solutions have embraced William Blake, transposition ciphers, Mayan numerology, The Mabinogion, Aleister Crowley, number theory and Carl Jung. They cross media boundaries, require visits to physical locations (mostly but not exclusively in the US) as well as the more obscure reaches of the internet, and no one has ever — publicly, at least — claimed to be responsible or worked out who is. Speculation is rife, wild, paranoid and infinitely varied. The truth may be out there, but it is remarkably well-hidden.

If you get to the far end of a Cicada puzzle chain, you supposedly are the sort of person the Cicada 3301 group is looking to recruit — but to what? Spying? Is this some bizarre pop-culture honeytrap created by a chess-playing Russian spymaster? Or an even more subtle Chinese Go sage — Go being the only strategy game at which a computer still stands no chance against a human? Or is it commercial: an invitation to crypto-currency banking? Or just a dining club with majestically insane entrance requirements? Is the whole thing just an enormous for-the-hell-of-it gag? Among those referenced in previous years is the late American novelist and co-creator of the Discordian movement, Robert Anton Wilson. Wilson’s books are massively involved, referencing in-jokes that mock secret societies and the paranoia of the Cold War period, and Discordianism is itself either a religion masquerading as a prank or vice versa. Would you be furious to solve the Cicada 3301 puzzle and find yourself in a pub with a small group of people who think a lot like you, read the same books, and don’t have anything in particular to say other than ‘great, you made it’? Or would that be the best outcome imaginable?

Ghosts of this kind are now a strange and somehow integral part of the internet landscape. In 2003, novelist William Gibson wrote about ‘the Footage’, a weird collection of video spots whose origin was unknown and which might or might not constitute an artwork or a coherent narrative. In the story, the absence of explanation or an identifiable single author for this compelling digital creation made the whole thing all the more intriguing. The Footage community factionalised, feuded, cooperated and investigated. What might be the point of it all? Viral self-promotion, espionage, artwork or prank? The Footage was fictional, the main thread in Gibson’s zeitgeist novel Pattern Recognition, but parts of the book feel urgently real, driven by Gibson’s remarkable instinct for the flavours of technological culture. A poem by Gibson, the text of which variously encrypted or erased itself over time, was referenced by a Cicada 3301 puzzle.

Just as shortwave radio is home to numbers stations (eerie synthesised or pre-recorded voices broadcasting strings of numbers, like something from one of the scarier episodes of Doctor Who, thought to be run by intelligence services to send instructions to agents in the field, and reported to have existed since just after the Second World War), so the internet is host to a wide variety of seemingly pointless signals that might or might not conceal something deeper. Numbers stations lend themselves to obsession, and the occasional indications of their purpose — or better, of the uses to which some numbers stations have been put, since not all of them may be there for the same reason — only increase their fascination even as they themselves become rarer, presumably superseded by other means. In 2001 the trial of the Cuban Five seemed to confirm that Cuban intelligence had used the Atención numbers station to communicate with agents on the US mainland.

Ordinary radio stations, of course, have taken to the online world enthusiastically. There’s no reason, on the face of it, why numbers stations shouldn’t do the same. Perhaps in some ways they already have — there are various digital entities with a similar mood, such as the Webdriver Torso YouTube channel: more than 77,000 videos, each 11 seconds long, and each consisting apparently of nothing more than one blue and one red rectangle on a white background. There are obvious disparities between this and the old numbers stations, which broadcast regularly for years during the Cold War; Webdriver Torso uploaded as many as 400 videos a day over the account’s busiest period at Christmas, then largely stopped, but has now started up again. It feels like a messier, noisier iteration of the same idea. YouTube is hardly as anonymous as listening to a broadcast covering hundreds of thousands of square miles; the site even lists how many people have watched each clip, and it’s not many. Hiding in a crowd of 40 is hardly worth the effort.

This seems, in fact, more like a strategy designed to catch someone’s attention. The internet as a culture has a kind of frenzied need to uncover the anonymous and share the secret. That might, of course, be the whole point — teaser ads have a long history, both online and off. Equally, Webdriver Torso could be part of the new Cicada 3301 puzzle. One of the ways in which it’s possible to transmit information secretly in the corrosively open digital environment, scrutinised at a granular level by GCHQ and the NSA, is steganography: the practice of hiding one kind of data inside another. This year’s Cicada puzzle requires the use of OutGuess, a universal steganography tool that allows users to conceal text within images. But Cicada 3301 being the kind of challenge that it is, you can’t just download and install OutGuess, you have to compile it from the source code. That’s the digital equivalent of making coq au vin by starting with a handful of grapes and an egg.

Recruitment into the security services via online puzzles sounds like something from the sillier sort of television drama, but it is a real possibility. At the same time, where we know it takes place it has a somewhat more staid and short-term flavour. Project Architeuthis, the US Navy’s open recruitment tool, was created apparently in imitation of Cicada 3301 and released through Facebook to attract the next generation of cryptographers. The NSA and GCHQ efforts are similar — dedicated single websites with puzzles on them. There’s not much theatre and certainly no mystery beyond the puzzles. They have the whisper of suited government types wanting to tell the kids that they, too, are cool — or at least, to intrigue prospective recruits with fascinating problems as a way of getting past any qualms they might have about working for The Man. Digital culture owes its ethos in large part to an oddball anarchic liberalism that flowered at MIT and Stanford during the early years of networking and was baked in at Google in the 1990s. It doesn’t on the face of it lean towards joy in serving government. Beyond that: if you were a polymath crypto-buff versed in coding, obscure philosophers, higher mathematics and runic alphabets, would you be impressed by someone who’d reach out to you via Facebook? It’s a bit like running crypto-puzzles on a daytime soap opera.

It’s worth remembering, as one peers down the rabbit hole of things like Cicada 3301, that almost anything can appear to be significant if you approach it looking for significance. The human brain is a very high- quality pattern recognition machine that occasionally gets a bit over-enthusiastic, which is why we see shapes and patterns in random static displayed on television screens, why we can’t leave the Jack the Ripper story alone, and why we experience a frisson at the suggestion of meaning in coincidental events. Combine that with the internet — a junkyard of unfinished projects, superannuated fakes and the quirky, random creations of designers and engineers — and you get a kind of madness of hypertext. The Webdriver Torso account could be no more than the testbed for a piece of automated software, its output the videographic equivalent of a Markov Chain — an apparently significant sequence of numbers appearing in a random output. Between that idea and the conviction that such artefacts are part of a grand secret network of communication lies the possibility that the individual instances are mostly meaningless, but create a fog of war that conceals a few very important streams of data from prying eyes — or that none of these things really means very much at all, but they are collectively intended to drain resources of time, money and personnel in an effort to burden those who would surveil us with an unsustainable bill. As with all conspiracy theories, the heart of it is a perverse reassurance: someone somewhere has a plan.

But that myth was exploded years ago. Whoever is behind the puzzles that populate the shadows of the internet, they’re probably no less confused than everyone else.

Nick Harkaway’s Tigerman is out now.

(Heinemann, £16.99)