An ‘Argo’ moment in Ukraine’s tumult

March 20, 2014, 2:51 PM UTC

Dozens of Ukrainians are holed up in a nondescript office building on a dead-end lane in Kiev. They huddle for hours over long wooden tables, gluing scraps of paper onto bigger sheets. At first glance, it looks like a giant art project, but in fact it is a much more forensic undertaking: These volunteers are trying to piece together company records shredded by one of the country’s most controversial oligarchs — and find evidence of corruption by ousted President Viktor Yanukovych.

The scene, which Fortune observed while reporting in early March on the aftermath of Yanukovych’s ouster, is reminiscent of a plot line in the 2012 Oscar-winning movie Argo, in which Iranian children are shown piecing together shredded documents taken from the U.S. Embassy in Tehran during the hostage crisis of 1979. The frenzied effort, a true event, revealed that a group of Americans had secretly escaped the embassy building.

Kiev’s “unshredders” are a bit more sophisticated. Many are high-level professionals and journalists who have access to scanners and computers to help them re-create destroyed documents. The painstaking task is unfolding 400 miles from Russian President Vladimir Putin’s lightning takeover of the Crimean Peninsula. But activists believe that uncovering corruption is no less crucial for Ukraine’s prospects: Convicting the culprits, they say, is the only way to ensure that the country will now drastically change — even while Russian troops are massing on the border.

One target: Serhiy Kurchenko, the 28-year-old billionaire CEO of gas-trading company VETEK. Kurchenko, who reportedly fled north to Belarus and then to Russia, rocketed to billionaire status in under two years, cornering a chunk of Ukraine’s liquefied-gas market and snapping up government contracts. EU and Ukrainian officials credit his spectacular rise to close ties with the President’s inner circle.

Prosecutors suspect that Kurchenko, in turn, was a central figure in the ousted government’s web of malfeasance, acting “as Yanukovych’s cash machine,” says journalist Oleg Khomenok. Ukraine’s interim government believes that the young mogul was a key moneyman for the Yanukovych family. “He would save money, like a safe, for Yanukovych’s son,” says Yegor Soboliev, nominated to head a new government commission to probe Yanukovych officials.

Kurchenko was not shy about flaunting his wealth or his power. Among his purchases: an oil refinery in Odessa for about $300 million and a top soccer club, Metalist Kharkiv, for about the same amount. When Forbes’s Ukrainian edition ran a stinging exposé in 2012, Kurchenko responded by buying the publishing company, Ukraine Media Holding, prompting several journalists to quit. (Forbes Inc. says it is revoking Kurchenko’s license for the title.) On March 5, the EU froze Kurchenko’s assets, along with those of 16 other Yanukovych associates. And Ukraine’s new interior minister has opened multiple criminal investigations into whether Kurchenko stole $1 billion in public funds. Kurchenko, who claims to be self-made and from a poor family, has said he is “an honest Ukrainian businessman.”

When Yanukovych’s regime imploded on Feb. 22, the VETEK offices quickly emptied, and records were rammed into shredding machines. What happened next feels indeed like a scene from a Hollywood screenplay. Minutes after Kurchenko fled, a local journalist received a tip leading her to a pile of garbage bags, stuffed with shredded paper, dumped in VETEK’s parking garage. She hauled the pile away. Activists posted a plea for help on Facebook, bringing hundreds of volunteers to the suburban offices of Internews, a USAID- funded media organization, where they began the unshredding effort.

Hordes of documents fished from the lake at Yanukovych’s mansion are now in prosecutors’ hands. It is not known exactly why they have not confiscated the Kurchenko shreds, which at first glance appear to be beyond saving: Each scrap has to be pasted onto sheets of paper and then scanned into a computer. “I hope we will find information that reveals how corrupt the previous government was,” says Andriy Kovalgov, a Ukrainian management consultant, previously with Boston Consulting Group, who flew from his current job in Moscow after reading the call for help. “Without any prosecution it will be hard to prove that they were bad, and we want to find real proof.”

One bag is filled with paper that looks like confetti, possibly the work of a very fine-tooth shredder. “This is probably the most important stuff,” says IT consultant Dmitry Alybyev, shaking his head. “This is for the next generation.” He has spent days scanning sheets of glued scraps into a computer.

Indeed, it may take years to restore the documents. Just how long? That answer probably lies halfway around the world in Silicon Valley. In 2011 the Pentagon’s high-tech research body, the Defense Advanced Research Projects Agency, or DARPA, held a contest to develop unshredding software. Otávio Good, now CEO of Quest Visual in San Francisco, won the $50,000 prize. Yet it took his team 33 days to restore just five documents.

By comparison, the pile from Kurchenko’s records could contain as many as 100,000 scraps in each bag. Even so, Good believes that the interest in Ukraine’s revolution is so strong that Silicon Valley engineers could be drawn to trying to tackle the problem. “I know a million programmers around here who might be interested in helping out with something like this,” he said when I called him in San Francisco to tell him about the Kiev documents. When he heard that hundreds of Ukrainians had already volunteered to glue the shreds onto paper and scan them, he said, “That’s half the battle.”

Ukraine’s activists are prepared to wait for the technology to catch up with their revolution. They have survived months of violent demonstrations on Kiev’s Independence Square and, to their astonishment, succeeded in driving Yanukovych from power. Now they have the sense that anything is possible. “The technology will be there,” says Denys Bigus, an investigative journalist in Kiev who is overseeing the unshredding work. “It is just a question of time.” Time, plus a determination to assemble evidence of wrongdoing.

This story is from the April 7, 2014 issue of Fortune.