Foreign firms win big from NSA spying

"Data is being courted by overseas cloud providers, so this is clearly hurting U.S. cloud providers," said Elad Yoran, chairman and CEO of Valutive, a cloud security solutions company. "Many places around the world are seeing this as an opportunity."

Another factor likely to accelerate the trend: Countries like Brazil and Germany are strengthening their data residency laws, which force companies to keep their data stored locally. In other words, if a company wants to store data in the cloud, it needs to do so on servers in the country in question.

A recent survey of 1,000 information and communications technology decision-makers from France, Germany, Hong Kong, the UK and the U.S. revealed that many businesses are in fact aggressively changing the way they store their data.

According to the survey, which was carried out by NTT Communications, 90 percent of respondents had changed the way they use the cloud and 16 percent had delayed or canceled contracts with cloud service providers.

"This is a big deal. It's a terrible problem being foisted on companies. And it's the Achilles' heel of cloud computing. It forces them to replicate their infrastructure around the world in the countries that are implementing these laws," Yoran said.

"The U.S. had such a strong position which is being in effect weakened by the proliferation of these laws and creates an opening for global competitors to get into the cloud market at the expense of business that would have otherwise gone to the U.S."

By CNBC's Cadie Thompson. Follow her on Twitter @CadieThompson.

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Foreign firms win big from NSA spying