Google's ( GOOG) quest to organize all of the world's information is running into opposition on the desktop, where the company hopes to make inroads against Microsoft ( MSFT).

At issue is a feature in Google's Desktop Search that lets people search for data on more than one computer. This requires information to be stored on the Mountain View, Calif., company's servers. Tech research firm Gartner has urged large companies not to use the service for security reasons.

"Google promises that this information will be encrypted and accessible to only a small set of Google employees who will not peruse it," Gartner says in a recent report. "Nevertheless, Gartner believes that its mere transportation outside the enterprise will represent an unacceptable security risk."

Though Google says it takes steps to safeguard data that it keeps for as long as 30 days, those assurances may not be enough to allay the concerns of large companies. Sometimes, companies are required to ensure that customers' data are never out of their jurisdiction.

"There are laws and policies that this subverts," says Whit Andrews, a research vice president at Gartner, in an interview. "Whether or not Google maintains security is not relevant to a large number of chief information officers ."

Google says it's mindful of concerns about security on Google Desktop Search. Individual users must personally activate the multicomputer search feature, which serves as a layer of security.

In a recent blog posting, Google's Enterprise team writes, "We understand that a company's data is more precious than gold -- and you don't go passing your gold around."

The company agrees with Gartner's conclusion that firms that let employees use Google Desktop Search should switch to the version for large companies and restrict its use.

Experts say having the ability to search more than one computer may increase efforts by the government to collect information from the search-engine giant, which is fighting a federal subpoena seeking data to uphold a law against child pornography.

"Clearly, the government has an interest in some of the information that Google is amassing," says Sarah Scalet, senior editor at CSO magazine. "To the best of my knowledge, Google is the first offering desk across computers."

The Electronic Freedom Foundation, an advocacy group, has also criticized the multicomputer search feature, saying that it increases the possibility that people's privacy rights will be compromised. The group is urging a boycott of Google because of the feature.

Concern over desktop search isn't limited to Google. Both Yahoo! ( YHOO) and Microsoft's MSN networks are testing similar features.

The desktop is of keen interest to Google. Though search advertising continues to explode in popularity, it's showing signs of maturity. Earlier this month, Google CEO Eric Schmidt told investors stunned by CFO George Reyes' comments about slowing growth that the company's prospects were as strong as ever.

Schmidt, who doesn't give investors much in the way of specific information, emphatically stated that Google considers Microsoft to be its most formidable competitor, even though the Redmond, Wash., company is far behind it in the search market.

"Clearly, with their efforts around search intensifying, it behooves Google to do what it can to ensure that it is and remains on the desktop," says Scott Kessler, an analyst with Standard & Poor's who rates Google a hold and doesn't rate Microsoft.

For its part, Microsoft is just as leery of Google's move onto its turf.

"There is a concern that Google will cherry-pick key operating-system features and get an increasing amount of revenue from Microsoft's customer base while making Microsoft's platform less secure and less reliable," says Rob Enderle, an independent technology analyst based in San Jose, Calif. He says the effect of that trend is to reduce Mister Softee's profit "while increasing Microsoft's support costs."