It sounds like a privacy breach waiting to happen: Take some of your company’s most classified information — employee records containing Social Security numbers, salaries — and put it on a bunch of remote servers that let you access the data via the public Internet.

Yet Workday, a private, venture-backed company, is successfully getting companies such as Sony Pictures and Flextronics to move their human resources software to an Internet-based system.

Workday, which last year had more than $60 million in bookings, contends it can securely lower customers’ tech costs (fewer servers to purchase and maintain) and improve efficiency (software upgrades take days, not months) by delivering complex applications and information over the Net, also known as the “cloud.”

“It cost me less than half of what I would have paid to do it in-house,” says Andy Schlei, vice president of information technology for Sony Pictures, which switched to Workday’s offering last year.

Workday’s credibility is boosted by its CEO, David Duffield, who co-founded pioneering human-resources-software firm PeopleSoft in 1987. In 2004, Oracle (ORCL) gobbled up the company after an 18-month hostile takeover battle.

Shortly after the deal closed, Duffield and co-CEO Aneel Bhusri formed Workday to essentially unseat Oracle and other enterprise-software companies, which generally require customers to install and maintain software on in-house servers.

HR software sounds dull, but it is a crucial part of any company’s operation; it tracks payroll, tax information, and other data about workers that corporations must collect. Duffield thinks Workday eventually will match PeopleSoft feature for feature. (Workday currently doesn’t offer financial management tools, for example.)

For big customers, though, Workday’s biggest shortcoming may be its business model: Tech officers at most large companies still harbor concerns about the security of cloud computing. (It’s noteworthy that while Sony Pictures has moved to Workday, the rest of Sony’s empire has not.)

Corporations maintain files on hundreds of thousands of employees and retirees, and “if you lose that data, you’re in a world of trouble,” says Josh Bersin, a human-resources-software analyst.

Lesser problems already have bedeviled Workday. The data center where the company houses its servers went down late last year, leaving customers without access to their data for several hours. (No security breaches so far.)

But the benefits of cloud computing seem to outweigh the risks. A few startups and even Oracle and SAP (SAP) have plans to develop software-as-a-service models similar to Workday’s.

Workday’s edge? Unlike incumbents that will have to retrofit software, its product has been designed from the outset as a web-based tool. That and a CEO who has done battle with the big guys before.