Could a virtual currency created by an anonymous Internet hacker someday replace the U.S. dollar? What seems like a ridiculous question has become more intriguing as trading in the digital money called Bitcoin has surged more than 300% in the past year to roughly 60,000 transactions per day.

Gavin Andresen, the 46-year-old lead software developer for the Bitcoin project, is eager to find the answer. "I'm hoping to learn," he says, whether "a nongovernmental global currency" is possible. "Can you get...