San Francisco

As I drive into San Francisco to meet tech entrepreneur Brian Armstrong, reminders of the California Gold Rush pop up everywhere, from Levi Strauss to the San Francisco 49ers. Various modern gold rushes have periodically swept the area for the past few decades, and the 31-year-old Mr. Armstrong is at the forefront of the latest frenzied scramble: virtual currency.

Bitcoin is the dominant player in the field, and Mr. Armstrong, as the CEO of Coinbase, thinks he has found a rich vein to mine. He wants to be the Visa and MasterCard of Bitcoin payment processing, taking those behemoths out of the picture as merchants and customers move to virtual transactions.

Credit-card companies "collect $500 billion in fees" today, he says confidently as we meet in the company conference room overlooking San Francisco Bay. As commerce eventually turns increasingly virtual and credit-card fees drop to match cheaper technology, he says, "it's going to be $50 billion."

But wait . . . Bitcoin? A lot of people still aren't sure what a virtual currency is, much less what a "Bitcoin wallet" like Coinbase might be. Mr. Armstrong offers a working Bitcoin definition for starters: "It's a distributed digital currency. There's no central authority. It's based on a consensus of people working on this around the world. It's both a currency and a payment method and a protocol, a commonly agreed-upon language so that computers can talk to each other and exchange currency or payments, at least at first."