Despite the mystery, the whiff of scandal, and general public unfamiliarity with the concept, somebody out there is buying, and selling, not just bitcoin but dozens of other cryptocurrencies as well. The total market capitalization for these unregulated electronic forms of payment was roughly $4.04 billion as of mid-February, according to coinmarketcap.com, a website that tracks trading in alternative currencies. More than 500 altcoins, as they are also known, were represented on the site recently.

Growing global demand for...