Tyler and Cameron Winklevoss, made famous for their tussles with Facebook Inc. Chief Executive Officer Mark Zuckerberg in the social network’s early years, are seeking investors interested in the online currency Bitcoin.

The Winklevoss Bitcoin Trust is offering 1 million shares with the objective of tracking the performance of the average price of Bitcoins, according to a filing yesterday with the U.S. Securities and Exchange Commission. Math-Based Asset Services LLC, which lists Cameron Winklevoss as CEO and Tyler Winklevoss as chief financial officer, sponsors the fund, the filing said.

Bitcoin is a virtual currency that can be used to buy and sell a broad range of items, from electronics to illegal narcotics. Created four years ago by a person or group using the name Satoshi Nakamoto, the value of Bitcoins has varied widely, reaching a high of $266 in the second quarter and a low of $45, according to the filing. The trust aims to attract investors who might be put off by the complexities and costs associated with trading in the digital currency.

“The shares are intended to provide institutional and retail investors with a simple and cost-efficient means, with minimal credit risk and using the trust’s proprietary security measures, of gaining investment benefits similar to those of directly holding Bitcoins,” the filing said.

Bitcoins are “mined” by computers that solve difficult cryptographic problems to verify transactions. As more Bitcoins are created, the computing challenges become more difficult. While early Bitcoin enthusiasts could mine coins on laptops, high-powered computer equipment is now necessary.

The Winklevoss brothers became well-known in 2010 for their portrayal in the movie “The Social Network,” which depicted their clashes with Zuckerberg over the originator of the idea for Facebook, which has grown to more than 1 billion users.