Agaton Strom for The New York Times

Bitcoin has been promoted as an alternative crypto-currency that exists outside the realms of governments and central banks. Now, two backers of the digital money are seeking to bring bitcoin into the investing mainstream — if they win the approval of the United States government.

Cameron and Tyler Winklevoss, the twins best known for their part in the history of Facebook, filed a proposal with securities regulators on Monday that would allow any investor to trade bitcoins, just as if they were stocks. The plan involves an exchange-traded fund, which usually tracks a basket of stocks or a commodity, but in this case would hold only bitcoins.

It is part of a broader effort to remove the stigma hovering over bitcoin and other online money endeavors, which have faced a barrage of regulatory questions and enforcement actions. Recently the world’s largest trading exchange for bitcoins, Mt.Gox, filed with the Treasury Department to register itself as a money services business and comply with money-laundering laws.

The proposal from the twins, who already have sizable bitcoin holdings, is an audacious one: the Winklevoss Bitcoin Trust could send digital money from the realm of computer programmers, Internet entrepreneurs and a small circle of professional investors like themselves into the hands of retail investors — virtually anyone with a brokerage account.

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“The trust brings bitcoin to Main Street and mainstream investors to bitcoin,” said Tyler Winklevoss, co-founder of Math-Based Asset Services, which would operate the proposed fund. “It eliminates the friction of buying and reduces the risks associated with storing bitcoin while offering similar investment attributes to direct ownership.”

Their proposal has the advantage of coming from the desk of Kathleen Moriarty, a lawyer at Katten Muchin, who played a leading role in the creation of the first exchange-traded fund and popular gold- and silver-backed E.T.F.’s.

But it is far from certain that securities regulators will approve. Even if they do, such a fund would face major challenges, including the current bottlenecks that stop bitcoins from being easily bought and sold.

“There are so many ways it could go wrong,” said Ugo Egbunike, a senior specialist in exchange-traded funds at the data company Index Universe.

On Monday, several market participants suggested that the proposal was a long shot that was merely an attempt to legitimize the digital currency. But Cameron Winklevoss expressed confidence that regulators would bless the new investment.

“We have assembled a team that has successfully launched novel products before, and we firmly believe in the chances of success for this product,” he said.

The filing is the latest eye-catching development in bitcoin’s history since it was founded by an anonymous hacker, or hackers, in 2009.

Unlike traditional money, bitcoins exist in no physical form and are not backed by a central bank. Instead, the coins are created by a network of users who solve complex mathematical problems — a method known as “mining” — to generate bitcoins. Only a finite number of bitcoins can be created — 21 million — with the current count at about 11 million. A limited number of stores and Web sites are accepting bitcoin as payment, but for now it is primarily a vehicle for speculators.

“The value of bitcoins is determined by the value that various market participants place on bitcoins through their transactions,” the brothers’ filing says.

The currency grabbed the attention of global markets in April when the value of a single bitcoin spiked to more than $250 from $110, before plummeting. While there were questions about the survival of the currency, the value of a bitcoin has recently hovered around $100, making the total market worth about $1 billion.

During the April swoon, the Winklevosses went public with their own bitcoin hoard, amounting to about 1 percent of all outstanding coins, or about $10 million.

Bitcoins can currently only be bought and sold on informal computer networks and on online marketplaces that require substantial technological savvy and are far more complicated than traditional exchanges. The inaccessibility, and the limited quantity of bitcoins, appeal to users who are skeptical of governments and central banks. But it has made the system vulnerable at times to hackers and technology flaws.

An exchange-traded fund would make it significantly easier to gain exposure to bitcoins, just as commodities-based funds have made investing in gold, silver and other precious metals more accessible.

The Winklevoss fund would buy one bitcoin for every five shares, making the value of a single share worth about a fifth of a single bitcoin. Regulated trading desks would have to handle the daily buying and selling of the shares. The company operated by the Winklevosses would have a proprietary method for storing the fund’s bitcoin holdings and would charge an annual management fee, which is not specified in the filing.

Monday’s submission comes at a precarious time for digital money. In May, the operators of another online currency, Liberty Reserve, were indicted on charges that they facilitated billions of dollars of money laundering. Both before and after that, state and federal regulators were scrutinizing many players in the growing bitcoin economy, including the largest place to buy and sell the coins, the Tokyo-based Mt.Gox.

Before Mt.Gox registered with the Treasury Department’s Financial Crimes Enforcement Network, some of its accounts in the United States were frozen. The company temporarily stopped its American customers from cashing out while it said it was “making improvements.”

Mt.Gox’s difficulties highlight the risks that could confront the owner of shares in a bitcoin fund. The securities filing made Monday has 18 pages of “risk factors,” noting, among other concerns, the heavy presence of speculators and “an uncertain regulatory landscape.”

Mr. Egbunike said regulators may hesitate to approve the proposal because of the questions surrounding bitcoins and recent scrutiny of exchange-traded funds more broadly. While such funds have made the buying and selling of commodities and other complicated financial assets easier for retail investors, they have given these investors access to products that they may not understand. For current bitcoin aficionados, an E.T.F. could diminish the currency’s free-spirited appeal.

But even if the Winklevosses’ proposal fails, some industry experts said that it marks a significant signpost in the push to give virtual currencies at least a veneer of respectability.

“Digital currencies are not going away,” said Carol Van Cleef, the head of law firm Patton Boggs’s emerging-payments practice. “And as bitcoin rises in popularity, you’re going to see traditional financial products and services being adapted to it.”