UPDATE: Cameron and Tyler Winklevoss, according to several published reports, became the first bitcoin billionaires over the weekend as the cryptocurrency surged to an all-time high of $11,773 on Sunday, a recovery from last week's 20 percent drop. Bitcoin prices weren't quite at records on Monday. But at a market value of nearly $191 billion, bitcoin was about halfway to the "small bull case scenario" described by the Winklevosses in 2013. Here's a story on the interview they did four years ago:
The Winklevoss twins are screaming bulls on bitcoin.
Cameron and Tyler Winklevoss — big investors in the digital currency — said Tuesday that bitcoin should be worth at least 100 times more than it's valued today.
"The small bull case scenario is a $400 billion market cap. So the market cap is around $4 billion right now," Tyler Winklevoss said in an interview at the DealBook conference that aired on CNBC's "Squawk Box."
The twins, who famously battled Mark Zuckerberg over the origins of Facebook, started buying bitcoin at $9. Their investment was worth $11 million in April at $120 per coin.
After a sharp drop, bitcoin has surged into record territory again, hitting $385 in early Tuesday trading on Mt. Gox — one of the many exchanges for the digital currency.
Cameron Winklevoss said he views their investment in bitcoin as a gold 2.0 play but also a bet on the technology: "The idea that payments are increasingly going to use a network like the bitcoin network to move money around the world."
The Winklevosses want to create a bitcoin exchange-traded fund (ETF), accessible to all investors. "We filed an amended S-1 in October. And we're just still going through the process," Cameron said.
He explained how bitcoin works: "Miners mint bitcoins every 10 minutes. It's basically a computer algorithm." He said the computers built to mine are so specific "you couldn't really do it as a hobbyist."
Bitcoin was created by Satoshi Nakamoto, a pseudonym, Tyler said. "We don't need to know him because it's based on ... trust in cryptography, not trust in individual."
As for what regulators in Washington think about bitcoin, Cameron said, "I think everyone recognizes the innovation and doesn't want to stifle it. They just want to make sure there's healthy regulations so it's used in a safe and productive manner."
Last month, bitcoin plunged after U.S. authorities shut down the Silk Road site, an accused online purveyor of drugs and other illegal services. Bitcoin had been hit by the perception that it was used primarily for transactions on Silk Road, and many had expected demand to dry up after the website was closed.
But Tyler Winklevoss said those concerns were never realized: "Prices are double what it was before Silk Road was shut down. So the demand to use bitcoin for illicit activity was clearly almost zero."
Mainstream merchants are slowly adopting bitcoin. Cameron pointed out that e-commerce platform Shopify announced it will accept bitcoin, and so has China portal Baidu.
The digital currency has even made steps into the physical realm, with ATM manufacturer Robocoin launching the first bitcoin ATM in a Vancouver coffee shop.
— By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.
Correction: This version shows that the Winklevosses' investment in bitcoin was worth $11 million in April.