According to the S.E.C., Mr. Singh also assigned fraudulent dates to a series of transactions to make it appear that FTX’s 2021 revenue was $50 million higher than it was, and then lied about the scheme to auditors. And last September and October, the complaint said, he withdrew roughly $6 million from FTX for his personal use, spending the money on charitable donations and a multimillion-dollar house, when he knew FTX customer funds were being misappropriated.

FTX filed for bankruptcy in November after the crypto equivalent of a bank run exposed an $8 billion hole in its accounts. Its implosion was the worst moment in a yearlong crypto industry meltdown that sent the market spiraling and cost investors billions of dollars in lost deposits.

The investigation into FTX has gained steam in recent weeks. On Thursday, federal prosecutors announced a revised indictment against Mr. Bankman-Fried that included several new charges and detailed the alleged scheme to defraud customers and investors and funnel tens of millions in illegal campaign contributions to political candidates and political action committees.

Mr. Bankman-Fried pleaded not guilty in January to the original indictment and is expected to return to court in the next few months to be arraigned on the revised charges, according to a court filing. A spokesman for Mr. Bankman-Fried declined to comment.

Mr. Singh is a graduate of the University of California, Berkeley. He worked as a software engineer on the applied machine-learning team at Facebook and then joined Alameda, the crypto hedge fund that Mr. Bankman-Fried founded and owned. Mr. Singh has also been a close friend of Mr. Bankman-Fried’s younger brother, Gabe, who ran Guarding Against Pandemics, an organization that received much of its financial support from FTX.

In 2019, Mr. Bankman-Fried, Mr. Wang and Mr. Singh founded FTX in Hong Kong, before moving the company to the Bahamas two years later. The three founders and Ms. Ellison were active in the effective altruism movement, a brand of philanthropy that urges donors to use data to maximize the long-term impact of their donations. They all sat on the board of the FTX Foundation, Mr. Bankman-Fried’s philanthropic operation, and lived together in a luxurious penthouse at Albany, a resort on the Bahamian island of New Providence.

As FTX grew, Mr. Bankman-Fried became its public face while Mr. Wang and Mr. Singh were crucial behind the scenes, responsible for writing the software code for FTX.