“Francis has been less than forthright with his ever-changing stories,” Ms. deSouza’s lawyers claimed in one filing.

No secret stash ever materialized. A spokeswoman for Mr. deSouza said he had disclosed the entirety of his cryptocurrency holdings at the beginning of the divorce. “As soon as Francis knew that the Bitcoin was caught up in the Mt. Gox bankruptcy, he told his ex-wife,” the spokeswoman said. “Had the Mt. Gox bankruptcy not occurred, the division of the BTC would have been entirely uncontroversial.”

Ms. deSouza declined to comment through her lawyer.

But the appeals court found that Mr. deSouza, 51, who is now the chief executive of the biotech company Illumina, had violated rules of the divorce process by failing to keep his wife fully apprised of his cryptocurrency investments.

He was ordered to give Ms. deSouza about half the total number of Bitcoins he had owned before the Mt. Gox bankruptcy, leaving him with 57 Bitcoins, worth roughly $2.5 million at today’s prices. Ms. deSouza’s Bitcoins are now worth more than $23 million.

Not all crypto divorces involve such large sums. A few years ago, Nick Himonidis, a forensic investigator in New York, worked on a divorce case in which a woman accused her husband of underreporting his cryptocurrency holdings. With the court’s authorization, Mr. Himonidis showed up at the husband’s house and searched his laptop. He found a digital wallet, which contained roughly $700,000 of the cryptocurrency Monero.

“He was like: ‘Oh, that wallet? I didn’t think I even had that,’” Mr. Himonidis recalled. “I was like, ‘Seriously, dude?’”

In another case, Mr. Himonidis said, he discovered that a husband had moved $2 million in cryptocurrency out of his account on the Coinbase exchange, a platform where people buy, sell and store digital currencies. A week after his wife filed for divorce, the man transferred the funds to digital wallets, and then left the United States.