The indictment of former House Speaker Dennis Hastert, which dropped Thursday, had detailed how he'd made payments to "compensate for and conceal his prior misconduct." But no one knew exactly what that misconduct was.

Now, two federal law enforcement sources tell the Los Angeles Times that the "misconduct involved sexual abuse." From the report:

"It goes back a long way, back to then," the source said. "It has nothing to do with public corruption or a corruption scandal. Or to his time in office." Thursday's indictment described the misconduct "against Individual A" as having "occurred years earlier."

Asked why Hastert was making the payments, the official said it was to conceal Hastert's past relationship with the male. "It was sex,'' the source said. The other official confirmed that the misconduct involved sexual abuse.

Hastert was indicted Thursday on charges that he concealed payments totaling more than $1 million to an anonymous individual and then lied to the FBI about it. The indictment does not described the alleged misconduct, but includes some details about "Individual A," the person to whom Hastert made the payments. "Individual A" was a resident of Yorkville, Ill., and Hastert, who was a high school teacher and wrestling coach there before he entered politics, knew "Individual A" for most of the person's life.

One of the LA Times' sources on Friday described "Individual A" as a man, and said the claims originate from Hastert's time as a teacher at the high school. A federal law enforcement official told NBC News Friday that Hastert had a "sexual relationship" with "Individual A," who was a student at the high school. According to a New York Times report, the man told FBI officials that Hastert had touched him "inappropriately."

The school district in which Hastert taught released a statement on the allegations on Friday, writing that officials didn't learn of the "concerns" about Hastert until Thursday. The district "has no knowledge of Mr. Hastert's alleged misconduct, nor has any individual contacted the District to report any such misconduct."

According to the indictment, Hastert met with "Individual A" several times in 2010, and Hastert agreed to pay the person $3.5 million to compensate for and hide the alleged misconduct. The indictment said Hastert had paid $1.7 million.

According to a report in BuzzFeed Friday, federal investigators "considered but did not pursue" additional charges against Hastert. Those charges would have mentioned another person, "Individual B," who according to the BuzzFeed report is "one of potentially several alleged victims."

The office of the U.S. Attorney for the Northern District of Illinois—which is handling the case—declined to confirm the LA Times report when asked by National Journal.

Hastert, 73, served as House speaker from 1999 to 2007, when he resigned after Democrats took the majority and started his own lobbying company, Hastert & Associates. He also worked as a senior adviser at Dickstein Shapiro, a law and lobbying firm in Washington. He resigned from that firm Thursday night after news of the charges broke.

House Speaker John Boehner released a statement Friday evening addressing the claims against Hastert.

"The Denny I served with worked hard on behalf of his constituents and the country," Boehner said. "I'm shocked and saddened to learn of these reports."

Earlier this month, the Illinois state legislature halted plans to build a $500,000 statue of Hastert in the state Capitol. Hastert himself requested the construction be canceled, on account of "the state's fiscal condition." A spokesman for the Illinois Democratic speaker of the House—who'd proposed the statue in a bill earlier this month—said lawmakers weren't concerned about the cost.

During his rise to the speakership, Hastert was regarded for his scandal-free record. However, in 2006, the House Ethics Committee found that Hastert and other leaders did not do enough to protect House pages from former Rep. Mark Foley, who sent sexually suggestive emails and instant messages to pages. Foley resigned because of the resulting scandal.

After ABC News first published Foley's instant messages, Hastert released a statement calling them "vile and repulsive to me, and to my colleagues." He said he and other House Republican leaders had no knowledge of the exchanges, and if Foley had not resigned, "I would have demanded his expulsion from the House of Representatives."

"The page program is an important part of this institution. It has inspired many generations to enter public service," Hastert said at the time. "It is a trust, and as a parent and as the Speaker of the House, I am disgusted that Congressman Foley broke that trust. Anyone who had knowledge of these vile instant messages should have turned them over to authorities immediately so that kids could be protected."

According to the Ethics Committee's investigation, Hastert was aware of accusations against Foley for months before any action was taken. The committee did not penalize Hastert.

This story has been updated with a statement from House Speaker John Boehner.

Lauren Fox and Ben Geman contributed to this article

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