If the payments constituted a bona fide settlement, the tax treatment would be more complicated. Some settlement payments are taxable, but payments to compensate for personal physical injuries are not. Payments for emotional distress related to personal physical injuries are not taxable either.

A key question then would be what sort of injury Mr. Hastert was making payments to compensate for, and whether it constituted a personal physical injury for tax purposes. It’s a question that has come up because of cases involving priests who have molested children.

“There is an internal I.R.S. document that’s available to the public in which they were dealing with some of these church issues, and it seemed to at least open up the possibility that they would treat a payment in exchange for sexual abuse as a physical injury,” Mr. Graetz said. “But it’s not clear that they would.”

Even if payments to compensate for sexual abuse are not taxable, another important question would be how much of the payments Mr. Hastert made were actually in compensation for such abuse. Settlement payments made in exchange for confidentiality are taxable — and if Mr. Hastert was motivated by his desire for silence, a large fraction of the payments might be ascribed to confidentiality and subject to tax.

This issue came up in a case involving, surprisingly enough, Dennis Rodman. In 1997, when Mr. Rodman was playing for the Chicago Bulls, he kicked Eugene Amos, a TV cameraman, in the groin during a game. Ultimately, he reached a settlement with Mr. Amos for $200,000, which included a provision agreeing to keep the terms of the settlement confidential.

The I.R.S. contended that Mr. Amos was not seriously injured and that most of the payment was in exchange for confidentiality; therefore, the service contended, taxes were due. Ultimately, a tax court reached a mixed ruling, allocating $120,000 of the settlement to physical injuries and $80,000 to confidentiality, with tax due on the latter.

Of course, it is not likely that Mr. Hastert and Individual A had a written settlement agreement. A settlement can be based on a verbal agreement, said Mr. Caron, but the lack of an agreement setting out what is paid for what would make it difficult for Individual A to argue all the payments should be excluded from tax.

All of which is to say, it’s likely at least some tax was due on the payments. And maybe it was paid — for all we know, Individual A may have been taking his secret cash payments and faithfully reporting them to the I.R.S. The indictment is silent on the matter.