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Some of the documents turned over by Mr. Snowden, principally to Great Britain’s The Guardian and to The Washington Post, provided precise details on how the U.S. tracks an al Qaeda operative.

Thus, officials argue, Islamic State operatives reading the series of Snowden documents and news stories know what types of communication to avoid or how to make them more secure.

For example, Mr. Snowden disclosed an NSA report that told of its involvement in finding and then killing bin Laden confidant Hassan Ghul in October 2012.

It was Ghul’s wife who unwittingly betrayed him by mentioning her husband’s living conditions in an email intercepted by the NSA.

“In Ghul’s case, the agency deployed an arsenal of cyberespionage tools, secretly seizing control of laptops, siphoning audio files and other messages and tracking radio transmissions to determine where Ghul might ‘bed down,’” The Post said, based on Mr. Snowden’s collection.

A Senate defense committee staffer said Thursday: “Our lax security has provided our adversaries with a gold mine of information about our tactics and procedures.”

Mr. Snowden’s leaks came in 2013 before the Islamic State became widely known as a vicious terrorist group and army rolled into one, determined to attack America. In June it rampaged through Iraq, brutally conquering territory, and recently beheaded two American journalists.

Today a fugitive from U.S. justice in Russia, Mr. Snowden won sympathy from liberals, libertarians and some conservatives for exposing the NSA’s mass collection of communications to spy on enemies and allies alike.

Now that the U.S. has a new and especially vicious enemy, the Islamic State may sway some Snowden supporters to take a second look.

What angers intelligence officials is that Mr. Snowden claims to be an activist and reformer on the issue of privacy, yet he exposed basic spying techniques for finding terrorists who want to kill Americans.

Snowden’s original pretext that we were violating the law or that we were doing things that were simply inappropriate — the spirit or the letter of the law — has not been borne out,” said Mr. Inglis. “He went way beyond disclosing things that bore on privacy concerns.”