Mr. Williams had written on his company blog about the Shadow Brokers, a mysterious group that had somehow obtained many of the hacking tools the United States used to spy on other countries. Now the group had replied in an angry screed on Twitter. It identified him — correctly — as a former member of the National Security Agency’s hacking group, Tailored Access Operations, or T.A.O., a job he had not publicly disclosed. Then the Shadow Brokers astonished him by dropping technical details that made clear they knew about highly classified hacking operations that he had conducted.

America’s largest and most secretive intelligence agency had been deeply infiltrated.

“They had operational insight that even most of my fellow operators at T.A.O. did not have,” said Mr. Williams, now with Rendition Infosec, a cybersecurity firm he founded. “I felt like I’d been kicked in the gut. Whoever wrote this either was a well-placed insider or had stolen a lot of operational data.”