WASHINGTON ?" Jake Williams awoke last April in an Orlando, Fla., hotel where he was leading a training session. Checking Twitter, Mr. Williams, a cybersecurity expert, was dismayed to discover that he had been thrust into the middle of one of the worst security debacles ever to befall American intelligence. 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