“They are teaching everything,” one Arab official familiar with the effort said. “Data mining, Web surveillance, all sorts of digital intelligence collection.”

Yet as Booz Allen profits handsomely from its worldwide expansion, Mr. McConnell and other executives of the government contractor — which sells itself as the gold standard in protecting classified computer systems and boasts that half its 25,000 employees have Top Secret clearances — have a lot of questions to answer.

Among the questions: Why did Booz Allen assign a 29-year-old with scant experience to a sensitive N.S.A. site in Hawaii, where he was left loosely supervised as he downloaded highly classified documents about the government’s monitoring of Internet and telephone communications, apparently loading them onto a portable memory stick barred by the agency?