I live in the DC area and the people I know who work at NSA typically say they work "for the Department of Defense". That's a sure sign they work at NSA, since

I live in the DC area and the people I know who work at NSA typically say they work "for the Department of Defense". That's a sure sign they work at NSA, since anyone else who works at DoD would just say more specifically whom they work for, like I did when I was a contractor at the Naval Research Lab.