Having worked briefly in the defense contracting industry, I concur with the other commenters. One thing worth pointing out though is that unlike with things like NSF grants, the overall standard to get government money for defense contractors is pretty low, and you get a lot of "bogosity" in many contracts awarded, including those that are funding PhD's in math-related areas who are supposedly doing research-type activities. As a result there is a really big difference in the type of work that goes on at say the NSA or the IDA compared to many other places. I saw projects that got funded for years that had very obvious flaws in their models that most of the posters here would easily point out. Even if companies eventually figure it out they are sort of stuck pursuing their old methods because that's what will bring in government money, not to mention what conceding they're wrong would do to their reputations.

Moral of the story: there is interesting math of an applied bent out there in the defense industry, but make sure you know what you're getting into.