The military also has access to extreme computing resources that are not available to the general public. If the pentagon cared to develop their own ASICs they could easily dominate the network.
Not going to lie I don't think the military or the pentagon is that sophisticated to build their own ASICs. They'd just buy ASICs from one of the Chinese miners that has already perfected the game. The primary resource at the US disposal is ridiculous sums of cash, but we aren't exactly on top when it comes to expertise and manufacturing.