PhD in Cryptography after Masters with experience I hold a masters in mathematics and philosophy (emphasis on logic) and, for personal reasons, I will be joining the US Navy as an officer doing cryptology.  I'm curious if I apply afterward to programs (math or computer science programs) specifically doing cryptology (or number theory or related) will they see my experience as a plus to my application, especially since I will not be able to say what I did (being top secret and whatnot).
Yes, it will be a plus. And no, you won't need to go into details. But get a letter of recommendation from a superior. 

But part of its being a plus is that it is closely related to your academic trajectory and not something different. 

And, with permission from the DoD, you can probably say some things, even if not especially detailed. You can, for example, possibly speak about non-classified papers that you found useful in your work. But more important, those non-classified papers that you want to consider for extension - whether related to your work or not.