On the other hand your work is secret and you will never be recognized for what you do.
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You would be recognized inside the NSA, a large technical population.
In addition, as with the CIA and other clandestine US government organizations, they appeal to patriotism and helping the national interest. That appeal seems to be fraying somewhat lately for the NSA.
If they're really trying to keep it secret, not even the NSA rank and file will know. It's all mostly need to know anyway.
Though I have no first-hand knowledge, I was under the impression that organizations like the NSA have internal peer-reviewed journals that their mathematicians can "publish" in, while remaining classified and unavailable to the public.
I have a friend who interned with the NSA in high school. Although what he did is classified, he was allowed to say that his work got published internally.
This is basically just a small step worse than many professions. Once you hit the pay wall on journal articles you want to read, how many people pay to go through?
There are some (if not many) mathematicians for which recognition is not a plus (and in some cases may even be a negative).
Not everyone works for public recognition. There are enough people who are willing to work on neat problems in exchange for plenty of money who are also willing to forgo public recognition.
Or, if movies have taught me anything, after you've done your work and it's fully documented & reproducible... you'll be killed
Never is a long time, in a decade or two you might be. BUT either way, some very brilliant NSA mathematicians know what you came up with and so do you. That's enough for a lot of people.