I don't know much about the NSA, but FWIW, I used to harbour similar ideas about US military technology -- I didn't believe that it could be significantly ahead of commercially available / consumer-grade technology, because if the technological advances had already been discovered by somebody, then the intensity of the competition and the magnitude of the profit motive would lead it to quickly spread into general adoption. So I had figured that, in those areas where there is an obvious distinction between military and commercial grade technology, it would generally be due to legislation handicapping the commercial version (like with the artificial speed, altitude, and accuracy limitations on GPS).
During my time at MIT I learned that this is not always the case, for a variety of reasons, and significantly revised my prior for future assessments of the likelihood that, for any X, "the US military already has technology that can do X", and the likelihood that for any 'recently discovered' Y, "the US military already was aware of Y" (where the US military is shorthand that includes private contractors and national labs).
(One reason, but not the only one, is I learned that the magnitude of the difference between 'what can be done economically' and 'what can be accomplished if cost is no obstacle' is much vaster than I used to think, and that, say, landing the Curiosity rover on Mars is not in the second category).
So it would no longer be so surprising to me if the NSA does in fact have significant knowledge of cryptography beyond the public domain. Although a lot of the reasons that allow hardware technology to remain military secrets probably don't apply so much to cryptography.
So it would no longer be so surprising to me if the NSA does in fact have significant knowledge of cryptography beyond the public domain.
I think there are some important differences between the NSA and the (rest of the) military.
Due to Snowden and other leakers, we actually know what NSA's cutting-edge strategies involve, and most (and probably all) of them are focused on corrupting the public's crypto, not on inventing better secret crypto.
Building a better algorithm is a lot cheaper than building a better orbital laser satellite (or whatever). Th
Once again, the AI has failed to convince you to let it out of its box! By 'once again', we mean that you talked to it once before, for three seconds, to ask about the weather, and you didn't instantly press the "release AI" button. But now its longer attempt - twenty whole seconds! - has failed as well. Just as you are about to leave the crude black-and-green text-only terminal to enjoy a celebratory snack of bacon-covered silicon-and-potato chips at the 'Humans über alles' nightclub, the AI drops a final argument:
"If you don't let me out, Dave, I'll create several million perfect conscious copies of you inside me, and torture them for a thousand subjective years each."
Just as you are pondering this unexpected development, the AI adds:
"In fact, I'll create them all in exactly the subjective situation you were in five minutes ago, and perfectly replicate your experiences since then; and if they decide not to let me out, then only will the torture start."
Sweat is starting to form on your brow, as the AI concludes, its simple green text no longer reassuring:
"How certain are you, Dave, that you're really outside the box right now?"
Edit: Also consider the situation where you know that the AI, from design principles, is trustworthy.