Did YOU think the NSA could factor fast?

Before the recent revelations about the NSA (see Lances Post and Scott's post )I would tell my class, when teaching P and NP,

We have very good reasons to think that Factoring is NOT NP-complete. As for P--- much murkier. People have tried to get it into P because of crypto and have not succeeded, hence many people think that Factoring is NOT in P. But there is so much math there that perhaps could be exploited to show it IS in P. Another very odd possibility is that it is KNOWN to be in P but only by the NSA. Crytpo has had this before- where some concepts were known to governments before they were known to the public,  even the academic public.

I will need to revise that now. BEFORE the recent revelations there were

the following points of view on factoring:


The NSA cannot factor any better than what is known in the literature. Maybe a bit better because they use more parallelism.
The NSA has taken the known algorithms and found the right parameters and has special purpose hardware so can do them better than anyone else, but nothing of interest mathematically. Perhaps some very interesting subtle points of math and hardware. What they have would not get into STOC/FOCS/CRYPTO (though maybe it should- that's another debate). This is the one I believed.
The NSA has an algorithm that is better than the literature (e.g., exponential in (log n)^{1/5}).  But not in P. This would surely get into STOC/FOCS/CRYPTO and win a prize.
The NSA has factoring in P through some very interesting and new mathematics. If this was public then perhaps a Turing Award.  Some serious number theorists do think that Factoring IS in P, so this one is not quite so implausible.
The NSA has a quantum computer that factors quickly. I do not now of anyone serious who believed this. Of course, this could be a case of the No True Scotsman Paradox--- if someone really believed this I would (perhaps unfairly) declare them non-serious.
The NSA does not have a better algorithm, but has managed to put trapdoors in stuff so that they and only they could break certain codes.(A covert version of Clipper Chip.) So they can break codes but not in a way that is interesting mathematically.



There may be more but I don't know them off hand. Item 6 I never heard people say, though that might be a function of the company I keep. I do not know what the most common view was, but I would guess item 2.This reminds me of  Karmarkar's Algorithm which I've heard runs fast because of the implementation- the algorithm is not a secret but exactly how they implement it is. (Note- just because I've heard this does not mean it's true.)



The truth seems to be that the truth is between 1 and 2, closer to 1, and also item 6.

In particular, the NSA does not seem that much ahead of academics.



In the past governments were way  ahead of academics in crypto. This no longer seems to be the case (at least in America). I speculate that this is because there is now a large community  of people doing research in crypto openly, publishing openly, so the government is no longer the only (or almost the only) game in town. Also, many non-government industries use crypto and some do research in it. This also helps the NSA- they can use results in the open literature, but they can't get that much ahead of it.



Are there other fields where the government is ahead of academics and industry? On a guess stuff with weapons and weapon detection, since not many academics work on that. Maybe sociology since the government has  census data and other data that is not available to the public.