Am I missing something? I thought that the whole point of using the difficulty of integer factorization as the strength of things like RSA was that it's not known to be solvable in polynomial time. "P==NP" is one of the unsolved problems of computer science.
I think that the state of the art is that we can factor in sub-exponential time.
P == NP => integer factorization can be done in polynomial time with a classic computer but not vice versa. In fact, many people believe P != NP && integer factorization can be done in polynomial time since FACTOR lies in this awkward space in the intersection of NP and co-NP. (Most other problem in this space are also in P, but we think P != NP, so...)
Now of course, if you put in quantum computers into the mix, Shor's algorithm can break both RSA and ECDSA in polynomial time.
Not really. The last big jump in complexity was in 1991, when the first 512-bit modulus, 2^512+1, was factored by NFS [1]. What has progressed the most, by far, has been the available computational power.
[1] http://www.ams.org/journals/mcom/1993-61-203/S0025-5718-1993...
You know much more than I do about this stuff, but I think I'm prepared to challenge you on this. :)
The practical NFS improvements since then might bring that down to 2^78 or even 2^72---and that's a lot of money saved---but when you're thinking of which key size to use it doesn't matter nearly as much as how 2^80 computation is something that is reasonably practical today, but was unthinkable in 1995.
If the original commenter's point was that RSA directly harmed the 3DS in some fundamental way, that would be a legit thing to push back on, I think.