Asymmetric cryptographic algorithms

Is it possible for any of them to survive to P=NP, assuming that NP-complete O(2^N) problems collapse to at best O(N²)?

>>19
Polynomial differences are usually disregarded, for obvious reasons. There is an intriguing possibility that the polynomial in question has a really really big degree, but that's not what OP asked.
I disagree.  Even if there is a O(N⁶) algorithm that solves 3SAT (which implies that P=NP), it still won't break any of today's cryptosystems.