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)?

>>20
Why, it would take only few hours to crack a 1024 bit RSA key on some of the current most powerful supercomputers or several minutes on the bitcoin network (if they don't lie about their performance). I mean, it might turn out to be some months rather a few hours, or maybe just seconds instead, anyway, it's well within reach. And that's on a general-purpose hardware, without anything resembling such a strong incentive.