P = NP and current cryptographic systems I've recently heard some people claiming that if the fact that P = NP is proven, most (all?) the current cryptographic algorithm considered secure like RSA will be unusable in secure systems.

My question is :

1. If P = NP is proven TODAY, will a RSA key (let say 3072 bits) be still enough to ensure a certain amount of security.

2. If not, what could we do to have at least the same amount of security (take a larger key length? a stronger algorithm?)
A proof of P = NP would prove that one-way functions do not exist. That in turn would imply, that almost no secure cryptographic primitives can exist according to the accepted definitions of security. (No symmetric encryption, no MACs, no pseudorandom generators, no signature schemes, ...)

However, it would just mean that no scheme can be provably secure. It does not mean that all schemes would be broken in practice. It might even be possible to adapt our definitions of security in a meaningful way.

In particular, it is very much conceivable that a proof of P=NP would be non-constructive. Such a proof would not help in any way. It would just mean that there exists an algorithm to efficiently break RSA (for a theoretical definition of efficiency, i.e. in polynomial time) but that does not mean that we know said algorithm. And even if the algorithm is known, it might not be efficient in practice.  An algorithm running in  $\mathcal{O}(n^{2^{100}})$ is technically a polynomial time algorithm, but it isn't very helpful.

So in conclusion, the question whether some keysize would still remain "secure" or how we could regain some measure of security cannot be answered in general, as it depends on the exact nature of the proof.