Because PvNP has yet to be proved does that mean that encryption might not exist?

Question

I'm not well versed enough on the topic of computational-complexity theory but what I think I know is that there is debate over whether or not all problems that can be checked fast can be solved fast. If this is true and all problems can be checked fast and solved fast would encryption be unattainable?

Answer 1

I think that your question is showing couple missconceptions.

First, encryption exists since the ancient times, the P vs NP problem has no bearing on it. The question you probably want to ask is not if it exists, but if it can be broken easily or not.

While there exists unbreakable encryption systems (the one time pad for example), some of the (older?) public key encryptions would maybe (and here is the second missconception) be "less secure" in some sense if P=NP.

Note that if P=NP, it would imply that the RSA can be broken in polynomial time. But, while people usually understand that this would make it breakable, this is not necessarily true. It would mean that, if the length of the key goes to infinity, then breaking it is faster than people though. But for keys of not too large length (and everything which is used today would very likely fall into this cathegory) the time could easily still be unreasonable. This is because, while exponentials and factorial grow faster than polynomials, for bounded values of $n$ there are lots and lots of polynomials which are still larger than a given exponential or factorial.