# Private key encryption based on NP-complete problem

Over a decade ago, a question was asked on Stack Overflow, which basically asked if there were any encryption schemes that are reducible to an NP-complete problem, in the sense that breaking the encryption implies breaking the underlying NP-complete problem, and hence proving $$P\not=NP$$.

As a concrete example, is there a symmetric key cryptosystem which can be proved to be CPA-secure under the assumption that some underlying NP-complete problem is hard to solve? That is, if the adversary is given the encryption of one of two messages, then an algorithm that can determine which message was encrypted can also be used to solve the underlying NP-complete problem (in polynomial time)?

In the original Stack Overflow question, the answer was an unequivacle "no". I ask this question today because 12+ years is a long time in the world of research, and I am curious if any progress has been made on this problem yet.