Take for example "Hamiltonian cycle for a large graph". The proof works by starting with a graph G that contains a hamiltonian cycle, then constructing an isomorphic graph H, and then either showing the mapping between the graphs G and H or releaving the cycle in H.
It is said that we prove that that we know a hamiltonian cycle in G without revealing it.
But this assumes the verifier does not have unlimited computational power. If he had it, he could ask to reveal the cycle in H, and use his unlimited computational power to work out the isomorphism. I understand that if the verifier had unlimited power, he could find the cycle in G directly. But that's not my point. What I find strange is that we are relying on "hard problems" in the proof itself.
Are there ZKP protocols that do not rely on hard problems? Hard problems are only hard according to the state of the art. It is not proven that NP is not P, therefore, in my mind, this sounds like security through obscurity in some sense.