[loglog]

> For that kind of implementation, ...

This is the key point, what is the meaning of "zero knowledge" here? It seems that you need to know something about the implementation, even if it is not the full implementation. Compare this to a zero knowledge proof that you have, say, a factorization gadget, which works by you running the gadget on adversarial input, thus convincing the adversary that you can factor any of their integers. That discloses no implementation details of your factorization gadget, which can be an efficient classical algorithm, a quantum computer, or a phone line to God.