The fundamental problem of quantum cryptography

It is known that statistical predictions of quantum theory do not depend on its interpretation. In particular, an experiment cannot distinguish between the Copenhagen interpretation (involving no hidden variables) and the de Broglie-Bohm interpretation based on nonlocal hidden variables. Quantum cryptographic protocols, such as BB84 or E91, are secure and mutually equivalent as long as one works within the framework of Copenhagen interpretation. But they are inequivalent and insecure if one considers attacks allowed by the de Broglie-Bohm interpretation. The fundametal problem of quantum cryptography is therefore this: Are all the statements about security of quantum protocols based on our belief in one of the two allowed interpretations of quantum mechanics? We show that this is not the case. Ekert-type protocols can be modified in a way that makes them secure even if the de Broglie-Bohm nonlocal hidden variables exist. Bennett-Brassard-type cryptography does not seem to allow for such a correction.