Universally Composable Privacy Amplification from Causality Constraints

We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so-called universally composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.