Universally-composable privacy amplification from causality constraints

The impossibility of arbitrarily-fast signaling implies that uniform randomness can be extracted from correlations which sufficiently violate a Bell inequality. In our scheme, Bell inequalities play the role usually played by entropies, and the randomness is obtained by processing outcomes of Bell-violating measurements with a constant hash function. This contrasts with previous schemes in classical/quantm information theory (e.g. two-universal hashing, extractors), where the hash function is necessarily random. Our results imply the security of privacy amplification and secret key distribution, with the sole assumption of no signaling--even according to the strongest notion of security, the so called universally-composable security. In the low-noise regime, the efficiency rate of our scheme tends to the one obtained by assuming that the eavesdropper is quantum-mechanical, although our assumption is weaker.