  We analyze a cryptographic protocol for generating a distributed secret key
from correlations that violate a Bell inequality by a sufficient amount, and
prove its security against eavesdroppers, constrained only by the assumption
that any information accessible to them must be compatible with the
non-signaling principle. The claim holds with respect to the state-of-the-art
security definition used in cryptography, known as universally-composable
security. The non-signaling assumption only refers to the statistics of
measurement outcomes depending on the choices of measurements; hence security
is independent of the internal workings of the devices --- they do not even
need to follow the laws of quantum theory. This is relevant for practice as a
correct and complete modeling of realistic devices is generally impossible. The
techniques developed are general and can be applied to other Bell
inequality-based protocols. In particular, we provide a scheme for estimating
Bell-inequality violations when the samples are not independent and identically
distributed.
