We analyze a protocol which generates secret key from correlations that violate the CHSH inequality by a sufficient amount, and prove its security against eavesdroppers which are only constrained by the fact that any information accessible to them must be compatible with the impossibility of arbitrarily fast signaling. The results of this paper alone show the security when the eavesdropper is not able to store nonclassical information. But if complemented with the results of arXiv:0807.2158 we can show unconditional security according to the strongest notion, the so called universally-composable security. A way to implement this protocol is to generate non-local correlations by measuring quantum systems, however, its security does not rely on the eavesdropper being constrained by the laws of quantum mechanics. The no-signaling assumption is imposed at the level of the outcome probabilities given the choice of the measurement, therefore, the protocol remains secure in situations where the honest parties distrust their quantum apparatuses. The techniques developed for this proof are very general and can be applied to other Bell inequality-based protocols. As an example we explain how to adapt this proof to a more efficient protocol whose key rates are comparable to the ones obtained by assuming that the eavesdropper is quantum mechanical.