On the Notion of Statistical Security in Simulatability Definitions

We investigate the definition of statistical security (i.e., security against unbounded adversaries) in the framework of reactive simulatability. This framework allows to formulate and analyze multi-party protocols modularly by providing a composition theorem for protocols. However, we show that the notion of statistical security, as defined by Backes, Pfitzmann and Waidner for the reactive simulatability framework, does not allow for secure composition of protocols. This in particular invalidates the proof of the composition theorem. We give evidence that the reason for the non-composability of statistical security is no artifact of the framework itself, but of the particular formulation of statistical security. Therefore, we give a modified notion of statistical security in the reactive simulatability framework. We prove that this notion allows for secure composition of protocols. As to the best of our knowledge, no formal definition of statistical security has been fixed for Canetti’s universal composability framework, we believe that our observations and results can also help to avoid potential pitfalls there.