Unifying simulatability definitions in cryptographic systems under different timing assumptions

The cryptographic concept of simulatability has become a salient technique for faithfully analyzing and proving security properties of arbitrary cryptographic protocols. We investigate the relationship between simulatability in synchronous and asynchronous frameworks by means of the formal models of Pfitzmann et al., which are seminal in using this concept in order to bridge the gap between the formal-methods and the cryptographic community. We show that the synchronous model can be seen as a special case of the asynchronous one with respect to simulatability, i.e., we present an embedding from the synchronous model into the asynchronous one that we show to preserve simulatability. We show that this result allows for carrying over lemmas and theorems that rely on simulatability from the asynchronous model to its synchronous counterpart without any additional work, hence future work on enhancing simulatability-based models can concentrate on the more general asynchronous case.