Encoding cryptographic primitives in a calculus with polyadic synchronization

We thoroughly study the behavioral theory of epi, a π-calculus extended with polyadic synchronization. We show that the natural contextual equivalence, barbed congruence, coincides with early bisimilarity, which is thus its co-inductive characterization. Moreover, we relate early bisimilarity with the other usual notions, ground, late and open, obtaining a lattice of equivalence relations that clarifies the relashionship among the “standard” bisimilarities. Furthermore, we apply the theory developed to obtain an expressiveness result: epi extended with (symmetrical) key encryption primitives may be fully abstractly encoded in the original epi calculus. The proposed encoding is sound and complete with respect to barbed congruence. Therefore, cryptographic epi (cryptoepi) gets behavioral theory for free, what contrasts with other process languages with cryptographic constructs that usually require a big effort to develop such theory. Therefore, it is thus possible to use crypto-epi to analyze and to verify properties of security protocols using equational reasoning. To illustrate this claim, we prove the correctness of a protocol of secure message exchange.