Symbolic protocol verification with dice: process equivalences in the presence of probabilities (extended version)

Symbolic protocol verification generally abstracts probabilities away, considering computations that succeed only with negligible probability, such as guessing random numbers or breaking an encryption scheme, as impossible. This abstraction, sometimes referred to as the perfect cryptography assumption, has shown very useful as it simplifies automation of the analysis. However, probabilities may also appear in the control flow where they are generally not negligible. In this paper we consider a framework for symbolic protocol analysis with a probabilistic choice operator: the probabilistic applied pi calculus. We define and explore the relationships between several behavioral equivalences. In particular we show the need to require randomized schedulers-indeed we exhibit a counterexample to one of the main results in a previous work that relied on non-randomized ones. As in other frameworks that mix both non-deterministic and probabilistic choices, schedulers may sometimes be unrealistically powerful. We therefore consider two subclasses of processes that avoid this problem. When considering purely non-deterministic protocols, as is done in classical symbolic verification, we show that a probabilistic adversary has-maybe surprisingly-a strictly superior distinguishing power for may testing, which, when the number of sessions is bounded, we show to coincide with purely possibilistic similarity. Finally, we consider fully probabilistic protocols and show that trace equivalence corresponds to a notion of may testing with purely probabilistic attackers. We also briefly discuss complexity and automation for these subclasses when the number of sessions is bounded