Bounding the Number of Agents, for Equivalence Too

Bounding the number of agents is a current practice when modeling a protocol. In 2003, it has been shown that one honest agent and one dishonest agent are indeed sufficient to find all possible attacks, for secrecy properties. This is no longer the case for equivalence properties, crucial to express many properties such as vote privacy or untraceability. In this paper, we show that it is sufficient to consider two honest agents and two dishonest agents for equivalence properties, for deterministic processes with standard primitives and without else branches. More generally, we show how to bound the number of agents for arbitrary constructor theories and for protocols with simple else branches. We show that our hypotheses are tight, providing counter-examples for non actiondeterministic processes, non constructor theories, or protocols with complex else branches.