Decidability of Deterministic Process Equivalence for Finitary Deduction Systems

Abstract

Deciding privacy-type properties of deterministic cryptographic protocols such as anonymity and strong secrecy can be reduced to deciding the symbolic equivalence of processes, where each process is described by a set of possible symbolic traces. This equivalence is parameterized by a deduction system that describes which actions and observations an intruder can perform on a running system.We present in this paper a notion of finitary deduction systems. For this class of deduction system, we first reduce the problem of the equivalence of processes with no disequations to the resolution of reachability problem on each symbolic trace of one process, and then testing whether each solution found is solution of a related trace in the other process. We then extend this reduction to the case of generic deterministic finite processes in which symbolic traces may contain disequalities.