Verification of initial-state opacity in security applications of discrete event systems

Abstract

In this paper, we formulate and analyze methodologies for verifying the notion of initial-state opacity in discrete event systems that are modeled as non-deterministic finite automata with partial observation on their transitions. A system is initial-state opaque if the membership of its true initial state to a set of secret states remains opaque (i.e., uncertain) to an intruder who observes system activity through some projection map. Initial-state opacity can be used to characterize security requirements in a variety of applications, including tracking problems in sensor networks. In order to model and analyze the intruder capabilities regarding initial-state opacity, we first address the initial-state estimation problem in a non-deterministic finite automaton via the construction of an initial-state estimator. We analyze the properties and complexity of the initial-state estimator, and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant. We also establish that the verification of initial-state opacity is a PSPACE-complete problem.