Local Verification of Current-State Opacity and Static-State Opacity in Distributed Discrete-Event Systems

Abstract

The integration of physical processes and cyber-networks in cyber-physical systems has made information security crucial, particularly in preventing unauthorized access and data leakage. Current-state opacity (CSO) in discrete-event systems (DESs) formalizes the security property that an intruder can never infer secret states based on its observation. This article addresses CSO and its verification in distributed DESs composed of multiple local systems. Existing methods of verifying CSO in distributed DESs either rely on sufficient conditions for local verification or require costly synchronization of local systems and observers. This article first proposes necessary and sufficient conditions for locally verifying CSO of distributed DESs, reducing the time complexity from $\mathcal {O}(2^{n^{m}})$ to $\mathcal {O}(mn)$, where $m$ is the number of local systems and $n$ is the largest state number of local systems. We also introduce static-state opacity (SSO), a new information security notion for distributed systems characterizing intruders’ incapability to deduce global secrets from local ones. We show that SSO can be verified (necessarily and sufficiently) through a matrix involving CSO of local systems with a time complexity of $\mathcal {O}(m2^{n})$. Furthermore, we explore the relationship between CSO and SSO, showing scenarios where they are equivalent.