Verification of Opacity Under a K-Delay Orwellian Observation Mechanism

Opacity, an important property of the information flow in discrete-event systems (DESs), characterizes whether the secret information in a system is ambiguous to a passive observer (called an intruder). Observation models play a critical role in the analysis of opacity. In this paper, instead of adopting a fully static observation model or a fully dynamic observation model, we use a novel Orwellian-type observation model to study the verification of the current-state opacity (CSO), where the observability of an unobservable event can be re-interpreted once certain/several specific conditions are met. First, a K-delay Orwellian observation mechanism (KOOM) is proposed as a novel Orwellian-type observation mechanism for extending the existing Orwellian projection. The main characteristics of the KOOM are delaying the inevitable information release and narrowing the release range for historical information to protect the secrets in a system to a greater extent than with the existing Orwellian projection. Second, we formulate the definitions of standard and strong CSO under the KOOM. Finally, we address the verification problem for these two types of opacity by constructing two novel information structures called a standard K-delay verifier and a strong K-delay verifier, respectively. An analysis of the computational complexity and illustrative examples are also presented for the proposed results. Overall, the proposed notions of standard and strong CSO under the KOOM capture the security privacy requirements regarding a delayed release in applications, such as intelligent transportation systems, etc.