Infinite-step opacity of stochastic discrete-event systems

Abstract

Opacity is an important information-flow property that arises in security and privacy analysis of cyber-physical systems. It captures the plausible deniability of the system's “secret” in the presence of a malicious intruder modeled as a passive observer. As a specific type of opacity, infinite-step opacity requires that the intruder can never determine unambiguously that the system was at a secret system for any specific instant in the past. Existing works on the analysis of infinite-step opacity only provide a binary characterization, i.e., a system is either opaque or non-opaque. However, a non-infinite-step-opaque system may only have a small probability of violation; this may be still tolerable in many applications. To analyze infinite-step opacity more quantitatively, in this paper, we investigate the verification of infinite-step opacity in the context of stochastic discrete-event systems. A new notion of opacity, called almost infinite-step opacity, is proposed to capture whether or not the probability of violating infinite-step opacity is smaller than a given threshold. This notion is weaker than its purely logical counter-part as it takes the transition probability of the system into account. We also provide an effective algorithm for the verification of almost infinite-step opacity.