Quantifying opacity of discrete event systems modeled with probabilistic Petri nets

Abstract

The verification and enforcement problem of opacity that falls into the category of security properties of information flows in a cyber-physical system has been extensively studied from the view of discrete event systems. Recent years have witnessed growing interest in the quantitative analysis of opacity. However, documented results on quantifying opacity in the literature are not formulated within the framework of Petri nets. By introducing a new class of Petri net as a modeling vehicle for opacity quantification, we suggest a novel notion of opacity referred to as worthy opacity, which describes the worth associated with the information that a system might leak during its evolution. Depending on how much system information is captured by an intruder, we propose two types of worthy opacity: stepwise and observational worthy opacity. We provide a necessary and sufficient condition for stepwise worthy opacity and prove its decidability. Observational worthy opacity is established by considering both system and observation aspects, with its verification shown to be undecidable. Compared with the existing works on quantifying opacity, we argue that the worthy opacity is of practical concern, as being aware of the information worth that a system may leak during its evolution is a more realistic guide than the probability that it may reveal a system secret.