Research On State-based Opacity Of Discrete-event Systems

Discrete event system(DES)is a kind of cyber physical system which is characterized by discrete states and driven by discrete events.Nowadays,information security and privacy are getting more and more significant attention from both industry and academia.Opacity is a fundamental property of discrete event system.It characterizes the ability of a system to keep some secret information from an intruder.On the one hand,various opacity of DES under standard framework have been investigated widely.However,based on practical systems which are modeled as discrete event systems,the observations of events may become nondeterministic for the reasons of the sensor limitations,sensor faults and packet losses in the network.The observation of events not only may be several but also depends on current states.Therefore,reconsidering the opacity of DES under nondeterministic observations has important significance.On the other hand,based on a standard setting in which an intruder has the complete knowledge of the system’s structure,the standard opacity can protect secret states of the system.However,the standard opacity does not have the ability to protect the secret states that had been passed.That indicates the standard opacity has no higher-level privacy and security.Therefore,the investigations on strong opacity of DES have great significance.Based on above analysis,this paper studies the opacity under nondeterministic observations framework in discrete-event systems and the strong opacity under standard framework in discrete-event systems by using matrix semi-tensor product technique and concurrent-composition technique,respectively.Specifically,the work of this paper mainly includes the following two parts:(1)For the discrete event system under nondeterministic observation framework,we defined three categories of opacity: initial-state opacity,current-state opacity and initial-and-final state opacity.For the purpose of the verifications of these three categories of opacity,the matrix-formed initial state estimator,current state estimator and initial-and-final state estimator are established respectively by using the matrix semi-tensor product technology.Based on the established state estimators,the homologous matrix-based criteria of these three categories of opacity are given.Finally,the computational complexity of using our verification method is analyzed.(2)For the discrete event system under under standard framework,the notions of strong current-state opacity and strong initial-state opacity are proposed.For the verification problems of these two categories of strong opacity,we constructed initial-state concurrent-composition observer and current-state concurrent-composition observer by using the concurrent-composition technique.Based on these two types of constructed concurrent-composition observers,we gave the sufficient and necessary conditions for these two categories of strong opacity.The time complexity of verifying these two categories of strong opacity using the concurrent-composition technique method is also analyzed.