Obfuscation mechanism for simultaneous public event information release and private event information hiding in discrete event systems

In this paper, we study the problem of simultaneous public event information release and private event information hiding in discrete event systems modeled by partially observed non-deterministic finite automata, where the public and private event information is respectively defined as unobservable fault and secret events. The notion of D-C-compossibility is introduced to characterize whether a system simultaneously conceals the occurrences of secret events while releasing the occurrences of fault events. When such a property does not hold, we investigate its enforcement through a defensive function. This function takes each observable event of a system as input and generates a suitably modified event sequence at the system's output using event deletion, insertion, or substitution. Specifically, our focus is on prioritizing the concealment of the secret events while maximizing the detection of the fault events through the use of defensive functions. The notion of D-C-enforceability that refers to the capability of a defensive function to employ a strategy for manipulating observations of a system to enforce D-C-compossibility is proposed. That is, a D-C-enforcing defensive function ensures that all occurrences of fault events can be revealed while concealing all occurrences of secret events. A D-C-diagnoser construction is proposed to enumerate all feasible defensive actions following system behavior. By taking advantage of the D-C-diagnoser, we obtain a necessary and sufficient condition for D-C-enforceability, along with a corresponding obfuscation strategy for defensive functions.