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In this paper, we investigate the enforcement of opacity via supervisorycontrol in the context of discrete-event systems. A system is said to be opaqueif the intruder, which is modeled as a passive observer, can never inferconfidently that the system is at a secret state. The design objective is tosynthesize a supervisor such that the closed-loop system is opaque even whenthe control policy is publicly known. In this paper, we propose a new approachfor enforcing opacity using non-deterministic supervisors. A non-deterministicsupervisor is a decision mechanism that provides a set of control decisions ateach instant, and randomly picks a specific control decision from the decisionset to actually control the plant. Compared with the standard deterministiccontrol mechanism, such a non-deterministic control mechanism can enhance theplausible deniability of the controlled system as the online control decisionis a random realization and cannot be implicitly inferred from the controlpolicy. We provide a sound and complete algorithm for synthesizing anon-deterministic opacity-enforcing supervisor. Furthermore, we show thatnon-deterministic supervisors are strictly more powerful than deterministicsupervisors in the sense that there may exist a non-deterministicopacity-enforcing supervisor even when deterministic supervisors cannot enforceopacity.

Opacity Enforcing Supervisory Control using Non-deterministic Supervisors