Synthesis of Dynamic Masks for Infinite-Step Opacity

Abstract

We investigate the problem of synthesizing dynamic masks that preserve infinite-step opacity in the context of discrete-event systems. A system equipped with a dynamic mask, which acquires information dynamically by turning sensors on/off, is said to be infinite-step opaque if an outside intruder that can access all information acquired can never infer that the system was at some secret state for some specific previous instant. Existing works on the dynamic mask synthesis problem only consider current-state opacity. However, synthesizing dynamic masks for infinite-step opacity, a notion stronger than current-state opacity, is much more challenging. The main reason is that delayed information is involved in this problem and whether or not a current secret will be revealed depends on sensing decisions to be synthesized in the future. In this paper, a new type of information state is proposed to capture all delayed information in the infinite-step opacity problem. An effective algorithm is then presented to solve the synthesis problem. Our result extends existing dynamic mask synthesis techniques from current-state opacity to infinite-step opacity.