Opacity is a security property that guarantees the confidentiality of secret information from a partial observer of the system. To address this problem, we propose a modular approach that uses Supervisory and Control Theory to design a global supervisor for Modular Discrete Event Systems (MDES). This approach assumes the attacker can observe the shared alphabet between modules, and takes into account the modular structure of the system; which significantly decreases computational complexity compared to monolithic methods. To achieve this, we introduce a reduced-complexity algorithm, based on the Hyper Symbolic Observation Graph. The HSOG is an abstraction graph that considers only events that have a direct impact on the opacity. This reduces the number of states to be considered, making the algorithm more efficient.

Discrete Event systems are dynamic systems with two main characteristics: their set of states is discrete and their dynamic is event driven (as opposed to time driven). In this paper, we study a security property for DES called opacity. A system$\mathcal{T}$, partially observed by a third party -called an attacker- is said to be opaque if the attacker can never conclude from its provided interface that$\mathcal{T}$is in a secret state. Given a critical system that may leak confidential information, an attacker and a subset of controllable actions, we propose an approach to synthesize a controller that enforces the system's opacity. This controller is designed as a function that applies, at run time, on the current executions to disable any controllable action that eventually leads to the violation of the system's opacity. Our approach is based on a novel graph called a Hyper Symbolic Observation Graph. The language obtained under control is proven to be maximal whatever is the relationship between the attacker and the controller observations.