Secret Protections With Costs and Disruptiveness in Discrete-Event Systems Using Centralities

In this article, we study a secret protection problem in discrete-event systems. The system is modeled by an automaton in which several states are assigned with different secret levels. Our aim is to protect some of the events in the system such that any sequence yielding a secret state contains a number of protected events no less than the required security level. We first study the secret-protecting problem with minimum cost, i.e., to design a protecting policy whose cost is minimal. We prove that the decision version of such a secret protection problem is NP-hard, which implies that there unlikely exists a polynomial algorithm to solve it. As a result, we developed a heuristic method to obtain a locally optimal solution to protect the secrets using the notion of
cost-weighted centrality
. Then, we consider the disruptiveness, i.e., the degree of disruptiveness of protecting policies to legal users' normal operations. We formulate the disruptiveness to users incurred by the protection of events as a penalty function, which describes the impact of events and transitions on the paths leading to marker states. A heuristic method based on the notion of
cost-penalty-weighted centrality
is analogously developed to obtain a protecting policy, which can well balance the cost and the disruptiveness to users.