Enforcing current-state opacity through shuffle in event observations

Opacity is a property that ensures that a secret behavior of the system is kept hidden from an Intruder. In this work, we deal with current-state opacity, and propose an Opacity-Enforcer that is able to change, in an appropriate way, the order of observation in the event occurrences in the system, so as to mislead the Intruder to always wrongly estimate at least one non-secret state. A necessary and sufficient condition for the feasibility of the Opacity-Enforcer synthesis is presented and also two algorithms to build the automaton that realizes such an enforcement.Opacidade é uma propriedade que garante que qualquer comportamento secreto do sistema permaneça escondido de um Intruso. Neste trabalho será considerado o problema da opacidade de estado atual e será proposto um Forçador de Opacidade capaz de permutar adequadamente a ordem de observação dos eventos ocorridos no sistema, de tal forma que o Intruso seja enganado e sempre estime, erroneamente, pelo menos um estado não secreto. Condições necessárias e suficientes para a síntese do Forçador de Opacidade são propostas a fim de que a mesma seja factível e são também apresentados dois algoritmos para construção do autômato que implementa a estratégia usada pelo Forçador de Opacidade

Reduced-Complexity Verification for K-Step and Infinite-Step Opacity in Discrete Event Systems

Opacity is a property that captures security concerns in cyber-physical systems and its verification plays a significant role. This paper investigates the verifications of K-step and infinite-step weak and strong opacity for partially observed nondeterministic finite state automata. K-step weak opacity is checked by constructing, for some states in the observer, appropriate state-trees, to propose a necessary and sufficient condition. Based on the relation between K-step weak and infinite-step weak opacity, a condition that determines when a system is not infinite-step weak opaque is presented. Regarding K-step and infinite-step strong opacity, we develop a secret-involved projected automaton, based on which we construct secret-unvisited state trees to derive a necessary and sufficient condition for K-step strong opacity. Furthermore, an algorithm is reported to compute a verifier that can be used to obtain a necessary and sufficient condition for infinite-step strong opacity. It is argued that, in some particular cases, the proposed methods achieve reduced complexity compared with the state of the art