  This study investigates the relationship between resilience of control
systems to attacks and the information available to malicious attackers.
Specifically, it is shown that control systems are guaranteed to be secure in
an asymptotic manner by rendering reactions against potentially harmful actions
covert. The behaviors of the attacker and the defender are analyzed through a
repeated signaling game with an undisclosed belief under covert reactions. In
the typical setting of signaling games, reactions conducted by the defender are
supposed to be public information and the measurability enables the attacker to
accurately trace transitions of the defender's belief on existence of a
malicious attacker. In contrast, the belief in the game considered in this
paper is undisclosed and hence common equilibrium concepts can no longer be
employed for the analysis. To surmount this difficulty, a novel framework for
decision of reasonable strategies of the players in the game is introduced.
Based on the presented framework, it is revealed that any reasonable strategy
chosen by a rational malicious attacker converges to the benign behavior as
long as the reactions performed by the defender are unobservable to the
attacker. The result provides an explicit relationship between resilience and
information, which indicates the importance of covertness of reactions for
designing secure control systems.
