  This paper addresses the question whether model knowledge can guide a
defender to appropriate decisions, or not, when an attacker intrudes into
control systems. The model-based defense scheme considered in this study,
namely Bayesian defense mechanism, chooses reasonable reactions through
observation of the system's behavior using models of the system's stochastic
dynamics, the vulnerability to be exploited, and the attacker's objective. On
the other hand, rational attackers take deceptive strategies for misleading the
defender into making inappropriate decisions. In this paper, their dynamic
decision making is formulated as a stochastic signaling game. It is shown that
the belief of the true scenario has a limit in a stochastic sense at an
equilibrium based on martingale analysis. This fact implies that there are only
two possible cases: the defender asymptotically detects the attack with a firm
belief, or the attacker takes actions such that the system's behavior becomes
nominal after a finite time step. Consequently, if different scenarios result
in different stochastic behaviors, the Bayesian defense mechanism guarantees
the system to be secure in an asymptotic manner provided that effective
countermeasures are implemented. As an application of the finding, a defensive
deception utilizing asymmetric recognition of vulnerabilities exploited by the
attacker is analyzed. It is shown that the attacker possibly stops the attack
even if the defender is unaware of the exploited vulnerabilities as long as the
defender's unawareness is concealed by the defensive deception.
