Game Model Based Intrusion Detection Method for Probability Distribution Attacks

In this paper, a game theoretical analysis method is presented for a kind of probability distribution attacks. By considering Cumulative Sum (CUSUM) as fusion intrusion detector, a non-cooperative game model is established to describe the confrontation between the attacker and the defender. The strategies of the players are selected to be attack power and detection threshold, and the payoffs are defined as the damage to the targeted systems with respect to false positive and negative rates. The optimization curves of the payoff functions are exploited to analyze the properties of Nash equilibrium. It’s proved that the Nash equilibrium of the game model must exist and must also be unique. Also, the specific expression of the Nash equilibrium point is provided, which gives a way to select the optimal detection strategies. Besides, communication periodicity and Kalman filtering based intrusion detection are introduced as two real scenarios to show the applicability of the presented method. At last, a numerical example is utilized to verify the conclusions.