Game theoretic approach of eavesdropping attack in millimeter-wave-based WPANs with directional antennas

Abstract

In this paper, we propose a game theoretic framework to analyze a passive eavesdropping attack in millimeter-wave-based wireless personal area networks. As the interaction between defenders and attackers in network security issues can be considered as a game, devices can be considered as players. Usually a player has insufficient information of other players such as strategies and payoffs especially in static situation. We assume that each player selects its strategy based on its belief about the information on opponents and the belief is known as a prior probability. The Bayesian game model is a relevant framework for this situation. It is assumed that each device is equipped with a directional antenna and knows the channel state. In the analysis, the exposure region (ER) that is determined by the antennas directions of players is considered and the ratio of ER for the total area of a network is calculated by using the probability density function of distance between players. The optimal strategies of two players, a transmitter and an eavesdropper, are derived in terms of Bayesian Nash equilibriums and payoffs for the players are computed for pure and mixed strategies in static situation. The analysis shows how the effects of using a directional antenna and the prior probability of transmitters belief are involved in the Nash equilibriums. Numerical results show the equilibriums and two players payoffs. Those values depend on several parameters such as beamwidth and prior probability of belief as well as its opponents strategies. It also shows the effect of directional antennas in the eavesdropping attack; the use of directional antenna seems to increase the transmitters payoff, while it seems to decrease the eavesdroppers payoff. The obtained results will provide the criteria for selecting appropriate strategy to transmitters when an eavesdropper exists in the network.