Mathematical Modeling of Cyber Attack and Defense

Abstract

In this paper, a new game formulation is proposed that combines simulation and game-theoretical approaches to the application of security games in cyberspace. The model presented here builds upon a security economic approach that models the adversary and defender motives and goals in the context of empirically derived countermeasure efficacy metrics. The approach is based on a two-player strategic game to determine optimal strategy selection for both adversary and defender. Besides, not only the solution to the game but also a mathematical and graphical representation of “what if” scenarios in the context of the game. In this study, it has been shown that game-theoretic calculations can serve as a useful tool for identifying effective strategies in cyberwar games. For scenarios that need to penetrate multiple layers in a defense-in-depth security configuration, the calculation of the attacker's and defensive costs and the probability of infiltration requires the presence of cost-benefit matrices and probability matrices. Inspection of the matrices allows players to deduce preferred strategies based on game-theoretical equilibrium solutions. The matrices also help in analyzing the anticipated effects of potential human-based choices of wargame strategies and counter-strategies. Also, a mathematical game-theoretical form has been defined. This paper shows how game-theoretical calculations can indeed provide a useful tool for effective decision-making during cyber wars.