Optimal DDoS Attack Strategy for Cyber–Physical Systems: A Multiattacker–Defender Game

This article studies the optimal distributed denial-of-service attack strategy for cyber–physical systems with multiple attackers and multiple defenders. An advanced attack strategy is proposed to cause the great damage to system in a multiattacker–defender form. First, a novel model of signal-to-interference-to-noise ratio for the multiattacker and multidefender is built. Taking the energy constraints into consideration, the objective of defenders is to minimize the system performance, while the attackers tend to deteriorate it by emitting interference energy. Thus, the optimal channel selection and optimal energy allocation strategies are proposed to answer which channel both of them should choose and how much power both of them should allocate to each channel in a finite time horizon. Second, a two-player zero-sum matrix game is formulated to solve the optimal problem by linear programming and obtain the Nash equilibrium. When the channel parameters are time-varying, a dynamic optimal channel selection problem is considered and a multistage game algorithm is proposed to find the Nash equilibrium. In addition, the designed optimal strategies of both players are demonstrated and analyzed. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.