A Game-Theoretic Framework for Optimum Decision Fusion in the Presence of Byzantines

Abstract

Abstract-Optimum decision fusion in the presence of malicious nodes -often referred to as Byzantines -is hindered by the necessity of exactly knowing the statistical behavior of Byzantines. By focusing on a simple, yet widely studied, set-up in which a Fusion Center (FC) is asked to make a binary decision about a sequence of system states by relying on the possibly corrupted decisions provided by local nodes, we propose a game-theoretic framework which permits to exploit the superior performance provided by optimum decision fusion, while limiting the amount of a-priori knowledge required. We first derive the optimum decision strategy by assuming that the statistical behavior of the Byzantines is known. Then we relax such an assumption by casting the problem into a game-theoretic framework in which the FC tries to guess the behavior of the Byzantines, which, in turn, must fix their corruption strategy without knowing the guess made by the FC. We use numerical simulations to derive the equilibrium of the game, thus identifying the optimum behavior for both the FC and the Byzantines, and to evaluate the achievable performance at the equilibrium. We analyze several different setups, showing that in all cases the proposed solution permits to improve the accuracy of data fusion. We also show that, in some instances, it is preferable for the Byzantines to minimize the mutual information between the status of the observed system and the reports submitted to the FC, rather than always flipping the decision made by the local nodes as it is customarily assumed in previous works.

Binary Hypothesis Testing With Byzantine Sensors: Fundamental Tradeoff Between Security and Efficiency

“…Finally, we should note that we do not assume any pattern of the bias y a i (k) for i ∈ I, i.e., the malicious bias injected may be correlated across the compromised sensors and correlated over time. Compared to the independence assumption in [5]- [10], [13], our assumption improves the effectiveness of the attacker and is more realistic in the sense that the attacker is malicious and will do whatever it wants. Remark 1.…”

“…The authors in [11] showed that the optimal detector is of a threshold structure when the fraction of Byzantine sensors is less than 0.5. A zero-sum game was formulated in each of [12]- [14], among which a closed-form equilibrium point of attack strategy and detector was obtained in [14], computation efficient and nearly optimal equilibrium point (exact equilibrium point only in certain cases) was obtained in [12], and numerical simulations were used to study the equilibrium point in [13].…”

“…While in [5]- [10], [13] the Byzantine sensors are assumed to generate malicious data independently, this work, as in [11], [12], [14], assumes that the Byzantine sensors may collude with each other. The collusion model is more reasonable since the attacker is malicious and will arbitrarily change the messages of the sensors it controlls.…”

“…Notice also that compared to the independence model, the collusion model complicates the analysis significantly. Unlike [6]- [10], [12], [13], where the sensors only send binary messages, this work, as in [5], [11], [14], assumes that the measurements of a benign sensor can take any value. Since the binary message model simplifies the structure of corrupted measurements, and, hence, implicitly limits the capability of an attacker, it is easier to be dealt with.…”

Strategic Surveillance Against Primary User Emulation Attacks in Cognitive Radio Networks

“…Consequently, the attacker will gain nothing from the selfish PUE attack. Also, the defender cannot distinguish the PU signal from the attacker's signal 7 . We hence obtain the payoff of each player for a pair of actions regarding the presence of the PU at the t th channel as given in Table I.…”