Audit Bit Based Distributed Bayesian Detection in the Presence of Byzantines

This paper considers the problem of distributed Bayesian detection in the presence of Byzantines who seek to degrade detection performance by falsifying data. The paper employs an audit bit based mechanism to mitigate Byzantine attacks that partitions sensors into groups. In this framework, local decisions from the sensors in each group reach the fusion center (FC) via multiple paths, which enable the FC to assess (i.e., to audit) the information that reaches it to improve detection performance. In this paper, we consider the audit bit based distributed detection mechanism in the Bayesian framework and derive the optimal fusion rule in the presence of Byzantines. Using probability of error to characterize detection performance of the FC under the optimal fusion rule, we prove that the proposed mechanism is more robust against Byzantine attacks than previously proposed schemes. We show that using the audit bit based mechanism the FC becomes blind (i.e., no useful information reaches the FC) if all the nodes in the network are Byzantines. Furthermore, the paper also introduces the notion of temporal mitigation, namely of mitigating Byzantine attacks over time using audit bits, as well as characterizes optimal Byzantine attacks over time. Extensive numerical results are provided throughout the paper that provide insights into the audit bit based distributed detection mechanism.