Further results on noise-enhanced distributed inference in the presence of Byzantines

The problem of Byzantine (malicious sensors) threats in a distributed detection framework for inference networks is addressed. Impact of Byzantines is mitigated by suitably adding Stochastic Resonance (SR) noise. Previously, Independent Malicious Byzantine Attack (IMBA), where each Byzantine decides to attack the network independently relying on its own observation was considered. In this paper, we present further results for Cooperative Malicious Byzantine Attack (CMBA), where Byzantines collaborate to make the decision and use this information for the attack. In order to analyze the network performance, we consider KL-Divergence (KLD) to quantify detection performance and minimum fraction of Byzantines needed to blind the network (αblind) as a security metric. We show that both KLD and αblind increase when SR noise is added at the honest sensors. When SR noise is added to the fusion center, we analytically show that there is no gain in terms of αblind or the network-wide performance measured in terms of the deflection coefficient. We also model a game between the network and the Byzantines and present a necessary condition for a strategy (SR noise) to be a saddle-point equilibrium.