  In this paper, we consider the problem of distributed Bayesian detection in
the presence of Byzantines in the network. It is assumed that a fraction of the
nodes in the network are compromised and reprogrammed by an adversary to
transmit false information to the fusion center (FC) to degrade detection
performance. The problem of distributed detection is formulated as a binary
hypothesis test at the FC based on 1-bit data sent by the sensors. The
expression for minimum attacking power required by the Byzantines to blind the
FC is obtained. More specifically, we show that above a certain fraction of
Byzantine attackers in the network, the detection scheme becomes completely
incapable of utilizing the sensor data for detection. We analyze the problem
under different attacking scenarios and derive results for different
non-asymptotic cases. It is found that existing asymptotics-based results do
not hold under several non-asymptotic scenarios. When the fraction of
Byzantines is not sufficient to blind the FC, we also provide closed form
expressions for the optimal attacking strategies for the Byzantines that most
degrade the detection performance.
