Minimum Byzantine Effort for Blinding Distributed Detection in Wireless Sensor Networks In this work, we consider the general problem of distributed detection in the presence of Byzantines using wireless sensor networks. Instead of attempting to mitigate Byzantine attacks as a system designer, we investigate the issue from the perspective of a Byzantine attacker. The probability for each individual sensor to be compromised (compromising probability) required to blind the system operation is adopted as the attack measure. Under the system setting that the fusion center (FC) declares the most likely hypothesis to be true based on the   M  ary data from   N   local sensors, a Byzantine attack policy that can blind the FC with the minimum compromising probability for each individual sensor is derived under the assumption that the Byzantine attacker knows the statistics of the local outputs. The closedform expression for a blindachieving Byzantine transition probability that is used to alter the statistics of the local outputs of compromised sensors is also established. Our results indicate that the statistics of the local outputs is essential for the minimization of an attackeru0027s effort.

Distributed Detection with Empirically Observed Statistics. We consider a binary distributed detection problem in which the distributions of the sensor observations are unknown and only empirically observed statistics are available to the fusion center. The source (test) sequences are transmitted through different channels to the fusion center, which also observes noisy versions of labelled training sequences generated independently from the two underlying distributions. The fusion center decides which distribution the source sequence is sampled from based on the observed statistics, i.e., the noisy training data. We derive the optimal typeII error exponent given that the typeI error decays exponentially fast. We further maximize the typeII error exponent over the proportions of channels for both source and training sequences and conclude that as the ratio of the lengths of training to test sequences tends to infinity, using only one channel is optimal. Finally, we relate our results to the distributed detection problem studied by Tsitsiklis.