  The problem of distributed inference with M-ary quantized data at the sensors
is investigated in the presence of Byzantine attacks. We assume that the
attacker does not have knowledge about either the true state of the phenomenon
of interest, or the quantization thresholds used at the sensors. Therefore, the
Byzantine nodes attack the inference network by modifying modifying the symbol
corresponding to the quantized data to one of the other M symbols in the
quantization alphabet-set and transmitting the false symbol to the fusion
center (FC). In this paper, we find the optimal Byzantine attack that blinds
any distributed inference network. As the quantization alphabet size increases,
a tremendous improvement in the security performance of the distributed
inference network is observed.
  We also investigate the problem of distributed inference in the presence of
resource-constrained Byzantine attacks. In particular, we focus our attention
on two problems: distributed detection and distributed estimation, when the
Byzantine attacker employs a highly-symmetric attack. For both the problems, we
find the optimal attack strategies employed by the attacker to maximally
degrade the performance of the inference network. A reputation-based scheme for
identifying malicious nodes is also presented as the network's strategy to
mitigate the impact of Byzantine threats on the inference performance of the
distributed sensor network.
