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.