This paper considers the noise-enhanced distributed detection problem in the presence of Byzantine (malicious) nodes by suitably adding stochastic resonance (SR) noise. We consider two metrics - the minimum number of Byzantines (αblind) needed to blind the fusion center as a security metric and the Kullback-Leibler divergence (DKL) as a detection performance metric. We show that αblind increases when SR noise is added at the honest nodes. When Byzantines also start adding SR noise to their observations, we see no gain in terms of αblind. However, the detection performance of the network does improve with SR. We also consider a game theoretic formulation where this problem of distributed detection in the presence of Byzantines is modeled as a minimax game between the Byzantines and the inference network, and numerically find Nash equilibria. The case when SR noise is added to the signals received at the fusion center (FC) from the sensors is also considered. Our numerical results indicate that while there is no gain in terms of αblind, the network-wide performance measured in terms of the deflection coefficient does improve in this case.