\textit{When an adversary gets access to the data sample in the adversarial robustness models and can make data-dependent changes, how has the decision maker consequently, relying deeply upon the adversarially-modified data, to make statistical inference? How can the resilience and elasticity of the network be literally justified $-$ if there exists a tool to measure the aforementioned elasticity?} The principle of byzantine resilience distributed hypothesis testing (BRDHT) is considered in this paper for cognitive radio networks (CRNs) $-$ without-loss-of-generality, something that can be extended to any type of homogeneous or heterogeneous networks $-$ while the byzantine primary user (PU) has a signal-to-noise-ratio (SNR) including the coefficient of $\frac{d\ell \big ( θ| \mathscr{s}_0 \big )}{d\ell \big ( θ\big )} $ which is in relation to the temporal rate of the $α-$leakage as the appropriate tool to measure the aforementioned resilience. Our novel online algorithm $-$ which is named $\mathbb{OBRDHT}$ $-$ and solution are both unique and generic over which an evaluation is finally performed by simulations $-$ e.g. an evaluation of the total error as the false alarm probability in addition to the miss detection probability versus the sensing time.