  \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 ( \theta | \mathscr{s}_0 \big )}{d\ell \big ( \theta \big
)} $ which is in relation to the temporal rate of the $\alpha-$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.
