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In wireless security, cognitive adversaries are known to inject jammingenergy on the victim's frequency band and monitor the same band forcountermeasures thereby trapping the victim. Under the class of cognitiveadversaries, we propose a new threat model wherein the adversary, uponexecuting the jamming attack, measures the long-term statistic ofKullback-Leibler Divergence (KLD) between its observations over each of thenetwork frequencies before and after the jamming attack. To mitigate thisadversary, we propose a new cooperative strategy wherein the victim takes theassistance for a helper node in the network to reliably communicate its messageto the destination. The underlying idea is to appropriately split their energyand time resources such that their messages are reliably communicated withoutdisturbing the statistical distribution of the samples in the network. Wepresent rigorous analyses on the reliability and the covertness metrics at thedestination and the adversary, respectively, and then synthesize tractablealgorithms to obtain near-optimal division of resources between the victim andthe helper. Finally, we show that the obtained near-optimal division of energyfacilitates in deceiving the adversary with a KLD estimator.

On Distribution-Preserving Mitigation Strategies for Communication under Cognitive Adversaries