In this article, we propose an online electronic counter-countermeasure (ECCM) framework designed to conceal the strategic decision-making processes of a cognitive radar (CR) operating under adversarial surveillance. We model the CR under two distinct decision paradigms: a static constrained utility-maximizing behavior and a dynamic expected utility-maximizing behavior. The radar's utility function is modeled via a von Mises--Fisher (vMF) distribution, with the distributional parameter constituting the private information to be protected from adversarial inference. We adopt a distribution privacy framework to conceal this private information and provide formal distribution privacy guarantees for cognition masking. In this work, we develop cognition-hiding algorithms for both static constrained utility maximization (WDPCH-SU), and dynamic expected utility maximization (WDPCH-DU). Through rigorous mathematical analysis, we show that both WDPCH-SU and WDPCH-DU satisfy
ε-distribution privacy (
ε-DistP) against inference-based adversarial attacks and present the privacy--performance trade-off bounds, quantifying utility loss (in static setting) and expected utility deviation (in dynamic setting) as functions of
ε. Numerical results show that WDPCH-SU gives about 15% improvement in utility loss at maximum privacy compared to the existing methodology while WDPCH-DU achieves a greater reduction in adversarial Fisher information without requiring explicit Fisher information constraints, at a moderate, analytically bounded utility deviation. These results are highly promising in many 6G communication scenarios such as network slicing for automated driving and swarm UAV coordination, where it is essential to keep the resource allocation policy robust against privacy attacks.