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In this letter, we consider a two-way relay cognitive satellite terrestrial network (CSTN) in the presence of a friendly jammer and an eavesdropper (Eve). In this system, we investigate the tradeoff between the secure spectrum efficiency (SSE) and the secure energy efficiency (SEE). To be specific, firstly, two frames corresponding to the busy and idle working states of the primary users (PUs) are designed to flexibly analyze the system performance. Secondly, the SSEs, SEEs, and utility functions for both the cognitive satellite network and the terrestrial primary network are deduced, respectively, considering the different working states of the PUs and the Eve. Finally, based on the Stackelberg Game model, the mathematically intractable problem on the spectrum-energy exchange is solved, thus we maximize the SSE and the SEE jointly. Numerical results are given to validate that there exists an SSE-SEE tradeoff …