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Non-orthogonal multiple access (NOMA) allows multiple users to share link resource for higher spectrum efficiency. It can be applied to unmanned aerial vehicle (UAV) and mobile edge computing (MEC) networks to provide convenient offloading computing service for ground users (GUs) with largescale access. However, due to the line-of-sight (LoS) of UAV transmission, the information can be easily eavesdropped in NOMA-based UAV-MEC networks. In this paper, we propose a secure communication scheme for the NOMA-based UAV-MEC system towards a flying eavesdropper. In the proposed scheme, the average security computation capacity of the system is maximized while guaranteeing a minimum security computation requirement for each GU. Due to the uncertainty of the eavesdropper's position, the coupling of multi-variables and the non-convexity of the problem, we first study the worst security situation through mathematical derivation. Then, the problem is solved by utilizing successive convex approximation (SCA) and block coordinate descent (BCD) methods with respect to channel coefficient, transmit power, central processing unit (CPU) computation frequency, local computation and UAV trajectory. Simulation results show that the proposed scheme is superior to the benchmarks in terms of the system security computation performance.

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