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Despite the wide utilization of unmanned aerial vehicles (UAVs), UAV communications are susceptible to eavesdropping due to air-ground line-of-sight channels. Intelligent reflecting surface (IRS) is capable of reconfiguring the propagation environment, and thus is an attractive solution for integrating with UAV to facilitate the security in wireless networks. In this paper, we investigate the secure transmission design for an IRS-assisted UAV network in the presence of an eavesdropper. With the aim at maximizing the average secrecy rate, the trajectory of UAV, the transmit beamforming, and the phase shift of IRS are jointly optimized. To address this sophisticated problem, we decompose it into three sub-problems and resort to an iterative algorithm to solve them alternately. First, we derive the closed-form solution to the active beamforming. Then, with the optimal transmit beamforming, the passive beamforming …