This paper proposes exploiting multiple aerial reconfigurable intelligent surfaces (ARISs) for the secrecy performance enhancement of non-orthogonal multiple access (NOMA) networks. More specifically, multiple ARISs are deployed to aid two legitimate NOMA users when multiple non-colluding eavesdroppers (NCEs) also try to receive and detect the messages. Moreover, the transmitter-user paths are combined with the transmitter-ARIS-user paths at the users to increase the received message power. The mathematical expressions of secrecy outage probabilities (SOPs) of the proposed networks (referred to as the NOMA-ARIS networks) are derived over realistic Nakagami-m channels recommended for the fifth/beyond generations (5G/B5G) of wireless systems. In addition, the asymptotic expressions of SOPs in the high transmit power region are also provided. Numerical findings unequivocally indicate that the SOPs of the proposed NOMA-ARIS networks are significantly lower than those of the classical NOMA networks without ARISs. Moreover, the lowest SOPs of the proposed NOMA-ARIS networks are achieved faster than those of the classical NOMA networks. Consequently, utilizing ARISs can significantly reduce the transmit power and dramatically improve the secrecy performance of NOMA networks. On the other hand, some valuable recommendations are discussed after deeply investigating the effects of crucial parameters such as the number of reflecting elements (REs) in ARISs, secrecy target rate, position of NCEs, fading order, and power allocation coefficients on the SOPs of the proposed NOMA-ARIS networks.
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