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In this paper, we develop a non-orthogonal multiple access (NOMA)-based two-way relay network with secrecy considerations, in which two users wish to exchange their NOMA signals via a trusted relay in the presence of single and multiple eavesdroppers. To ensure secure communications, the relay not only forwards confidential information to the legitimate users but also keeps emitting jamming signals all the time to degrade the performance of any potential eavesdropper. Moreover, we equip the relay and each user with the full-duplex technique in the multiple-access phase to combat the eavesdropping and improve the data transmission efficiency, respectively. We propose different decoding schemes based on the successive interference cancellation for the legitimate users, relay, and eavesdroppers. Closed-form expressions for the achievable ergodic secrecy rates of all data symbols under both single- and …