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This paper considers the secrecy outage performance of a multiple-relay assisted non-orthogonal multiple access (NOMA) network over Nakagami-m fading channels. Two time slots are utilized to transmit signals from the base station to destination. At the first time slot, the base station broadcasts the superposition signal of the two users to all decode-and-forward relays by message mapping strategy. Subsequently, the selected relay transmits superposition signal to the two users via power-domain NOMA technology. Three relay selection schemes, i.e., optimal single relay selection (OSRS) scheme, two-step single relay selection (TSRS) scheme, and optimal dual relay selection (ODRS) scheme are proposed and the secrecy outage performance is analyzed. As a benchmark, we also examine the secrecy outage performance of the NOMA systems with traditional multiple relay forwarding (TMRF) scheme in which …