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We propose a novel non-orthogonal multiple access (NOMA)-inspired jamming and relaying scheme to enhance the physical layer security of untrusted relay networks. Particularly, during the first phase, with the application of the downlink NOMA principle, the source sends a superimposed version of a desired signal and a jamming signal, where the jamming signal is designed to deliberately confuse the untrusted relay by exploiting the beamforming design and adapting the transmission rate at the source. During the second phase, relying on the uplink NOMA principle, the untrusted relay forwards its received signals and, simultaneously, the source transmits a new desired signal that cannot be wiretapped by the untrusted relay to maximize the secrecy sum rate. Scenarios of single-antenna and multiple-antenna relaying are considered, and the impact of different antenna configurations at the source and the …