Aiming at the scenario where the eavesdropper try to eavesdrop on the confidential messages of secondary trusted users, two physical-layer network coding (PNC) strategies, namely dual power superposition (PS-PS) encoding strategy and bit-level exclusive-or power superposition (XOR-PS) encoding strategy, are proposed to improve the security performance of cognitive non-orthogonal multiple access (NOMA) networks with the help of the data transmitted by the primary user. Considering the overlay spectrum sharing mechanism and the imperfect successive interference cancellation (SIC) technology, we first derive the closed-form accurate expressions of the outage probability and intercept probability of the secondary network with these two schemes over Rayleigh fading, and also give the asymptotic outage probability in the high signal-to-noise ratio (SNR) regime. Then, the correctness of the theoretical results is verified by simulation. For comparison, we also use the scheme without the assistance of the primary user as the benchmark scheme, which is represented by NPS. Finally, the simulation results show that the security of the proposed PS-PS and XOR-PS schemes is much better than that of the NPS scheme in the case of without reducing the outage performance.