Cognitive radio (CR) and non-orthogonal multiple access (NOMA) are two technologies witnessed to offer tremendous possibilities for the next generation wireless networks to maximise their usage of available spectrum. In this work, we evaluate the performance of a downlink overlay secure CR-NOMA system while the secondary transmitter (ST) is used as a decode-and-forward (DF) relay to assist the primary transmitter (PT) to transmit information to the destination i.e., primary user (PU), while covertly transmitting its own information to the secondary user (SU) against the eavesdropper (Eve) of PT. The secrecy performance comparison between two users i.e., PU and SU are obtained under perfect and imperfect successive interference cancellation (SIC), respectively. Furthermore, this paper investigates the secrecy performance comparison between the proposed overlay downlink CR-NOMA system comprising of single antenna (SA) and multiple antennas (MA) in terms of various performance metrics such as secrecy sum rate (SSR), the average secrecy rate (ASR), the average secrecy sum rate (ASSR), strictly positive secrecy rate (SPSC) and secrecy outage probability (SOP). It is to be noted that in our proposed system, MAs are equipped at both PT and ST with the main purpose to provide cooperative diversity and we employ both maximal ratio combining (MRC) and selection combining (SC) diversity techniques for processing the received signals at the PU/Eve which further improves the system's capacity and enhances the secrecy performance. In addition, for characterizing the secrecy performance of the proposed overlay CR-NOMA network, we present thoroughly the derivations of novel closed-form analytical expressions of the performance metrics such as SOP, SPSC and the ASR by taking into account both perfect SIC (pSIC) and imperfect SIC (ipSIC) scenarios. Based on the analytical frameworks, the numerical and simulation results are obtained under different network parameters. Towards this end, the outcomes of the simulation are shown to prove both the reliability of the mathematical analysis and the accuracy of the suggested technique.INDEX TERMS Non-orthogonal multiple access, physical layer security, overlay cognitive radio, secrecy rate, average secrecy rate, strictly positive secrecy rate.