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• Cooperative NOMA Systems. • Physical-Layer Security. • Secure Communication Systems. • Passive Eavesdropping. A key feature of the non-orthogonal multiple access (NOMA) technique is that users with better channel conditions have prior knowledge about the information of other weak users. Given this prior knowledge, the idea that a strong user can serve as a relay node for other weak users in order to improve their performance, is known as cooperative NOMA. In this paper, we study the physical layer security of such a cooperative NOMA system. In order to reduce the complexity of the analytical process, the considered system in this paper has three users, in which the performance of the weaker users are enhanced by the stronger users. Given that there is an eavesdropper in the system that can hear all the transmissions, we study the secrecy performance of all the users. More specifically, we make an attempt to derive the ergodic secrecy capacity (ESC) and secrecy outage probability (SOP) of all the users. Due to the intractable nature of the exact analysis for the weak users, we provide the closed form expressions of the ESC and SOP for these users at the high SNR regime, while providing the exact analysis for the strongest user. Targeting on the optimality, we further reveal that better secrecy performance of the system is achievable through an appropriate power control mechanism. Finally, based on the analytical methodology of the three-user cooperative system, we provide insightful observations on the performance (in terms of ESC and SOP) of a multi-phase cooperative NOMA system with N users at the high SNR regime. Through rigorous numerical simulations, we verify the correctness of our analytical derivations under different practical scenarios while providing evidence of achieving optimal secrecy performance with the proposed power control scheme. [ABSTRACT FROM AUTHOR]