The objective of this paper is to propose techniques for enhancing the physical layer security (PLS) performance of half-duplex cooperative non-orthogonal multiple access (HD-CNOMA) network in the presence of an external passive eavesdropper. We propose an artificial noise (AN)-aided framework and derive approximate analytical expressions for the secrecy outage probabilities (SOPs) of the downlink users. It is demonstrated that the proposed AN-aided framework significantly reduces the SOPs of the users and completely resolves the zero-diversity order problem, which is prevalent in HD-CNOMA network without AN. To further enhance the PLS performance, we determine optimal power allocation coefficients (OPACs) for the downlink users at the base station (BS) that minimizes the system SOP (SSOP) of the AN-aided HD-CNOMA network. With the help of extensive numerical and simulation investigations, it is shown that the proposed OPAC leads to significant reduction of the SSOP, while lowering the SOPs of the users, compared to random/equal setting of the PACs.