Reconfigurable intelligent surface (RIS) has the capability of boosting system performance by manipulating the wireless propagation environment. This paper investigates a downlink RIS-aided non-orthogonal multiple access (NOMA) system, where a RIS is deployed to enhance physical-layer security (PLS) in the presence of an eavesdropper. In order to improve the main link's security, the RIS is deployed between the source and the users, in which a reflecting element separation scheme is developed to aid data transmission of both the cell-center and the cell-edge users. Additionally, the closed-form expressions of secrecy outage probability (SOP) are derived for the proposed RIS-aided NOMA scheme. To obtain more deep insights on the derived results, the asymptotic performance of the derived SOP is analyzed. Moreover, the secrecy diversity order is derived according to the asymptotic approximation in the high signal-to-noise ratio (SNR) and main-to-eavesdropper ratio (MER) regime. Furthermore, based on the derived results, the power allocation coefficient and number of elements are optimized to minimize the system SOP. Simulations demonstrate that the theoretical results match well with the simulation results and the SOP of the proposed scheme is clearly less than that of the conventional orthogonal multiple access (OMA) scheme obviously.