In this paper, we consider a reconfigurable intelligent surface (RIS)-enhanced uplink non-orthogonal multiple access (NOMA) communication system, where the users transmit confidential information to the base station (BS) in the presence of an eavesdropper. We evaluate the impact of transmit power, distance of users and eavesdropper from RIS, and split factor of the RIS on the secrecy performance of the considered system under Nakagami-m fading channels. The simulation results reveal that the secrecy rate increases with an increase in both the transmit power of the users and the distance of the eavesdropper from RIS, while the secrecy rate degrades with an increase in the distance of users from the RIS. Moreover, there is an increase in the secrecy rate of weak user of the NOMA pair and a decrease in the secrecy rate of NOMA strong user with an increase in the split ratio as the number of RIS elements for the weak user increases.