Re-configurable Intelligent Surfaces (RIS) technology is increasingly becoming a potential component for next-generation wireless networks, offering enhanced performance in terms of throughput, spectral, and energy efficiency. However, the broadcast nature of RIS-assisted wireless communication makes it vulnerable to malicious attacks at the physical layer. At the same time, physical layer authentication is gaining popularity as a solution to secure wireless networks, thwarting different attacks such as cloning, spoofing, and impersonation by using the random features of the physical layer. In this paper, we investigate RIS-assisted wireless communication systems to unlock the potential of using RIS for physical layer authentication (PLA). In particular, we exploit two distinct features of the physical layer: pathloss and channel impulse response (CIR) for PLA in RIS-assisted wireless communication. We construct hypothesis tests for the estimated features and derive closed-form error expressions. Further, we consider the critical error, i.e., missed detection, as our objective function to minimize by optimizing the phase shift of the RIS pannel. We compare the performance of our proposed mechanisms with PLA schemes using the same features but with no RIS. Furthermore, we thoroughly evaluate our proposed schemes using performance metrics such as the probability of false alarm (PFA), the probability of missed detection (PMD), and the receiver operating characteristic (ROC) curves. The results demonstrate a clear positive impact of RIS on PLA, as it effectively reduces PMD values to zero when determining the optimal phase shift.