In this work, we provide a unique post-quantum three-party key exchange protocol that makes use of the ring learning with error assumption. This protocol is inspired by the authenticated key exchange protocol developed by Rewal et. al [1]. We revisit the recently suggested system by Rewal et. al. [1], which is a communication efficient three-party password authenticated key exchange, in which we found that scheme is not fully correct and also demonstrate that scheme is not safe from user's anonymity assaults. We provide a enhanced scheme that is both effective and resistant to the mentioned assault. We also demonstrate its security in a ROM (Random Oracle Model). A comparison analysis that includes performance and security evaluations is also provided, proving the suitability of the suggested design.