The 3rd Generation Partnership Project (3GPP) has implemented the Authentication and Key Agreement (AKA) protocol in 5G communication networks to ensure user equipment privacy. Due to the high density and concurrent communication, the primary goal is to provide an efficient authentication for massive enhanced Machine Type Communication (eMTC) devices. However, certain security flaws have been discovered in the 5G-AKA protocol, and no scheme has yet been developed that meets the needs of a group of eMTC devices, such as signaling congestion avoidance, key forward/backward secrecy (KFS/KBS) establishment, resistance against malicious attacks, and session key secrecy. Furthermore, the current group-based 5G communication network techniques do not require the group membership update mechanism at each device joining or leaving the group. To address these issues, we present a lightweight and secure technique for assembling a secure ecosystem of eMTC devices in a 5G network. The protocol employs the incremental hash mechanism to complete group member joining/leaving activities. For a thorough assessment of LS-AKA, the Random Oracle Model (ROM) is used to do formal security proofs, and informal security analysis shows that it is resistant to malicious attacks. In addition, the performance and simulation results of the existing and suggested protocols in terms of signaling, communication, and computing overhead are analyzed. According to the assessment results, the LS-AKA protocol improves the privacy and confidentiality of the 5G-enabled smart environment.