AbstractWith rapid development of next-generation mobile networks and communications (5G networks), group-oriented applications in resource-constrained smart environments (RSEs), such as smart homes and smart classrooms, have attracted great attentions. Due to the insecure communications between resource-constrained devices, secure group communications in RSE toward 5G face many challenges. In RSE toward 5G, lightweight communications and low computational overheads are crucial. Besides, the private tokens used to generate the group key are expected to be reused multiple times. However, the conventional frameworks for secure group communications cannot meet these requirements. A practical construction of extremely lightweight constant-round membership authenticated group key establishment framework is proposed in this paper for RSE toward 5G, which not only implements identity authentication among the members and group key establishment but also ensures extremely lightweight computation and communication costs by each group member. In our proposed scheme, the increase in the number of group members will not lead to a linear or logarithmic increase in the communication and calculation costs at the member side. Our framework also resists external and internal attacks and meets all the desirable security features. In this framework, the privacy of tokens can be well protected, so that they can be reused for multiple times. Therefore, our scheme significantly reduces the costs of communication and calculation, and it is more efficient compared with the related schemes in the literature. This proposal is fairly suitable for lightweight membership authentication and group key establishment in RSE toward 5G.