The next generation of network communications (5G) has the particularity of being heterogeneous, which has different abilities with storage, computing and communication. Group communications is more and more popular for Intelligent Transportation Systems (ITS) in 5G since various smart devices have been constantly connected to ITS over the past decades. One of the main challenges faced by the group communications for ITS towards 5G is how to make the communications secure among these heterogeneous devices. Membership authentication is used to ensure that all users are legitimate group members in ITS communication systems towards 5G. A new type of authentication, called t-secure m-user n-group authentication scheme ((t, m, n) GAS), has been proposed in 2013. GAS is different from conventional peer-to-peer authentications which authenticate users one at a time. GAS can authenticate m users at once. GAS is specially designed for group communications which involve multiple users. Since then, extended research papers on group authentication have been published. A discrete-logarithm-based GAS with multiple authentications has been proposed in the original paper. In this paper, based on homomorphic secret sharing (HSS), a novel multiple group authentication is presented, which is more lightweight and robust than the original scheme. The security of the proposed scheme is unconditionally secure without any assumption. More importantly, since polynomial evaluations with a smaller modulus are needed in our proposed scheme, it is more efficient than the original scheme which needs modular exponentiations with a larger modulus, thus this design is more suitable for lightweight multiple group authentication in ITS towards 5G.