Shamir’s secret sharing scheme is one of the substantial threshold primitives, based on which many security protocols are constructed such as group authentication schemes. Notwithstanding the unconditional security of Shamir's secret sharing scheme, protocols that are designed based on this scheme do not necessarily inherit this property. In this work, we evaluate the security of a lightweight group authentication scheme, introduced for IoT networks in IEEE IoT Journal in 2020, and prove its weakness against the Linear subspace attack, which is a recently-proposed cryptanalytical method for secret sharing-based schemes. Then, we propose an efficient and attack-resistant group authentication protocol for IoT networks.