As a result of the rapid developments in digital technologies, smart cities have been adorned with several digital gadgets based on the Internet of Things (IoT). The essential part of smart cities operations is IoT communications. IoT devices generate, process, and exchange a large amount of security-critical and privacy-sensitive data regularly, resulting in attractive targets for threats and attacks. Group-oriented communication plays a critical role in the IoT world, such as data gathering and area monitoring. The lower time complexity of Group-based authentication (GBA) makes these protocols very popular for efficient and secured communication. This paper uses a polynomial-based group authentication scheme and membership verification to ensure efficient and threat-free communication among IoT devices. Furthermore, a Bi-variate polynomial is used instead of the single variable polynomial to add the novelty of the work. Along with novelty, the protected nature of the bi-variate polynomial makes the proposed scheme very secure and reliable. Security analysis of the proposed work shows its efficiency over existing schemes.