<p>The convergence of Smart Grid (SG) technology and the Internet of Things (IoT) presents a transformative opportunity for modernizing traditional power grids. A secure and reliable connection between smart meters and service providers is paramount for the effective operation of SG systems. In this paper, we introduce the Energy-Efficient IoT Resilient Authentication Framework (EERAF), an innovative solution that leverages elliptic curve cryptography to facilitate secure communication and authentication. Our framework establishes a protected channel that enhances the integrity and confidentiality of data exchanged between smart meters and service providers. To validate the security of EERAF, we conduct a rigorous formal analysis utilizing the random oracle model and Ban Logic for mutual authentication. Furthermore, we assess the proposed protocol with the Scyther tool, demonstrating its robustness against a spectrum of security threats. Compared to existing authentication protocols, EERAF not only achieves superior security standards but also significantly reduces computational and communication overhead. Ultimately, our framework provides a reliable and energy-efficient solution to improve connectivity in the Internet of Electric Things, addressing the pressing need for secure, scalable, and sustainable smart grid communications.</p>