Energy Internet (EI) is a two-way data flow that allows electric service providers and consumers to investigate and change their energy usage. EI should be free of cyber-attacks in order to provide secure, efficient, and dependable communication system operations. Using elliptic curve cryptography and the hash function, this paper proposes a key agreement and authentication framework for vehicular to grid networks. Using key agreement, a vehicular user can securely access services provided by the grid server in this protocol. We also talk about informal security analysis of the proposed protocol which is based on security attacks and security attributes. We show the correctness of the proposed framework through a formal security analysis of the proposed framework using a random oracle model. In addition, we demonstrate that the proposed framework has lower computation and communication costs than other V2G frameworks