Fog computing is a system of decentralized computing in which data, applications, compute, and data storage are distributed among the data source (i.e., smart devices) and the cloud in the most logical and effective locations. Fog computing inherits security and privacy issues from cloud computing, ensuring enhanced security and privacy. Authentication is crucial for security in fog computing systems, requiring a new technique with lightweight encryption and mutual authentication to prevent malicious attacks and protect communication channels. Thus, we designed a secure and mutual authentication scheme for fog computing based on a hybrid (Advanced Encryption Standard and Elliptic Curve cryptography) algorithm. The scheme improves secure authentication and key exchange schemes between edge devices and fog nodes. The scheme was verify for security analysis using formal security verification under the widely known and accepted AVISPA (Automated Validation of Internet Security Protocols and Applications) tool. We proved our scheme using Burrows Abdi Needham’s logic (BAN logic) to ensure that the scheme was secure through mutual authentication. The results show that our scheme provides better and more secure communication and authentication service than the existing schemes. Keywords: authentication, fog computing, hybrid cryptography