The expanded development of cloud computing is emerging as a new paradigm is known as Fog Computing. The focus of the fog is to achieve fine data processing in the cloud. Apart from everything, authentication is the primary security guard to the system. Since fog is a booming paradigm, the traditional authentication techniques lacks in latency issues and fails to satisfy the requirements of fog computing. In this paper, a new Mutual Authentication Technique using ID (MATID) is introduced to entrust complete mutual authentication between fog users and fog nodes. In this technique, fog users and fog nodes have to register themselves in a common Identity Issuer (IDI) to get their authentication message respectively to collaborate in the network. Fog users and fog nodes have to perform only simple hash functions and XOR operations. Our technique mainly focuses on mutual authentication, trustworthiness and reduced computational and communication costs. It ensures higher security and easily adapted to the fog computing environment