The extension of the cloud that provides services to a massive scale of end users to enhance efficient performance is coined as Fog Computing. Whenever a new paradigm arises, a challenging and vital issue is authentication for security. This paper proposes a new improvised Trustworthy Mutual Authentication Technique (TMAT) to achieve complete mutual authentication between end users and fog nodes using IDs in fog computing. Here, the trusted ID issuer is implemented between end users and fog nodes. They receive their authentication ticket while registering themselves with the Trusted ID Issuer (TID). It involves only simple XOR operations and one-way hash functions. The efficiency of the technique is analyzed by implementing various pseudo-random number generators (PRNG) and is obtained within a limited resource environment. This technique is more secure and efficient by avoiding the storage of a master key and repetitions of session keys. It ensures Dynamic Authentication with the usage of minimal infrastructure architecture.