One of the essential challenges to Fog computing security is authentication between service offering Fog servers and Fog users. This security confirmation is critical as a large number of users are offered services in Fog Computing. To address this challenge, in this paper, we first propose an efficient mutual authentication method between Clouds-Fogs-Edges. The solution enables authentication between edge users and the Fog servers that newly enter the system. The method makes the Fog servers to store one secret key per user and the user performs hash-based encryptions/decryptions. The proposed system is supported by Blockchain technique to achieve data integrity when confidential data are transferred between edge devices and nodes. The transactions between the nodes are recorded in the blocks which are hashed so that all edge and fog nodes are encircled by a secured system. Whenever any malicious edge server enters the network, it is identified based on ledger maintained at the nodes. The security and performance analysis shows the scheme is applicable for the Fog computing environment.