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Many people and organizations are accessing data in the cloud due to the rapid growth of cloud computing .Fog computing interface used between cloud and the end devices to reduce the overhead of the cloud computing and better network services, with secure data transmission requirement. In this paper, Identity Based Broadcast Encryption with Decrypting Time Interval (IBBE-DTI) scheme is proposed for protecting the data securely. This facilitates the data to be encrypted with authentication token which is the combination of private key and identities of users who wants the data. To increasing the security, data owner additionally set decrypting time interval along with the data to be encrypted which leads to additional key namely Time Secret Key (TSK) for decryption. This paper proposed a dual verification process for efficient user authentication based on authorization token, which will be defined by the data owner, and a Unique Signature, which will generate by the fog processor at the time of encryption. This proposed work supports both security of data and verifies the user authentication for efficient data transmission with low computation overhead.