## 3 Preliminaries  
### Network System  
Figure 1 shows the system model, and the notations are summarized in Table 2. In this work, we consider the cloud and fog layers as trusted entities. On the other hand, the end user's layer is untrusted entities. System-parameter generation, system security-level determination, attribute center work, the scheduling of fog-computing resources, the processing of end-user access authentication requests and key generation are all tasks that fall under the purview of the cloud service provider. Fog nodes communicate with end users, the authentication of users, the outsourcing of data encryption and assuring that legitimate end  
users can decrypt the information by fulfilling the specific attribute requirements. The data owner encrypts the plaintext with his private key so that unauthentic users cannot decrypt the ciphertext. When the access user makes an access request, it will first check whether the ciphertext can be correctly decrypted or not. The fog node is designated for outsourcing decryption if it can be correctly decrypted. After receiving decrypted ciphertexts from the fog node, the user decrypts the ciphertext to obtain the plaintext. Consequently, we discuss the functionality of each entity:  
1. Central Authority (\(CA\)): Is the system's global authorized certificate authority. It accepts all end users and the attribute authorities in the system to be registered. The \(CA\) establishes a specific global end-user identity (\(uid\)) and a unique attribute authority identity (\(aid\)) in the network for each end user. In this proposed method, the \(CA\) is responsible for the registration requests from both end users and \(AAs\). However, it is not involved in attribute operations and private keys. Hence, the system is still secure if there is an attack on the \(CA\). This is because the \(CA\) cannot leak the end user's private information. 2. Attribute Authority (\(AA\)): Is accountable for entitling and revoking the end users' attributes according to the attribute identity (\(aid\)). Each attribute authority (\(AA\)) produced its public key and provided attribute-related secret keys according to the end users. When the \(AA\) is attacked, it only affects the security of its related attributes and cannot affect the system's security. Consequently, the overall network is more secure than the approach used in a single authorization center. 3. Cloud Service Provider (\(CSP\)): Leverages the storage of data and key management. When an attribute-revocation event occurs, the revoked end user's access is averted to re-encrypt the ciphertext. 4. Fog Node: Undertakes the encryption and decryption. The data owner and end users outsource the cryptography process to fog nodes, thus reducing the computation burden of the end users. 5. Data Owners (\(DO\)s): Are defined by an \(a_{p}\) for that data that require the encryption. They also leverage the targeted end users and the scope of the authorized end users. 6. End users: We consider the object of the attribute revocation as the end users. When end users want to access the data, they can download them and decrypt them through fog nodes from the cloud-server provider. Users can view the data that adhered to the access policies. Thus, unauthorized and unattributed end users cannot access the data, thereby controlling fine-grained information.