## 1 Introduction  
Fog computing is a promising computational framework extending cloud computing to the network's edge for a smooth interconnection between cloud computing and resource-constraint devices [1; 2; 3; 4]. The primary benefit of fog computing is the delivery of robust capabilities to resource-constraint devices in terms of processing and storage while being closer to end devices [5]. Security concerns have yet to be resolved regardless of the advantages of fog computing [6]. This includes data protection and access control for devices with limited resources [7]. Resource-constrained devices are more susceptible and unreliable because fog nodes are considered on the edge of the network and are inexpensive as compared to cloud servers. The novel proposed solution to these issues is to encrypt the information before uploading it to the fog node. As a result, the attribute-based encryption (ABE) notion is a one-to-many cryptographic approach [8]. The traditional ABE is an encryption process depending on multiple attributes of the private and public keys [9]. However, the scheme is inappropriate for end devices due to limited computational resources, complex management and high computational times [10; 11; 12]. Nevertheless, the encryptor may not be required to recognize the end user's precise details and only needs to embed the attribute into the ciphertext. End users decrypt information only if their attributes match the access structure. The procedure enables access control over data encryption between secret keys and ciphertext via access policies and assigned attributes. In this regard, the ciphertext policy-attribute-based encryption (CP-ABE) allows data owners to establish the access policy for various end-user attributes to decrypt the ciphertext. For instance, ciphertext validity can be ensured by public verification, and valid ciphertexts must be stored or transmitted. In the primitive process, end users in the fogs generated private keys from multiple authorities whose geographical locations or functions might differentiate. Another cryptographic primitive process known as server-aided revocable bilateral ABE can be used to secure and lightweight bilateral access control systems. This includes fine-grained data users and data-owner access control simultaneously, outsourced data source identification, server-aided user revocation and data decryption with exponentiation computation. Moreover, the CP-ABE can verify the outsourcing of encryption and decryption to any untrusted encryption and decryption service provider. This allows us to outsource encryption and decryption processes by using modular exponentiation for the single untrusted server to generate the transformation of keys. The existing CP-ABE-based solutions, however, primarily concentrate on how end users can manage secured data access. Few works considered the access control requirements of fog nodes from resource-constraint devices. However, several instances of end-user equipment access to the network makes end-user management extremely difficult. Also, the encryption and decryption operations of CP-ABE require several exponentiations modules directly related to the number of attributes. This poses a fundamental problem for end users to access and change the data on resource-constrained gadgets, having a limited storage capacity and computation. We propose the MA-CP-ABE technique to enable attribute revoking and computation outsourcing for resource-constraint devices in fog computing. The contributions of this work are summed up below:  
1. We propose a multiauthority ciphertext policy-attribute-based encryption (MA-CP-ABE) scheme that enables multiauthority attribute revocation and computation outsourcing. In this regard, we propose a seven-layer reference model, i.e., edge node, communication, edge computing, data accumulation, data abstraction, applications, users and centers. 2. We investigate an attribute-revocation scheme by exploiting MA-CP-ABE.