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Fog computing as an extension of cloud computing provides computation, storage and application services to end users. Ciphertext-policy attribute-based encryption (CP-ABE) is a well-known cryptographic technology for guaranteeing data confidentiality and fine-grained data access control. It enables data owners to define flexible access policy for data sharing. However, in CP-ABE systems, the problems of the time required to encrypt, decrypt and attribute update are long-standing unsolved in the literature. In this paper, we propose the first access control (CP-ABE) scheme supporting outsourcing capability and attribute update for fog computing. Specifically, the heavy computation operations of encryption and decryption are outsourced to fog nodes, thus the computation operations for data owners to encrypt and users to decrypt are irrelevant to the number of attributes in the access structure and secret keys …