SummaryIn this big data era, service providers tend to put the data in a third‐party cloud system. Social networking websites are typical examples. To protect the security and privacy of the data, data should be stored in encrypted form. This brings forth new challenges: how to allow different users to access only the authorized part of the data without decryption of the data. Attribute‐based encryption (ABE) offers fine‐grained access control policy over encrypted data such that users can decrypt successfully only if their attributes satisfy the policy. However, one drawback of ABE is that the computational cost grows linearly with the complexity of ciphertext policy or the number of attributes. The situation becomes worse for mobile devices with limited computing resources. To solve this problem, we adopt the offline/online technique combining with the verifiable outsourced computation technique to propose a new ciphertext‐policy ABE scheme using bilinear groups in prime order, supporting the offline/online key generation and encryption, as well as the verifiable outsourced decryption. As a result, most computations of key generation and encryption can be executed offline, and the majority of computational workload in decryption can be outsourced to third parties. The scheme is selectively chosen‐plaintext attack‐secure in the standard model. We also provide the proof of verifiability on outsourced decryption. The simulation results show that our proposed scheme can effectively reduce the computational cost imposed on resource‐constrained devices. Copyright © 2016 John Wiley & Sons, Ltd.