Abstract: It is quite common for data owners to share the data via mobile phones in cloud computing. But because the cloud is not fully trusted, a series of privacy concerns emerge from it, and various schemes based on the attribute-based encryption have been proposed to these problems. However, most work either cannot support the keyword search function for the encrypted data, or bring a large of online computational cost in encryption and decryption phase. The efficiency of the data sharing and information query as well as the fined-grained of the data sharing will be affected by the most attribute-based encryption mechanism. To deal with these challenging concerns, we propose a new cryptographic primitive named online/offline ciphertext-policy attribute-based searchable encryption scheme (OO-CP-ABSE). By using the online/offline attribute-based encryption and the outsourcing decryption technique, we construct our scheme with minimum online computational cost on the data owner side and least decrypted computational cost on the data user side. Furthermore, we give the description of the application of OO-CP-ABSE in cloud computing for mobile devices. At last, we also present the efficiency of our scheme in comparison to other schemes and the security in terms of data confidentiality, keyword privacy, controlled searching, trapdoor privacy.