Abstract: Attribute-based encryption (ABE) is a type of public key encryption that allows users to encrypt and decrypt messages based on users attributes. In such a system, the decryption of a ciphertext is possible only if the set of the attributes of the user key matches the access policy of the ciphertext. Given its expressiveness, ABE is currently being considered for many network applications, especially for cloud storage and cloud computing. However, one of the main drawbacks of ABE is that the running time of encryption and decryption grows with the complexity of the access formula or the number of attributes. In practice, this makes encryption and decryption be possible bottlenecks for a lot of applications. In this work, we introduce outsourcing ABE system to mitigate this problem. In the outsourcing ABE system, users can outsource a part of the storage and computing tasks to some semi-honest servers. It is significant for mobile devices to save storage and computational resources. Then, we propose a specific outsourcing ciphertext-policy ABE (CP-ABE) scheme using the composite order bilinear groups. In our scheme, the local computation of (online) encryption and decryption can reach constant level. Finally, we prove its adaptive security in the standard model using the methodology of dual system encryption.