Cloud computing enables data owners to outsource their computationally intensive tasks and store private data to the shared cloud. To enhance the security while preserving the flexibility of data sharing, Attribute Based Encryption (ABE) was introduced to provide a fine-grained access control. A key issue in ABE based systems is the high computational overhead, which could be prohibitive for resource constrained mobile devices. In this paper, we propose a scheme to securely and efficiently outsource the computationally intensive access control operations of ABE to the shared cloud, thus reliving the computational burden of mobile users which can greatly improve the battery lifetime. In a high level view, data owners only need to specify access policies on the encrypted data so that access control can be done automatically by the cloud. Our proposed scheme guarantees that it is computationally infeasible for the untrusted cloud to recover the encrypted file and that the cloud is enforced to complete the full functionality of access control, even in situations where the cloud may be compromised by malicious data users. Our theoretical analysis and experiment results both demonstrate that our scheme can achieve high performance gain for resource constrained mobile devices.