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Cloud computing is an emerging computing paradigm in which IT resources and capacities are provided as services over the Internet. Promising as it is, this paradigm also brings forth new challenges for data security and access control when users outsource sensitive data for sharing on cloud servers, which are likely outside of the same trust domain of data owners. To maintain the confidentiality of, sensitive user data against untrusted servers, existing work usually apply cryptographic methods by disclosing data decryption keys only to authorized users. However, in doing so, these solutions inevitably introduce heavy computation overhead on the data owner for key distribution and data management when fine-grained data access control is desired, and thus do not scale well. In this paper, we present a way to implement, scalable and fine-grained access control systems based on attribute-based encryption (ABE). For the purpose of secure access control in cloud computing, the prevention of illegal key sharing among colluding users is missing from the existing access control systems based on ABE. This paper addresses this challenging open issue by defining and enforcing access policies based on data attributes and implementing user accountability by using traitor tracing. Furthermore, both the user grant and revocation are efficiently supported by using the broadcast encryption technique. Extensive analysis shows that the proposed scheme is highly efficient and provably secure under existing security models.