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In the era of cloud computing, the technique of access control is vital to protect the confidentiality and integrity of cloud data. From the perspective of servers, they should only allow authenticated clients to gain the access of data. Specifically, the server will share a communication channel with the client by generating a common session key. It is thus regarded as a symmetric key for encrypting data in the current channel. An access control mechanism using attribute-based encryptions is most flexible, since the decryption privilege can be granted to the ones who have sufficient attributes. In the paper, the authors propose a secure access control consisting of the attributed-based mutual authentication and the attribute-based encryption. The most appealing property of our system is that the attribute keys associated with each user is periodically updatable. Moreover, we will also show that our system fulfills the security of fuzzy selective-ID assuming the hardness of Decisional Modified Bilinear Diffie-Hellman (DMBDH) problem.