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In database outsourcing service, the data owners store their databases at the servers which belong to potentially untrusted service providers. It is necessary to protect outsourced data from unauthorized access. However, by using existing access control mechanisms, data owners are incapable of controlling access to individual sensitive attributes of their data. In this paper, we propose an Efficient Fine-grained Access Control mechanism, named EFGAC, which can restrict access to the more sensitive columns of the shared relation. EFGAC can handle most of dynamic updates on users or dataset or access rights efficiently without the need of the systematic reconstruction or database re-keying. Experimental results show that EFGAC can save a worthy amount of key derivation time of users and reduce the number of keys held by each user in the system. Especially, we suggest strategies which are useful for the data owner in deciding the necessary number of keys in both static and dynamic cases of outsourcing.