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Networked storage systems provide storage services for users over networks. Secure networked storage systems store encrypted data to guarantee data confidentiality. However, using encryption schemes somehow restricts the access control function over stored data. We address the access control function for a secure networked storage system by proposing a fine-grained access control mechanism. In our mechanism, a user cannot only read or write data but also grant the reading permissions of a single file or a whole directory of files to others with low cost. Moreover, these functions are supported in a confidential way against honest-but-curious storage servers. Our technical contribution is to propose a hybrid encryption scheme for a typical structure of a file system by integrating a hierarchical proxy re-encryption scheme and a hierarchical key assignment scheme. We measure the computation overhead for reading, writing, and granting operations by experiments. Our experimental results show that getting a finer access control mechanism does not cost much.