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We consider the security problem for retrieving data from a web site (or a large database system) via Internet. Consider the situation that a user visits a web site to get information. He wants to retain anonymity of his identity, while the web site would like to authenticate the user's identity. We proposed an anonymous authentication scheme to provide a solution for these two seemingly conflicting requirements. Our anonymous authentication scheme is based on cryptographic techniques. Together with a novel time-dependent hierarchical key assignment scheme, we proposed a data access system that has the following distinct features simultaneously: (1) anonymous authentication, (2) cryptographic access control, (3) saving on-line encryption time, and (4) a flexible subscription system.