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Dictionary attacks are the best known threats on the password-based authentication schemes. Based on Reverse Turing Test (RTT), some usable and scalable authentication schemes are proposed to defeat online dictionary attacks mounted by automated programs. However it is found that these authentication schemes are vulnerable to various online dictionary attacks. In this paper, a practical decision function is presented, based on which RTT authentication schemes are constructed and shown to be secure against all the known online dictionary attacks. After formally modeling of the adversary, the static and dynamic security of the authentication schemes are proved formally.
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