Authentication protocol is variously designed by attribute-based encryption. In some case, there is situation that need the authentication with revealed ID of users. Zhu et al present attribute authentication protocol containing ID. But their protocol did not have security under collusion attack and impersonation attack. In this paper, we propose enhanced protocol from Zhu et al.'s protocol. The protocol was constructed based on fuzzy attribute-based authentication protocol on the basis of Lagrange polynomial interpolation. Our protocol has some good features which are safer than existing protocol. We also showed that our protocol has sufficient security under assumption of specific attack situations. So, we expect this protocol will be widely used to various environment which needs the multi-factor identifications.
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