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Quite recently, two smart-card-based passwords authenticated key exchange protocols were proposed by Lee et al. and Hwang et al. respectively. However, neither of them achieves two-factor authentication fully since they would become completely insecure once one factor is broken. To overcome these congenital defects, this paper proposes such a secure authenticated key exchange protocol that achieves fully two-factor authentication and provides forward security of session keys. And yet the authors' scheme is simple and reasonably efficient. Furthermore, they can provide the rigorous proof of the security for it.
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