In 1992, Bellovin and Merritt proposed Encrypted Key Exchange (EKE) protocols for preventing dictionary attacks on weak chosen passwords. In 1995, Steiner, Tsudik, and Waidner proposed a minimal DHEKE protocol which simplified the Diffie-Hellman based one of Bellovin and Merritts' protocols. In this paper, we propose two improvements on the minimal DHEKE protocol. These two improvements can reduce the computational cost further.
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