More efficient password authenticated key exchange based on RSA

In [17], Zhu, et al. proposed a RSA-based password authenticated key exchange, scheme which supports short RSA public exponents. The scheme is the most efficient one among all the RSA-based schemes currently proposed when implemented on low-power asymmetric wireless networks. We observe that its performance can further be improved by proposing two modifications. The first modification shortens the size of the message sent from the server to the client. The second modification dramatically reduces the size of the message sent from the client to the server and therefore can be used to reduce the power consumption the client for wireless communications in a significant way. We also generalize our modified schemes and formalize the security requirements of all underlying primitives that the generic scheme is constituted. A new primitive called password-keyed permutation family is introduced. We show that the security of our password-keyed permutation family is computationally equivalent to the RSA Problem in the random oracle model.