A steady on the generalized key agreement and password authentication protocol

We study how to generalize a key agreement and password authentication prot ocol on the basis of the well known hard problems such as a discrete logari thm problem and a Diffie-Hellman problem. The key agreement and password au thentication protocol is necessary for networked or internet-worked environ ments to provide the user knowledge-based authentication and to establish a new cryptographic key for the further secure session. The generalized prot ocol implies in this paper to require only weak constraints and to be gener alized easily in any other cyclic groups which preserve two hard problems. The low entropy of password has made it difficult to design such a protocol and to prove its security soundness. In this paper, we devise a protocol w hich is easy to be generalized and show its security soundness in the rando m oracle model. The proposed protocol reduces the constraints extremely onl y to avoiding a smooth prime modulus. Our main contribution is in solving t he password's low entropy problem in the multiplicative group for the gener alization.