Carl Bosley
New York University

A Framework for Password-Based Authenticated Key Exchange 

In this paper we present a general framework for password-based
authenticated key exchange protocols, in the common reference string
model. Our protocol is actually an abstraction of the key exchange
protocol of Katz et al. and is based on the recently introduced
notion of smooth projective hashing by Cramer and Shoup. We gain a
number of benefts from this abstraction. First, we obtain a modular
protocol that can be described using just three highlevel
cryptographic tools. This allows a simple and intuitive understanding
of its security. Second, our proof of security is signifcantly
simpler and more modular. Third, we are able to derive analogues to
the Katz et al. protocol under additional cryptographic assumptions.
Specifcally, in addition to the DDH assumption used by Katz et al.,
we obtain protocols under both the Quadratic and N-Residuosity
assumptions. In order to achieve this, we construct new smooth
projective hash functions. 

Rosario Gennaro and Yehuda Lindell