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Paper details
Number 4 - December 2019
Volume 29 - 2019
Password-authenticated group key establishment from smooth projective hash functions
Jens-Matthias Bohli, María Isabel González Vasco, Rainer Steinwandt
Abstract
Thus, they can be implemented without complex infrastructures that typically involve public keys and certificates. In this
paper, a provably secure password-authenticated protocol for group key establishment in the common reference string
(CRS) model is presented. While prior constructions of the group (PAKE) can be found in the literature, most of them rely
on idealized assumptions, which we do not make here. Furthermore, our protocol is quite efficient, as regardless of the
number of involved participants it can be implemented with only three communication rounds. We use a (by now classical)
trick of Burmester and Desmedt for deriving group key exchange protocols using a two-party construction as the main
building block. In our case, the two-party PAKE used as a base is a one-round protocol by Katz and Vaikuntanathan, which
in turn builds upon a special kind of smooth projective hash functions (KV-SPHFs). Smooth projective hash functions
(SPHFs) were first introduced by Cramer and Shoup (2002) as a valuable cryptographic primitive for deriving provable
secure encryption schemes. These functions and their variants proved useful in many other scenarios. We use here as a main
tool a very strong type of SPHF, introduced by Katz and Vaikuntanathan for building a one-round password based two party
key exchange protocol. As evidenced by Ben Hamouda et al. (2013), KV-SPHFs can be instantiated on Cramer–Shoup
ciphertexts, thus yielding very efficient (and pairing free) constructions.
Keywords
group key exchange, password authentication, smooth projective hashing