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Password-Authenticated Group Key Establishment from Smooth Projective Hash Functions
Authors: Jens-Matthias Bohli, Maria Isabel Gonzalez Vasco, Rainer SteinwandtAbstract:
Password-authenticated key exchange (PAKE) protocols allow users sharing a password to agree upon a high entropy secret. In this paper, a provably secure password-authenticated pro- tocol for group key establishment in the common reference string (CRS) model is presented. Our protocol is quite efficient, as regardless of the number of involved participants it can be imple- mented 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 main building block. In our case, the two party PAKE used as a base is a one-round protocol by Katz and Vaikuntanatan, which in turn builds upon a special kind of smooth projective hash functions (KV-SPHFs). As evidenced by Benhamouda et al., KV-SPHFs can be instantiated on Cramer-Shoup ciphertexts, thus yielding very efficient (and pairing free) constructions.
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