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A provably secure password-authenticated protocol for group key establishment in the Common Reference String (CRS) model is presented. The construction assumes the participating users to share a common password and combines projective hashing as introduced by Cramer and Shoup with a construction of Burmester and Desmedt. The protocol is constant-round. Namely, it is a three-round protocol that can be seen as generalization of a two-party proposal of Gennaro and Lindell. In distributed applications, low-entropy passwords are still a dominating tool for authentication. Reflecting this, significant research efforts are currently devoted to the exploration of password-authenticated key establishment protocols.
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