Cryptology ePrint Archive: Report 2006/079

Towards Provably Secure Group Key Agreement Building on Group Theory

Jens-Matthias Bohli and Benjamin Glas and Rainer Steinwandt

Abstract: Known proposals for key establishment schemes based on combinatorial group theory are often formulated in a rather informal manner. Typically, issues like the choice of a session identifier and parallel protocol executions are not addressed, and no security proof in an established model is provided. Successful attacks against proposed parameter sets for braid groups further decreased the attractivity of combinatorial group theory as a candidate platform for cryptography. We present a 2-round group key agreement protocol that can be proven secure in the random oracle model if a certain group-theoretical problem is hard. The security proof builds on a framework of Bresson et al., and explicitly addresses some issues concerning malicious insiders and also forward secrecy. While being designed as a tool for basing group key agreement on non-abelian groups, our framework also yields a 2-round group key agreement basing on a Computational Diffie-Hellman assumption.

Category / Keywords: cryptographic protocols / group key establishment, provable security, conjugacy problem, automorphisms of groups

Publication Info: accepted at VietCrypt 2006

Date: received 28 Feb 2006, last revised 30 Aug 2006

Contact author: rsteinwa at fau edu

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Version: 20060830:131459 (All versions of this report)

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