Paper 2006/079

Towards Provably Secure Group Key Agreement Building on Group Theory

Jens-Matthias Bohli, Benjamin Glas, and Rainer Steinwandt


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.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. accepted at VietCrypt 2006
group key establishmentprovable securityconjugacy problemautomorphisms of groups
Contact author(s)
rsteinwa @ fau edu
2006-08-30: revised
2006-03-01: received
See all versions
Short URL
Creative Commons Attribution


      author = {Jens-Matthias Bohli and Benjamin Glas and Rainer Steinwandt},
      title = {Towards Provably Secure Group Key Agreement Building on Group Theory},
      howpublished = {Cryptology ePrint Archive, Paper 2006/079},
      year = {2006},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.