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Towards Provably Secure Group Key Agreement Building on Group Theory

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Progress in Cryptology - VIETCRYPT 2006 (VIETCRYPT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4341))

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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.

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Author information

Authors and Affiliations

  1. Institut für Algorithmen und Kognitive Systeme, Fakultät für Informatik, Am Fasanengarten 5, 76128, Karlsruhe, Germany

    Jens-Matthias Bohli

  2. Institut für Technik der Informationsverarbeitung, Fakultät für Elektrotechnik & Informationstechnik, Engesserstraße 5, 76128, Karlsruhe, Germany

    Benjamin Glas

  3. Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431, USA

    Rainer Steinwandt

Authors
  1. Jens-Matthias Bohli
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  2. Benjamin Glas
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  3. Rainer Steinwandt
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Editor information

Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Phong Q. Nguyen

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Bohli, JM., Glas, B., Steinwandt, R. (2006). Towards Provably Secure Group Key Agreement Building on Group Theory. In: Nguyen, P.Q. (eds) Progress in Cryptology - VIETCRYPT 2006. VIETCRYPT 2006. Lecture Notes in Computer Science, vol 4341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11958239_22

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  • DOI: https://doi.org/10.1007/11958239_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68799-3

  • Online ISBN: 978-3-540-68800-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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