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Open AccessArticle

Building Group Key Establishment on Group Theory: A Modular Approach

1
Department of Information Technology, Mannheim University of Applied Sciences, 68163 Mannheim, Germany
2
MACIMTE, U. Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
3
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 197; https://doi.org/10.3390/sym12020197
Received: 26 December 2019 / Revised: 15 January 2020 / Accepted: 19 January 2020 / Published: 30 January 2020
(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)
A group key establishment protocol is presented and proven secure in the common reference string mode. The protocol builds on a group-theoretic assumption, and a concrete example can be obtained with a decision Diffie–Hellman assumption. The protocol is derived from a two-party solution by means of a protocol compiler presented by Abdalla et al. at TCC 2007, evidencing the possibility of meaningfully integrating cryptographic and group-theoretic tools in cryptographic protocol design. This compiler uses a standard ring configuration, where all users behave symmetrically, exchanging keys with their left and right neighbor, which are later combined to yield a shared group key. View Full-Text
Keywords: group key establishment; group theory; provable security; protocol compiler group key establishment; group theory; provable security; protocol compiler
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Bohli, J.-M.; González Vasco, M.I.; Steinwandt, R. Building Group Key Establishment on Group Theory: A Modular Approach. Symmetry 2020, 12, 197.

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