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Journal of Mathematical Cryptology

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Mean-set attack: cryptanalysis of Sibert et al. authentication protocol

Natalia Mosina / Alexander Ushakov
  • Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, 07030, USA. E-mail:
Published Online: 2010-08-23 | DOI: https://doi.org/10.1515/jmc.2010.006


We analyze the Sibert et al. group-based (Feige–Fiat–Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge. In addition, we provide experimental evidence that our approach is practical and can succeed even for groups with no efficiently computable length function such as braid groups. The novelty of this work is that we are not attacking the protocol by trying to solve an underlying complex algebraic problem, namely, the conjugacy search problem, but use a probabilistic approach, instead.

Keywords.: Group-based cryptography; zero knowledge; authentication protocol; probability on graphs and groups; braid group; mean-set; mean-set attack principle; shift search problem

About the article

Received: 2009-06-18

Revised: 2010-05-21

Published Online: 2010-08-23

Published in Print: 2010-10-01

Citation Information: Journal of Mathematical Cryptology, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/jmc.2010.006. Export Citation

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Natalia Mosina and Alexander Ushakov
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