A practical attack on a braid group based cryptographic protocol

Authors:
Alexei Myasnikov;Vladimir Shpilrain;Alexander Ushakov
Affiliations:
Department of Mathematics, McGill University, Montreal, Quebec;Department of Mathematics, The City College of New York, New York, NY;Department of Mathematics, CUNY Graduate Center, New York, NY
Venue:
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Year:
2005

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Abstract

In this paper we present a practical heuristic attack on the Ko, Lee et al. key exchange protocol introduced at Crypto 2000 [11]. Using this attack, we were able to break the protocol in about 150 minutes with over 95% success rate for typical parameters. One of the ideas behind our attack is using Dehornoy's handle reduction method as a counter measure to diffusion provided by the Garside normal form, and as a tool for simplifying braid words. Another idea employed in our attack is solving the decomposition problem in a braid group rather than the conjugacy search problem.