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Journal of Mathematical Cryptology

Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran

Editorial Board Member: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti

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Cryptanalysis of the shifted conjugacy authentication protocol

Jonathan Longrigg1 / Alexander Ushakov2

1 Department of Mathematics, University of Newcastle, Newcastle, NE1 7RU, UK. Email:

2 Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email:

Citation Information: Journal of Mathematical Cryptology. Volume 2, Issue 2, Pages 109–116, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/JMC.2008.005, September 2008

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In this paper we present the first practical attack on the shifted conjugacy-based authentication protocol proposed by P. Dehornoy in [P. Dehornoy, Using shifted conjugacy in braid-based cryptography, Algebraic Methods in Cryptography, Contemporary Mathematics 418, American Mathematical Society, 2006, pp. 65–74.]. We discuss the weaknesses of that primitive and propose ways to improve the protocol.

Keywords.: Braid group cryptography; authentication protocol; shifted conjugacy; ultra summit set; centralizer

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