Reduction of conjugacy problem in braid groups, using two garside structures

Authors:
Maffre Samuel
Affiliations:
XLIM, University of Limoges, France
Venue:
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Year:
2005

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Abstract

We study the Conjugacy Search Problem used in braid-based cryptography. We develop an algorithm running in Garside groups generalizing braid groups. The method permits, in some case, to reduce drastically the size of the secret in braid groups. We use the fact that braid groups admit two different Garside structures to improve the efficiency of the reduction. This paper emphasizes the importance of the particular way used to produce Conjugacy Search Problem instances. The chosen method influences directly the reduction and then also the security.