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Conjugacy Search in Braid Groups

From a Braid-based Cryptography Point of View

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We demonstrate that recent advances in the theory of braid groups, in particular a new invariant of conjugacy classes of braids, the ultra summit set, make some braid-based cryptographic protocols insecure for almost all randomly chosen keys. As part of this we present an overview of the known algorithms for solving the conjugacy decision and search problems in braid groups and an assessment of their practical performance from the point of view of braid-based cryptography.

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  1. School of Computing and Mathematics, University of Western Sydney, Penrith South DC, NSW, 1797, Australia

    Volker Gebhardt

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  1. Volker Gebhardt
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Correspondence to Volker Gebhardt.

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Gebhardt, V. Conjugacy Search in Braid Groups. AAECC 17, 219–238 (2006). https://doi.org/10.1007/s00200-006-0008-7

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  • DOI: https://doi.org/10.1007/s00200-006-0008-7

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