Open Access
September, 2003 Computation of Centralizers in Braid groups and Garside groups
Nuno Franco, Juan González-Meneses
Rev. Mat. Iberoamericana 19(2): 367-384 (September, 2003).


We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in \cite{FGM}, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups \cite{AAG}. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.


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Nuno Franco. Juan González-Meneses. "Computation of Centralizers in Braid groups and Garside groups." Rev. Mat. Iberoamericana 19 (2) 367 - 384, September, 2003.


Published: September, 2003
First available in Project Euclid: 8 September 2003

zbMATH: 1064.20040
MathSciNet: MR2023190

Primary: 20F36
Secondary: 20F10 , 94A60

Keywords: Braid group , ‎centralizer‎ , cryptography , Garside group

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 2 • September, 2003
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