Revista Matemática Iberoamericana

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Volume 19, Issue 2, 2003, pp. 367–384
DOI: 10.4171/RMI/352

Published online: 2003-08-31

Computation of Centralizers in Braid groups and Garside groups

Nuno Franco[1] and Juan González-Meneses[2]

(1) Universidade de Évora, Portugal
(2) Universidad de Sevilla, Spain

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.

Keywords: Braid group, Garside group, centralizer, cryptography

Franco Nuno, González-Meneses Juan: Computation of Centralizers in Braid groups and Garside groups. Rev. Mat. Iberoam. 19 (2003), 367-384. doi: 10.4171/RMI/352