JournalsrmiVol. 19, No. 2pp. 367–384

Computation of Centralizers in Braid groups and Garside groups

  • Nuno Franco

    Universidade de Évora, Portugal
  • Juan González-Meneses

    Universidad de Sevilla, Spain
Computation of Centralizers in Braid groups and Garside groups cover
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Abstract

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.

Cite this article

Nuno Franco, Juan González-Meneses, Computation of Centralizers in Braid groups and Garside groups. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 367–384

DOI 10.4171/RMI/352