Computation of centralizers in Braid groups and Garside groups.

Nuno Franco; Juan González-Meneses

Revista Matemática Iberoamericana (2003)

  • Volume: 19, Issue: 2, page 367-384
  • ISSN: 0213-2230

Abstract

top
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 [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.

How to cite

top

Franco, Nuno, and González-Meneses, Juan. "Computation of centralizers in Braid groups and Garside groups.." Revista Matemática Iberoamericana 19.2 (2003): 367-384. <http://eudml.org/doc/39600>.

@article{Franco2003,
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 [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.},
author = {Franco, Nuno, González-Meneses, Juan},
journal = {Revista Matemática Iberoamericana},
keywords = {Teoría de grupos; Criptografía; braid groups; Artin groups; Garside groups; conjugacy problem; conjugacy classes; normal forms; centralizers; generating sets},
language = {eng},
number = {2},
pages = {367-384},
title = {Computation of centralizers in Braid groups and Garside groups.},
url = {http://eudml.org/doc/39600},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Franco, Nuno
AU - González-Meneses, Juan
TI - Computation of centralizers in Braid groups and Garside groups.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 2
SP - 367
EP - 384
AB - 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 [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.
LA - eng
KW - Teoría de grupos; Criptografía; braid groups; Artin groups; Garside groups; conjugacy problem; conjugacy classes; normal forms; centralizers; generating sets
UR - http://eudml.org/doc/39600
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.