# 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

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topFranco, 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 -

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