Article
Computation of centralizers in braid groups and Garside groups
Author/s | Gonçalves Soares Franco, Nuno María
González-Meneses López, Juan |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2003 |
Deposit Date | 2016-05-13 |
Published in |
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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 [9] ... 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] Franco, N. and Gonzalez-Meneses, J.: Conjugacy problem for braid groups and Garside groups, to appear in Journal of Algebra. Available at http://arxiv.org/math.GT/0112310, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2] Anshel, I., Anshel, M. and Goldfeld, D.: An algebraic method for public-key cryptography. Math. Res. Lett. 6 (1999), no. 3-4, 287–291. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers. |
Project ID. | SFRH/BD/2852/2000
BFM2001-3207 |
Citation | Gonçalves Soares Franco, N.M. y González-Meneses López, J. (2003). Computation of centralizers in braid groups and Garside groups. Revista Matemática Iberoamericana, 19, 367-384. |
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