Revista Matemática Iberoamericana

Computation of Centralizers in Braid groups and Garside groups

Nuno Franco and Juan González-Meneses

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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.

Article information

Rev. Mat. Iberoamericana, Volume 19, Number 2 (2003), 367-384.

First available in Project Euclid: 8 September 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 94A60: Cryptography [See also 11T71, 14G50, 68P25, 81P94]

Braid group Garside group centralizer cryptography


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

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