Cumplido Cabello, MaríaGonzález-Meneses López, JuanSilvero Casanova, Marithania2020-01-152020-01-152019-10Cumplido Cabello, M., González-Meneses López, J. y Silvero Casanova, M. (2019). The root extraction problem for generic braids. Symmetry, 11 (11), 1-15.2073-8994https://hdl.handle.net/11441/91652We show that, generically, finding the k-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid x on n strands and canonical length l, and an integer k > 1, computes a k-th root of x, if it exists, or guarantees that such a root does not exist. The generic-case complexity of this algorithm is O(l(l + n)n3 log n). The non-generic cases are treated using a previously known algorithm by Sang-Jin Lee. This algorithm uses the fact that the ultra summit set of a braid is, generically, very small and symmetric (through conjugation by the Garside element ∆), consisting of either a single orbit conjugated to itself by ∆ or two orbits conjugated to each other by ∆.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Braid groupsAalgorithms in groupsGroup-based cryptographyinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.3390/sym11111327