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Cryptography with right-angled Artin groups


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Opened Access Cryptography with right-angled Artin groups

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Author: Flores Díaz, Ramón Jesús
Kahrobaei, Delaram
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2016
Published in: Theoretical and Applied Informatics, 28 (3), 8-16.
Document type: Article
Abstract: In this paper we propose right-angled Artin groups as a platform for secret sharingschemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we de ne two new problems: SubgroupIsomorphism Problem and Group Homomorphism Problem. Based on them, we also proposetwo new authentication schemes. For right-angled Artin groups, the Group Homomorphismand Graph Homomorphism problems are equivalent, and the later is known to be NP-complete.In the case of the Subgroup Isomorphism problem, we bring some results due to Bridson whoshows there are right-angled Artin groups in which this problem is unsolvable.
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DOI: 10.20904/283008

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