Cryptography with right-angled Artin groups

Authors

Ramon Flores, University of Seville
Delaram Kahrobaei, CUNY Graduate CenterFollow

Document Type

Article

Publication Date

2016

Abstract

In this paper we propose right-angled Artin groups as a platform for secret sharing schemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we define two new problems: Subgroup Isomorphism Problem and Group Homomorphism Problem. Based on them, we also propose two new authentication schemes. For right-angled Artin groups, the Group Homomorphism and 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 who shows there are right-angled Artin groups in which this problem is unsolvable.

Comments

This article was originally published in Theoretical and Applied Informatics, available at DOI: 10.20904/283008.

This work is distributed under a Creative Commons Attribution (CC-BY) license.