Cryptography with right-angled Artin groups
Cryptography and Security
2017-02-15 v3 Group Theory
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.
Keywords
Cite
@article{arxiv.1610.06495,
title = {Cryptography with right-angled Artin groups},
author = {Ramón Flores and Delaram Kahrobaei},
journal= {arXiv preprint arXiv:1610.06495},
year = {2017}
}