Cryptography with right-angled Artin groups

In this paper we propose right-angled Artin groups as platform for a secret sharing scheme based on the efficiency (linear time) of the word problem. We define two new problems: subgroup isomorphism problem for Artin subgroups and group homomorphism problem in right-angled Artin groups. We show that the group homomorphism and graph homomorphism problems are equivalent, and the later is known to be NP-complete. We propose two authentication schemes based on subgroup isomorphism problem and group homomorphism problem in right-angled Artin groups. In the case of subgroup isomorphism problem, we bring some results due to Bridson who shows there are right-angled Artin groups in which this problem is unsolvable. Note that our schemes are similar to what Grigoriev and Shpilrain proposed for graphs.