Cryptography with right-angled Artin groups
This work addresses cryptographic security for data protection by introducing new group-theoretic problems, but it appears incremental as it builds on prior graph-based research.
The paper tackles the problem of designing secret sharing and authentication schemes by proposing right-angled Artin groups as a platform, leveraging the linear-time efficiency of the word problem and defining new problems like Subgroup Isomorphism and Group Homomorphism, with results showing equivalence to NP-complete problems and unsolvability in some cases.
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.