# Cryptography with right-angled Artin groups

arXiv: https://arxiv.org/abs/1610.06495 · HTML: https://mlsanity.com/paper/1610.06495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2016.

## Built on by (most cited first, 1 of 1)

- [Learning the Word Problem: Geodesic Lengths and Cryptographic Applications](https://mlsanity.com/paper/2607.26241/) (2026)

## Abstract (arXiv)

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.