Some applications of arithmetic groups in cryptography

TL;DR

This paper explores the use of exponentially distorted subgroups in linear groups, including new examples in $SL_n(\

Contribution

It introduces new examples of exponentially distorted subgroups in $SL_n(\

Findings

Examples of exponentially distorted subgroups in linear groups.

Construction of cryptographic platforms using these subgroups.

Abstract

In this paper we will give various examples of exponentially distorted subgroups in linear groups, including some new example of subgroups of $SL_n(\mathbb{Z}[x])$ for $n \ge 3$, and show how they can be used to construct symmetric-key cryptographic platforms.