A simple generalization of El-Gamal cryptosystem to non-abelian groups

TL;DR

This paper extends the El-Gamal cryptosystem to non-abelian groups by using automorphisms of unitriangular matrix groups, demonstrating similar security properties to the classical system.

Contribution

It introduces a generalized MOR cryptosystem based on non-abelian groups, specifically unitriangular matrices, and proves its security is equivalent to the traditional El-Gamal system.

Findings

Cryptosystem built on unitriangular groups mimics El-Gamal security

Security of the new system is equivalent to El-Gamal over finite fields

Provides a new approach to non-abelian cryptography

Abstract

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equivalent to the El-Gamal cryptosystem over finite fields.