A simple generalization of the ElGamal cryptosystem to non-abelian groups II

TL;DR

This paper explores a generalization of the ElGamal cryptosystem to non-abelian groups, specifically analyzing the MOR cryptosystem over special linear groups and demonstrating its superior security over traditional ElGamal.

Contribution

It introduces a new approach to cryptosystems using non-abelian groups and analyzes the automorphism group of the special linear group for cryptographic applications.

Findings

MOR cryptosystem has better security than ElGamal over finite fields

Automorphism group of special linear group is effectively analyzed

Potential for more secure cryptographic schemes using non-abelian groups

Abstract

This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that the MOR cryptosystem has better security than the ElGamal cryptosystem over finite fields.