Completely Regular Semigroups and the Discrete Log Problem

TL;DR

This paper explores using completely regular semigroups to develop a potentially more secure cryptosystem for the discrete log problem, aiming to enhance resistance against traditional attack methods.

Contribution

It introduces a novel cryptographic scheme based on completely regular semigroups, offering an alternative to group-based systems for discrete log security.

Findings

Proposes a cryptosystem using completely regular semigroups

Suggests improved security against trial multiplication attacks

Provides theoretical analysis of the scheme's security properties

Abstract

We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear to offer protection to a standard trial multiplication attack.