The MOR cryptosystem and finite $p$-groups

TL;DR

This paper explores the MOR cryptosystem based on automorphism groups of finite p-groups, providing a comprehensive analysis for p'-automorphisms and highlighting open problems for p-automorphisms.

Contribution

It offers a complete study of the MOR cryptosystem for finite p-groups with a focus on p'-automorphisms and identifies open challenges for p-automorphisms.

Findings

Complete analysis for p'-automorphisms in finite p-groups.

Identification of open problems for p-automorphisms.

Insights into the cryptographic potential of automorphism groups.

Abstract

The ElGamal cryptosystem is the most widely used public key cryptosystem. It uses the discrete logarithm problem as the cryptographic primitive. The MOR cryptosystem is a similar cryptosystem. It uses the discrete logarithm problem in the automorphism group as the cryptographic primitive. In this paper, we study the MOR cryptosystem for finite $p$-groups. The study is complete for $p^\prime$-automorphisms. For $p$-automorphisms there are some interesting open problems.