Using semidirect product of (semi)groups in public key cryptography

TL;DR

This survey explores a general key exchange protocol based on semidirect products of (semi)groups, highlighting its advantages over traditional Diffie-Hellman and discussing optimal platform choices for security and efficiency.

Contribution

It introduces a flexible key exchange protocol using semidirect products of (semi)groups and analyzes its security features and practical implementations.

Findings

Protocol can be based on any (semi)group, including non-commutative groups.

Using non-commutative (semi)groups enhances security features.

Varying automorphisms creates new security assumptions.

Abstract

In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. The focus then shifts to selecting an optimal platform (semi)group, in terms of security and efficiency. We show, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension.