A generalization of Burmester-Desmedt GKE based on a non-abelian finite group action

TL;DR

This paper generalizes the Burmester-Desmedt group key exchange protocol to non-abelian finite groups using group actions, enhancing security in the context of quantum threats and proving its security within a formal model.

Contribution

It introduces a novel non-abelian group key exchange protocol based on finite group actions and provides a formal security proof in Katz and Yung's model.

Findings

Protocol is secure against quantum adversaries.

Extends existing abelian group protocols to non-abelian groups.

Potential applications in secure mobile group communications.

Abstract

The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast messaging or pay-per-view, could be compromised. In this work we propose a generalization of the well known group key exchange protocol proposed by Burmester and Desmedt to the non-abelian case by the use of finite group actions and we prove that the presented protocol is secure in Katz and Yung's model.