A generalization of Burmester-Desmedt GKE based on a non-abelian finite group action
Daniel Camazón Portela, Álvaro Otero Sánchez, Juan Antonio López Ramos
TL;DR
The paper addresses secure group key exchange for dynamic, multi-user groups in a post-quantum setting. It generalizes the Burmester–Desmedt BD protocol to non-abelian finite group actions, presenting a multi-round GKE scheme and a formal security model. The authors prove forward secrecy under a DDH-like group-action assumption and discuss reductions via distribution indistinguishability, while proposing hard-group-action constructions as practical platforms. This work provides a PQ-secure GKE alternative for multicast-style scenarios and broadens the application of non-abelian group actions in cryptographic protocols.
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.