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arXiv:2412.00387

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

Daniel Camazón Portela, Álvaro Otero Sánchez, Juan Antonio López Ramos

Published Nov 30, 2024• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.2412.00387

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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.
With the rapid development of cloud computing and mobile networks, more and more application scenarios require a secret group key for secure communication. Group Key Exchange (GKE) protocol provides a secret group key for three or more members. Burmester and Desmedt presented an influential GKE protocol, which has a broadcast version and a cyclic version. In this paper, we investigate the security weaknesses of the Burmester-Desmedt protocol. We report that both the broadcast version and the cyclic version of the Burmester-Desmedt protocol suffer member tampering attacks if the two members that belong to both group A and group B are corrupted. That is, two corrupted members can add some unknowing members of group A to group B and trick the legal members of group B to believe that these unknowing members share the secret group key with them after a protocol run. Furthermore, to defeat the member tampering attack, we propose digital signature-based improvements on the broadcast version and the cyclic version of the Burmester-Desmedt protocol. We hope our research results will encourage the development of more robust and effective GKE protocols that stand rigorous security analysis.
Abstract. Task-specific groups are often formed in an ad-hoc manner within big structures, like companies. Take the following typical scenario: A high rank manager decides that a task force group for some project needs to be built. This order is passed down the hierarchy where it finally reaches a manager who calls some employees to form a group. The members should communicate in a secure way and for efficiency reasons symmetric systems are the common choice. To establish joint secret keys for groups, group key exchange (GKE) protocols were developed. If the users are part of e.g. a Public Key Infrastructure (PKI), which is usually the case within a company or a small network, it is possible to achieve authenticated GKE by modifying the protocol and particularly by including signatures. In this paper we recall a GKE due to Burmester and Desmedt which needs only O(log n) communication and computation complexity per user, rather than O(n) as in the more well-known Burmester-Desmedt protocol, and runs in a constant number of rounds. To achieve authenticated GKE one can apply compilers, however, the existing ones would need O(n) computation and communication thereby mitigating the advantages of the faster protocol. Our contribution is to extend an existing compiler so that it preserves the computation and communication complexity of the non-authenticated protocol. This is particularly important for tree based protocols.
Abstract. In this paper we analyse the security of two authenticated group key agreement schemes based on the group key agreement protocol of Burmester and Desmedt. One scheme was proposed by Burmester and Desmedt, and uses a separate authentication scheme to achieve authentication among the participants. We show that this scheme suffers from a number of security vulnerabilities. The other scheme was generated using the general protocol compiler of Katz and Yung. We show that in some circumstances, even if key confirmation is implemented, this scheme still suffers from insider attacks (which are not covered by the security model used by Katz and Yung). 1
We consider the problem of authenticated group key exchange among n parties communicating over an insecure public network. A number of solutions to this problem have been proposed; however, all prior provably-secure solutions do not scale well and, in particular, require O (n) rounds. Our main contribution is the first scalable protocol for this problem along with a rigorous proof of security in the standard model under the DDH assumption; our protocol uses a constant number of rounds and requires only O (1) \full modular exponentiations per user. Toward this goal (and adapting work of Bellare, Canetti, and Krawczyk), we first present an efficient compiler that transforms any ngroup key-exchange protocol secure against a passive eavesdropper to an authenticated protocol which is secure against an active adversary who controls all communication in the network. This compiler adds only one round and O (1) communication (per user) to the original scheme. We then prove secure | against a passive adversary | a variant of the two-round group key-exchange protocol of Burmester and Desmedt. Applying our compiler to this protocol results in a provably-secure three-round protocol for authenticated group key exchange which also achieves forward secrecy.
Modern multi-user communication systems, including popular instant messaging tools, social network platforms, and cooperative-work applications, oer exible forms of com- munication and exchange of data. At any time point concurrent communication sessions involv- ing dierent subsets of users can be invoked. The traditional tool for achieving security in a multi-party communication environment are group key exchange (GKE) protocols that provide participants with a secure group key for their subsequent communication. Yet, in communica- tion scenarios where various user subsets may be involved in dierent sessions the deployment of classical GKE protocols has clear performance and scalability limitations as each new session should be preceded by a separate execution of the protocol. The motivation of this work is to study the possibility of designing more exible GKE protocols allowing not only the computation
Identity-based key agreement protocols allow the participants in a group exchange information over an open network with each other. However, in most of proposed IDbased protocol, identities of group users are exposed, so that eavesdroppers can easily learn who belongs to the specific group. In this paper, we proposed a complete anonymous group key agreement protocol based on the Burmester and Desmedt mechanism and ID-based encryption cryptosystems. The proposed protocol is provably-secure in the random oracle model, and achieves the following security attribute: complete anonymity, unlinkability, group key secrecy, perfect forward secrecy for the group session key and entity authentication.