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COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

Scalable group key exchange protocol with provable security

Chengbang Li, Chunxiang Xu

Published Mar 1, 2013• 4 citations
Publisher

Abstract

Purpose The purpose of this paper is to introduce a scalable group key exchange (GKE) protocol with provable security, which is used to establish a confidential channel. Design/methodology/approach The protocol in this paper uses line structure, rather than formal ring structure or tree structure, to reduce the amount of calculation and communication. Findings In the protocol, every participant just need send two messages. The security can be proved under the Decisional Diffie‐Hellman (DDH) problem. Originality/value Using the protocol provides an efficient and secure method to allow group users to share a common key.

DOI
10.1108/03321641311296990

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Purpose The purpose of this paper is to introduce a scalable group key exchange (GKE) protocol with provable security, which is used to establish a confidential channel. Design/methodology/approach The protocol in this paper uses line structure, rather than formal ring structure or tree structure, to reduce the amount of calculation and communication. Findings In the protocol, every participant just need send two messages. The security can be proved under the Decisional Diffie‐Hellman (DDH) problem. Originality/value Using the protocol provides an efficient and secure method to allow group users to share a common key.
Protocols for group key exchange (GKE) are cryptographic algorithms that describe how a group of parties communicating over a public network can come up with a common secret key. Due to their critical role in building secure multicast channels, a number of GKE protocols have been proposed over the years in a variety of settings. However despite many impressive achievements, it still remains a challenging problem to design a secure GKE protocol which scales very well for large groups. Our observation is that all provably-secure constant-round GKE protocols providing forward secrecy thus far are not fully scalable, but have a computational complexity that scales only linearly in group size. Motivated by this observation, we propose a new GKE protocol that not only offers full scalability in all directions but also attains provable security against active adversaries. Full scalability is achieved by using a complete binary tree structure where users are arranged on both internal and leaf nodes. Security is proved via reduction to the decisional Diffie-Hellman assumption in a well-defined formal model of communication and adversarial capabilities.
Distributed operating systems are designed to run over a collection of computing nodes that are spatially disseminated and communicate through a computer network. The computing nodes interact collaboratively with each other in order to pursue a common purpose. Protecting group communication between the collaborating nodes against potential attacks is one of the major challenges faced by the designers of distributed operating systems. This challenge can be effectively addressed by a group key exchange (GKE) protocol which allows a group of communicating parties to build a secure multicast channel over an insecure network. In this work, we propose a scalable GKE protocol that achieves both constant round complexity and logarithmic computation complexity. Our GKE protocol achieves its scalability by employing a complete binary tree structure combined with a so-called ”nonce-chained authentication technique”. Besides the scalability, our protocol features provable security against active adversaries in a well-defined communication model.
We extend the well-known Tree-Diffie-Hellman technique used for the design of group key exchange (GKE) protocols with robustness, i.e. with resistance to faults resulting from possible system crashes, network failures, and misbehavior of the protocol participants. We propose a fully robust GKE protocol using the novel tree replication technique: our basic protocol version ensures security against outsider adversaries whereas its extension addresses optional insider security. Both protocols are proven secure assuming stronger adversaries gaining access to the internal states of participants. Our security model for robust GKE protocols can be seen as a step towards unification of some earlier security models in this area.
Authenticated key-exchange protocols allow two participants A and B , communicating over a public network and each holding an authentication means to exchange a shared secret value. Methods designed to deal with this cryptographic problem ensure A (resp. B ) that no other participants aside from B (resp. A ) can learn any information about the agreed value and often also ensure A and B that their respective partner has actually computed this value. A natural extension to this cryptographic method is to consider a pool of participants exchanging a shared secret value and to provide a formal treatment for it. Starting from the famous two-party Diffie--Hellman (DH) key-exchange protocol and from its authenticated variants, security experts have extended it to the multiparty setting for over a decade and, in the past few years, completed a formal analysis in the framework of modern cryptography. The present paper synthesizes this body of work on the provably-secure authenticated group DH key exchange.
Group key exchange (GKE) is one of the basic building blocks in securing group communication. A number of solutions to GKE problem have been proposed, but most of them are not scalable and require a number of rounds linear with the number of group members. We present a method of constructing constant-round and identity-based protocol via secret sharing for GKE within universally composability (UC) framework. The resultant protocol focuses on round efficiency and three rounds of communication are required. The protocol allows the batch verification of messages signed by all other group participants. Moreover, compared with other identity-based protocols, the key generation center (KGC) in our protocol is not always online.
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.