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Electronics Letters

Scalable key exchange transformation: from two-party to group

J. Y. Hwang, S.M. Lee, Donghwan Lee

Published Jun 10, 2004• 14 citations
Publisher

Abstract

A modular method which derives a scalable construction of a group key exchange (GKE) scheme from a two-party key exchange (KE) one is presented. By combining the method presented with the compiler by Katz and Yung [1] a scalable compiler can be obtained that transforms any two-party KE protocol secure against a passive eavesdropper to an authenticated GKE one secure against a stronger active adversary.

DOI
10.1049/el:20040449

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•Jan 1, 2006•1 citation
A modular method which derives a scalable construction of a group key exchange (GKE) scheme from a two-party key exchange (KE) one is presented. By combining the method presented with the compiler by Katz and Yung [1] a scalable compiler can be obtained that transforms any two-party KE protocol secure against a passive eavesdropper to an authenticated GKE one secure against a stronger active adversary.
Abstract. This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. 2-TGKE and 3-TGKE compilers require a total of O (n lg n) communication, when compared to the existing compiler for circular topology, where the communication cost is O ` n 2 ´. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [18], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), which are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power. Finally, we present a constant round authenticated group key exchange (2-TAGKE) obtained by applying Diffie-Hellman protocol and the technique in [18] to our compiler 2-TGKE. We prove the security of our compilers in a stronger Real or Random model and do not assume the existence of random oracles.
This work presents the first scalable, efficient and generic compilers to construct group key exchange (GKE) protocols from two/three party key exchange (2-KE/3-KE) protocols. We propose three different compilers where the first one is a 2-KE to GKE compiler (2-TGKE) for tree topology, the second one is also for tree topology but from 3-KE to GKE (3-TGKE) and the third one is a compiler that constructs a GKE from 3-KE for circular topology. Our compilers 2-TGKE and 3-TGKE are first of their kind and are efficient due to the underlying tree topology. For the circular topology, we design a compiler called 3-CGKE. By extending the compilers 2-TGKE and 3-TGKE using the techniques in [?], scalable compilers for tree based authenticated group key exchange protocols (2-TAGKE/3-TAGKE), that are secure against active adversaries can be constructed. As an added advantage our compilers can be used in a setting where there is asymmetric distribution of computing power and hence applicable for low power devices such as PDA's, palmtops, sensor network nodes and mobile phones.
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.
Abstract We revisit a generic compiler from a two-party key exchange (KE) protocol to a group KE (GKE) one by Just and Vaudenay. We then give two families of GKE protocols fromstaticassumptions, which are obtained from the general compiler. The first family of the GKE protocols is a constant-round GKE by using secure key derivation functions (KDFs). As special cases, we have such GKE fromstaticRing-LWE (R-LWE), where “static” means that the parameter size in the R-LWE does not depend on the number of group members,n, and also from the standard SI-DDH and CSI-DDH assumptions. The second family consists of two-round GKE protocols from isogenies, which are proven secure fromnewisogeny assumptions, the first (resp. second) of which is based on the SIDH (resp. CSIDH) two-party KE. The underlying newstaticassumptions are based on indistinguishability betweena product value of supersingular invariantsand a random value.
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.