Abstract

Protocols for group key exchange 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 group key exchange protocols have been proposed over the years in a variety of settings. However despite many impressive achievements, there seems to have been no previous systematic look at the growing problem of key exchange over integrated wired and wireless (IWW) networks which consist of two distinct types of users: users having low-performance mobile devices with some form of battery power and users having high-performance stationary computers with no power constraint. The contribution of the present work is to fill this deficiency by providing a secure and efficient protocol for resource-aware group key exchange over the rapidly expanding IWW networks. By evenly spreading much of the total amount of computation across high power users, our protocol avoids any potential performance bottleneck of the system while keeping the burden on low power users at minimal. Our protocol also achieves provable security against powerful active adversaries under the decisional Diffie–Hellman assumption. We provide a rigorous proof of security for the protocol in a well-defined formal model of communication and adversarial capabilities.

Keywords: Authenticated group key exchange; Integrated wired and wireless networks; Mobile devices; Provable security; Decisional Diffie–Hellman (DDH) assumption

Article Outline

1. Introduction

2. Formal setting

2.1. Security model

2.1.1. Participants

2.1.2. Partnership

2.1.3. Adversary

2.2. Security definition and assumptions

2.2.1. Freshness

2.2.2. Security

2.2.3. Decisional Diffie–Hellman (DDH) assumption

2.2.4. Signature schemes

3. Group key exchange secure against passive adversaries

3.1. Setup

3.2. Basic protocol (BP)

3.3. Generalized protocol (GP)

4. Security result for WAW

4.1. Single vs. multiple Test queries

4.2. Proof of security for BP

4.3. Proof of security for GP

5. Group key exchange secure against active adversaries

5.1. WAW⁺

5.2. Efficiency

5.3. Security result for WAW⁺

6. Proof of Theorem 3

7. Conclusion

Acknowledgements

References