Paper 2009/115

Scalable Compilers for Group Key Establishment : Two/Three Party to Group

S. Sree Vivek, S. Sharmila Deva Selvi, Deepanshu Shukla, and C. Pandu Rangan

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 $\mathcal{O}\left(n\lg n \right)$ communication, when compared to the existing compiler for circular topology, where the communication cost is $\mathcal{O}\left(n^2 \right)$. By extending the compilers 2-TGKE and 3-TGKE using the techniques in \cite{DLB07}, 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 \cite{DLB07} 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.