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In AFRICACRYPT2010, Abdalla, Chevalier, Manulis, and Pointcheval proposed an improvement of group key exchange (GKE), denoted by GKE+S, which enables on-demand derivation of independent secret subgroup key for all potential subsets. On-demand derivation is efficient (actually, it requires only one round) compared with GKE for subgroup (which requires two or more rounds, usually) by re-using values which was used for the initial GKE session for superior group. In this paper, we improve the Abdalla et al. GKE+S protocol to support key randomization. In our GKE+S protocol, the subgroup key derivation algorithm is probabilistic, whereas it is deterministic in the original Abdalla et al. GKE+S protocol. All subgroup member can compute the new subgroup key (e.g., for countermeasure of subgroup key leakage) with just one-round additional complexity. Our subgroup key establishment methodology is inspired by the “essential idea” of the NAXOS technique. Our GKE+S protocol is authenticated key exchange (AKE) secure under the Gap Diffie-Hellman assumption in the random oracle model.

Flexible Group Key Exchange with On-demand Computation of Subgroup Keys Supporting Subgroup Key Randomization