A group key agreement protocol (GKA) allows a set of players to establish a shared secret key which can be used to secure a subsequent communication. Several efficient constant-round GKAs have been proposed. However, their performance degrades if some players fail during protocol execution. This is a problem in practice, e.g. for mobile nodes communicating over wireless media, which can loose connectivity during the protocol execution. Current constant-round GKA protocols are either efficient and non-robust or robust but not efficient: Assuming a reliable broadcast communication medium, the standard encryption-based group key agreement protocol can be robust against arbitrary number of node faults, but the size of the messages broadcast by every player is proportional to the number of players. In contrast, non-robust group key agreement can be achieved with each player broadcasting just constant-sized messages. We propose a novel 2-round group key agreement protocol which tolerates up to T node failures using O(T)-sized messages, for any T. To exemplify the usefulness of this flexible trade-off between message size and fault tolerance, we show that the new protocol implies a fully-robust group key agreement with O(log n)-sized messages and expected round complexity close to 2, assuming random node faults. The proposed protocol is secure under the (standard) Decisional Square Diffie-Hellman assumption.
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