Key agreement for key hypergraph

In this paper, we propose a key agreement protocol for a key hypergraph. In a key hypergraph, a party is represented as a vertex and a group of parties is represented as a hyperedge. A key agreement protocol for a key hypergraph establishes all the keys for hyperedges in a key hypergraph at the same time. A naive approach would be to run a group key protocol concurrently for each hyperedge. By using the randomness re-use technique, we propose an efficient key agreement protocol for a key hypergraph, which is of two rounds. We formalize the key exchange model for a key hypergraph which is an extension of a group key exchange model and especially incorporates insider attacks. The proposed key agreement protocol for a key hypergraph provides key independence and forward secrecy in the random oracle model under the computational Diffie-Hellman assumption.