In the paper we study parallel key exchange among multiple parties. The status of parallel key exchange can be depicted by a key graph. In a key graph, a vertex represents a party and an edge represents a relation of two parties who are to share a key. We first propose a security model for a key graph, which extends the Bellare-Rogaway model for two-party key exchange. Next, we clarify the relations among the various security notions of key exchange. Finally, we construct an efficient key exchange protocol for a key graph using the randomness re-use technique. Our protocol establishes the multiple keys corresponding to all edges of a key graph in a single session. The security of our protocol is proven in the standard model.

key exchange, key graph, security notions, randomness re-use