Simple and efficient group key agreement based on factoring

Group key agreement protocols are designed to allow a group of parties communicating over a public network to agree on a session key in a secure manner. While a number of solutions have been proposed over the years, all of them are inadequate for a group where members are spread across a wide area network; their communication overhead is significant in terms of the number of communication rounds or the number of messages sent, both of which are recognized as the dominant factors that severely slow down the protocols in wide area networks. In this paper we first present a communication-efficient group key agreement protocol and then prove its security against a passive adversary in the random oracle model under the factoring intractability assumption. The proposed protocol provides perfect forward secrecy and runs only in two communication rounds while achieving optimal message complexity. Therefore, the protocol is well suited for networking environments with high communication latency.