Efficient group Diffie-Hellman key agreement protocols

In a group Diffie–Hellman (GDH) key agreement protocol, all group members collaboratively establish a group key. Most GDH key agreement protocols took natural generalization of the original Diffie–Hellman (DH) key agreement protocol to arrange all group members in a logic ring or a binary tree and to exchange DH public keys. The computational cost and the communication rounds are the two most important factors that affect the efficiency of a GDH protocol when there are a large number of group members. In this paper, we propose GDH key agreement protocols based on the secret sharing scheme. In addition, we use a one-way key confirmation and digital certificates of DH public keys to provide authentication of group keys. In the proposed authenticated GDH key agreement protocol, each group member requires to broadcast three-round messages, n modular exponentiations, n polynomial interpolations and n one-way functions. Our proposed solution is efficient, robust and secure. 2014 Elsevier Ltd. All rights reserved.