A Group Key Agreement Scheme Revisited

In PKC'2004, a constant-round group key exchange protocol is proposed. It takes advantage of the properties of the ElGamal encryption scheme combined with the standard secret sharing technique. In this paper, we show that the scheme can be greatly simplified because the standard secret sharing technique does not work well. Based on the observation, we present a revisited scheme. It saves about 4/5 cost of the original scheme. In addition, its security can be directly reduced to the underlying Schnorr's signature scheme and the ElGamal encryption.

1 Introduction

A group key agreement protocol allows a set of users, communicating over a public network, to agree on a private session key. This secret key can then be used to create a confidential communication channel amongst the entities. The main features of a group key agreement scheme are security and efficiency, in the presence of an active adversary. On top of that a key agreement scheme should guarantee the privacy property, i.e. that no eavesdropper should be able to gain information about the key after having seen the messages exchanged between the parties being involved in the protocol. In general, the efficiency quantified as the number of communication rounds, as well as the space and computing resources required, is to be considered as a crucial property when designing key agreement protocols.