Diffie-Hellman key distribution extended to group communication

Ever since 2-party Diffie-Hellman key exchange was first proposed in 1976, there have been efforts to extend its simplicity and elegance to a group setting. Notable solutions have been proposed by Ingemarsson et al. (in 1982) and Burmester/Desmedt (in 1994). In this paper, we consider a class of protocols that we call natural extensions of Diffie-Hellman to the n-party case. After demonstrating the security of the entire class based on the intractability of the Diffie-Hellman problem we introduce two novel and practical protocols and compare them to the previous results. We argue that our protocols are optimal with respect to certain aspects of protocol complexity.