Communication Complexity of Group Key Distribution

Communication complexity has always been an important issue when designing group key distribution systems. This paper systematically studies what can be achieved for the most common measures of protocol complexity. Lower bounds for the total number of messages, the total number of exchanges, and the number of necessary rounds are established, whereby models that allow broadcasting have to be distinguished from those that do not. For every measure of protocol complexity, we furthermore show that the corresponding bound is realistic for Diffie-Hellman-based protocols by referring to or introducing protocols that match the bound or exceed it by only one.