Communication in key distribution schemes

A (g, b) key distribution scheme allows conferences of g users to generate secret keys, such that disjoint coalitions of b users cannot gain any information on the generated key (in the information-theoretic sense). We study the relationships between communication and space efficiency of key distribution schemes. We prove that communication does not help in the context of unrestricted schemes. On the other hand, we show that for restricted schemes, which are secure only when used by a limited number of conferences, communication can substantially improve the space efficiency. We also present lower bounds on the space efficiency of restricted schemes.