Interaction in key distribution schemes

Abstract

A (g,b) key distribution scheme allows conferences of g users to generate secret keys, so that disjoint coalitions of b users cannot gain any information on the key (in the information theoretic sense). In this work we study the relationships between interaction and space efficiency of key distribution schemes. We prove that interaction does not help in the context of zcnrestricted schemes. On the other hand, we show that for restricted schemes, which are secure for a limited number of conferences, interaction can substantially improve the space efficiency.