Perfectly Secure Key Distribution for Dynamic Conferences

Abstract

In this paper we analyze perfectly secure key distribution schemes for dynamic conferences. In this setting,anymember of a group oftusers can compute a common key using only his private initial piece of information and theidentitiesof the othert−1 users in the group. Keys are secure against coalitions of up tokusers; that is, even ifkusers pool together their pieces they cannot compute anything about a key of any conference comprised oftother users. First we consider a noninteractive model where users compute the common key without any interaction. We prove the tight bound on the size of each user's piece of information of[formula]times the size of the common key. Then, we consider the model where interaction is allowed in the common key computation phase and show agapbetween the models by exhibiting a one-round interactive scheme in which the user's information is onlyk+t−1 times the size of the common key. Finally, we present its adaptation to network topologies with neighbourhood constraints and to asymmetric (e.g., client-server) communication models.