Trade-offs Between Communication and Storage in Unconditionally Secure Schemes for Broadcast Encryption and Interactive Key Distribution

In 1993, Beimel and Chor presented an unconditionally secure interactive protocol which allows a subset of users in a network to establish a common key. This scheme made use of a key predistribution scheme due to Blom. In this paper, we describe some variations and generalizations of the Beimel-Chor scheme, including broadcast encryption schemes as well as interactive key distribution schemes. Our constructions use the key pre-distribution scheme of Blundo et al, which is a generalization of the Blom scheme. We obtain families of schemes in which the amount of secret information held by the network users can be traded oo against the amount of information that needs to be broadcast. We also discuss lower bounds on the storage and communcation requirements of protocols of these types. Some of our schemes are optimal (or close to optimal) with respect to these bounds.