Generation of key predistribution schemes using secret sharing schemes

Abstract

In a key predistribution scheme a trusted authority distributes pieces of information among a set of users in such a way that users belonging to a specified privileged subset can compute individually a secret key common to this subset. In such a scheme, a family of forbidden subsets of users cannot obtain any information about the value of the secret. In this paper, we present a new construction of a key predistribution scheme using a family of vector space secret sharing schemes. The set of privileged users and the family of forbidden subsets is described in terms of the family of vector space access structures. A generalization using linear secret sharing schemes is given. We show that a particular case of this construction is any key predistribution scheme in which pieces of information and secrets are linear combinations of random numbers. Using this result, we show explicitly that the most important key predistribution schemes can be seen as a particular case of this construction. For this construction, the question of when given secrets can be predistributed is discussed.