Generation of Key Predistribution Schemes using Secret Sharing Schemes

In a key predistribution scheme a trusted authority distributes pieces of information among a set of users of such a way that specified privileged subsets of users can compute a secret key individually. 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 combination 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.