Linear Key Predistribution Schemes

In a key predistribution scheme, some secret information is distributed among a set of users. For a given family of privileged groups, this secret information must enable every user in a privileged group to compute a common key associated with that group. Besides, this common key must remain unknown to some specified coalitions of users outside the privileged group. We present in this paper a new model, based on linear algebraic techniques, for the design of key predistribution schemes that unifies all previous proposals. This new model provides a common mathematical formulation and a better understanding of key predistribution schemes. Two new families of key predistribution schemes that are obtained by using this model are presented. Those families provide, for some specification structures, schemes that have better information rates than the ones given in previous proposals or fit in situations that have not been considered before.