A note on time-bound hierarchical key assignment schemes

A time-bound hierarchical key assignment scheme is a method to assign time-dependent encryption keys to a set of classes in a partially ordered hierarchy, in such a way that each class can compute the keys of all classes lower down in the hierarchy, according to temporal constraints. In this paper we consider the unconditionally secure setting for time-bound hierarchical key assignment schemes and distinguish between two different goals: security with respect to key indistinguishability and against key recovery. We first present definitions of security with respect to both goals; then, we prove a tight lower bound on the size of the private information distributed to each class; finally, we show an optimal construction for time-bound hierarchical key assignment schemes.