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.