Provably-secure 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 the key of a higher class can be used to derive the keys of all classes lower down in the hierarchy, according to temporal constraints.In this paper we design and analyze time-bound hierarchical key assignment schemes which are provably-secure and efficient. We first consider the unconditionally secure setting and we show a tight lower bound on the size of the private information distributed to each class. Then, we consider the computationally secure setting and obtain several results: We first prove that a recently proposed scheme is insecure against collusion attacks. Hence, motivated by the need for provably-secure schemes, we propose two different constructions for time-bound hierarchical key assignment schemes. The first one is based on symmetric encryption schemes, whereas, the second one makes use of bilinear maps. These appear to be the first constructions of time-bound hierarchical key assignment schemes which are simultaneously practical and provably-secure.