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 each class can compute 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 consider two different goals: security with respect to key indistinguishability and against key recovery. Moreover, we distinguish security against static and adaptive adversarial behaviors. We explore the relations between all possible combinations of security goals and adversarial behaviors and, in particular, we prove that security against adaptive adversaries is (polynomially) equivalent to security against static adversaries. Finally, we propose two different constructions for time-bound key assignment schemes. The first one is based on symmetric encryption schemes, whereas the second one makes use of bilinear maps. Both constructions support updates to the access hierarchy with local changes to the public information and without requiring any private information to be re-distributed.