Paper 2006/225

Provably-Secure Time-Bound Hierarchical Key Assignment Schemes

Giuseppe Ateniese, Alfredo De Santis, Anna Lisa Ferrara, and Barbara Masucci

Abstract

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 both the unconditionally secure and the computationally secure settings 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 in the unconditionally secure setting and we show tight lower bounds on the size of the private information distributed to each class. Then, we consider the computational setting and we further 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. Afterwards, we prove that a recently proposed scheme is insecure against key recovery. 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. These appear to be the first constructions for time-bound hierarchical key assignment schemes which are simultaneously practical and provably-secure.