On the Relations Between Security Notions in Hierarchical Key Assignment Schemes for Dynamic Structures

Abstract

A hierarchical key assignment scheme distribute some private information and encryption keys to a set of classes in a partially ordered hierarchy, so that the private information of higher classes can be employed to derive the keys of classes lower down in the hierarchy. A hierarchical key assignment scheme for dynamic structures allows to make dynamic updates to the hierarchy, such as addition, deletion and modification of classes and relations among them, as well as the revocation of users. In this work we analyze security notions for hierarchical key assignment schemes supporting dynamic structures. In particular, we first propose the notion of key recovery for those schemes. Furthermore, we extend to such schemes the strong key indistinguishability and strong key recovery security definitions proposed by Freire et al. for hierarchical key assignment schemes. Finally, we investigate the relations occurring between all the state-of-the-art security notions for hierarchical key assignment schemes supporting dynamic structures, showing implications and separations which hold between such notions. In detail, we prove that also in the case of dynamic structures, security with respect to strong key indistinguishability is equivalent to the one with respect to key indistinguishability.