Key Indistinguishability versus Strong Key Indistinguishability for Hierarchical Key Assignment Schemes

A hierarchical key assignment scheme is a method to assign some private information and encryption keys to a set of classes in a partially ordered hierarchy, in such a way that the private information of a higher class can be used to derive the keys of all classes lower down in the hierarchy. In this paper we analyze the security of hierarchical key assignment schemes according to different notions: security with respect to key indistinguishability and against key recovery, as well as the two recently proposed notions of security with respect to strong key indistinguishability and against strong key recovery . We first explore the relations between all security notions and, in particular, we prove that security with respect to strong key indistinguishability is not stronger than the one with respect to key indistinguishability. Afterwards, we propose a general construction yielding a hierarchical key assignment scheme offering security against strong key recovery, given any hierarchical key assignment scheme which guarantees security against key recovery.