  The access control problem in a hierarchy can be solved by using a
hierarchical key assignment scheme, where each class is assigned an encryption
key and some private information. A formal security analysis for hierarchical
key assignment schemes has been traditionally considered in two different
settings, i.e., the unconditionally secure and the computationally secure
setting, and with respect to two different notions: security against key
recovery (KR-security) and security with respect to key indistinguishability
(KI-security), with the latter notion being cryptographically stronger.
Recently, Freire, Paterson and Poettering proposed strong key
indistinguishability (SKI-security) as a new security notion in the
computationally secure setting, arguing that SKI-security is strictly stronger
than KI-security in such a setting. In this paper we consider the
unconditionally secure setting for hierarchical key assignment schemes. In such
a setting the security of the schemes is not based on specific unproven
computational assumptions, i.e., it relies on the theoretical impossibility of
breaking them, despite the computational power of an adversary coalition. We
prove that, in this setting, SKI-security is not stronger than KI-security,
i.e., the two notions are fully equivalent from an information-theoretic point
of view.
