On the Relations Between Security Notions in Hierarchical Key Assignment Schemes for Dynamic Structures
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 i
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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. Keywords: Access control · Key assignment · Dynamic structures · Dynamic adversary · Strong key recovery · Strong key indistinguishability
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Introduction
The main aim of the access control management is to provide only authorized users with the access to certain resources. More precisely, based on their relative responsibilities and roles, the users of a system are usually grouped into hierarchies, characterized by some disjoint classes (security classes). Hierarchical structures find a natural way of application in many different areas. The use of cryptography to deal with key management issues in hierarchical structures was first addressed by Akl and Taylor [2], which introduced a c Springer International Publishing Switzerland 2016 J.K. Liu and R. Steinfeld (Eds.): ACISP 2016, Part II, LNCS 9723, pp. 37–54, 2016. DOI: 10.1007/978-3-319-40367-0 3
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hierarchical key assignment scheme where each class is provided with a key that can be employed, together with some public information generated by a Trusted Authority (TA), to derive the key of any class lower down in the hierarchy. Following the seminal work due to Akl and Taylor, many schemes have been proposed in the literature, each providing different trade-offs for what concerns the quantity of public and private information, as well as the complexity of key derivation (e.g., [3,4,6,14,16,17,21,24,25,27,29,30,32–35,40]). Again, other schemes have been proposed, either supporting more general access control policies [18,20,31,41] or satisfying further time-dependent constraints [7,8,15,22,23,28,37–39,42]. However, it is important to remark that despite many schemes have been proposed in the literature, many of them are not provided with a formal securi
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