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 the key of a higher class can be used to derive 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 first consider the unconditionally secure setting and we show a tight lower bound on the size of the private information distributed to each class. Then, we consider the computationally secure setting and obtain several results: We first prove that a recently proposed scheme is insecure against collusion attacks. Hence, motivated by the need for provably-secure schemes, we propose two different constructions for time-bound hierarchical key assignment schemes. The first one is based on symmetric encryption schemes, whereas, the second one makes use of bilinear maps. These appear to be the first constructions of time-bound hierarchical key assignment schemes which are simultaneously practical and provably-secure. Copyright 2006 ACM

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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 design and analyze hierarchical key assignment schemes which are provably-secure and support dynamic updates to the hierarchy with local changes to the public information and without requiring any private information to be redistributed. • We first consider the problem of constructing a hierarchical key assignment scheme by using as a building block a symmetric encryption scheme. We propose a new construction which is provably secure with respect to key indistinguishability, requires a single computational assumption, and improves on previous proposals. • Then, we show how to reduce key derivation time at the expense of an increment of the amount of public information, by improving a previous result. • Finally, we show how to construct a hierarchical key assignment scheme by using as a building block a public-key broadcast encryption scheme. In particular, one of our constructions provides constant private information and public information linear in the number of classes in the hierarchy.

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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. Sometimes, it is necessary to make dynamic updates to the hierarchy, in order to implement an access control policy which evolves with time. All security models for hierarchical key assignment schemes have been designed to cope with static hierarchies and do not consider the issue of performing dynamic updates to the hierarchy. In this paper, we define the concept of hierarchical key assignment schemes supporting dynamic updates, formalizing the relative security model. In particular, we provide the notion of security with respect to key indistinguishability, by considering the dynamic changes to the hierarchy. Moreover, we show how to construct a hierarchical key assignment scheme supporting dynamic updates, by using as a building block a symmetric encryption scheme. The proposed construction is provably secure with respect to key indistinguishability, and provides efficient key derivation and updating procedures, while requiring each user to store only a single private key

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