Cryptographic Hierarchical Access Control for Dynamic Structures

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.