Security and Tradeoffs of the Akl-Taylor Scheme and Its Variants

In 1983 Akl and Taylor [Cryptographic Solution to a Problem of Access Control in a Hierarchy, ACM Transactions on Computer Systems, 1(3), 239---248, 1983] first suggested the use of cryptographic techniques to enforce access control in hierarchical structures. Over time, their scheme has been used in several different contexts, including mobile agents environments and broadcast encryption. However, it has never been fully analyzed from the security point of view. We provide a rigorous analysis of the Akl-Taylor scheme and prove that it is secure against key recovery. We also show how to obtain different tradeoffs between the amount of public information and the number of steps required to perform key derivation. Moreover, we propose a general construction to set up a key assignment scheme secure w.r.t. key indistinguishability, given any key assignment scheme secure against key recovery. Finally, we show how to use our construction, along with our tradeoffs, to obtain a variant of the Akl-Taylor scheme, secure w.r.t key indistinguishability, requiring a constant amount of public information.