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, Efficient Provably-Secure
Hierarchical Key Assignment Schemes

Alfredo De Santis, Anna Lisa Ferrara, and Barbara Masucci

Dipartimento di Informatica ed Applicazioni, Università di Salerno
84084 Fisciano (SA), Italy



Abstract. 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 re-
quiring any private information to be re-distributed.
– We first show an encryption based construction which is provably
secure with respect to key indistinguishability, requires a single com-
putational 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 a construction 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.


1 Introduction

The hierarchical access control problem is defined in a scenario where the users
of a computer system are organized in a hierarchy formed by a certain number
of disjoint security classes. Hierarchical structures arise from the fact that some
users have more access rights than others, and are widely employed in many
different application areas, including database management systems, computer
networks, operating systems, military, and government communications.
In 1983, Akl and Taylor [1] suggested the use of cryptographic techniques to
enforce access control in hierarchical structures. In particular, they designed a
hierarchical key assignment scheme where each class is assigned an encryption
key that can be used, along with some public parameters, to compute the key
assigned to all classes lower down in the hierarchy. This assignment is carried
out by a Trusted Authority (TA), which is active only at the distribution phase.
A recent work by Crampton et al. [10] provides a detailed classification of many
schemes proposed in the last twenty years and evaluates their merits. Atallah

L. Kučera and A. Kučera (Eds.): MFCS 2007, LNCS 4708, pp. 371–382, 2007.

c Springer-Verlag Berlin Heidelberg 2007

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