Managing key hierarchies for access control enforcement: Heuristic approaches

Abstract

Data outsourcing is emerging today as a successful paradigm allowing individuals and organizations to resort to external servers for storing their data, and sharing them with others. The main problem of this trend is that sensitive data are stored on a site that is not under the data owner's direct control. This scenario poses a major security problem since often the external server is relied upon for ensuring high availability of the data, but it is not authorized to read them. Data need therefore to be encrypted. In such a context, the application of an access control policy requires different data to be encrypted with different keys so to allow the external server to directly enforce access control and support selective dissemination and access. The problem therefore emerges of designing solutions for the efficient management of an encryption policy enforcing access control, with the goal of minimizing the number of keys to be maintained by the system and distributed to users.

In this paper, we prove that the problem of minimizing the number of keys is NP-hard and present alternative approaches for its solution. We first formulate the minimization problem as an instance of an integer linear programming problem and then propose three different families of heuristics, which are based on a key derivation tree exploiting the relationships among user groups. Finally, we experimentally evaluate the performance of our heuristics, comparing them with previous approaches.

Introduction

Data outsourcing has become increasingly popular in recent years. The main advantage of data outsourcing is that it promises higher availability and more effective disaster protection than in-house operations. However, since data owners physically release their information to external servers that are not under their control, data confidentiality (and even integrity) may be put at risk. Besides protecting such data from attackers and unauthorized users, there is the need to protect the privacy of the data from the so called honest-but-curious servers, that is, servers that, while trustworthy to properly manage the data, may not be trusted by the data owner to read their content. The problem of protecting data when outsourcing them to an external honest-but-curious server has emerged to the attention of researchers very recently. Existing proposals (e.g., Ceselli et al., 2005, Hacigümüs et al., 2002a, Wang and Lakshmanan, 2006) in the data outsourcing area typically store the data in encrypted form and associate with the encrypted data additional indexing information. Such indexes are used by the external DBMS to select the data to be returned in response to a query. Existing approaches however do not address the problem of supporting different access privileges (authorizations) for different users and result therefore limited in today's scenarios, where remotely stored data may need to be made accessible in a selective way (i.e., different users may be authorized to access different views of the data).

There is therefore an increasing interest in the definition of security solutions that allow the enforcement of access control policies on outsourced data. A promising solution in this direction consists in integrating access control and encryption. Although traditional approaches assume a strict separation between policies and mechanisms, and such a separation has often been beneficial, in the data outsourcing scenario their combination is proving successful. Combining cryptography with access control essentially requires that resources should be encrypted differently depending on the access authorizations holding on them, so to make their decryption possible only to authorized users (Damiani et al., 2006, De Capitani di Vimercati et al., 2007a). The application of this approach in data outsourcing scenarios allows owners to encrypt data, according to an encryption policy regulated by authorizations, outsource the data to the external servers, and distribute to users the needed encryption keys. Proper encryption and key distribution automatically ensure therefore obedience of the access control policy, while not requiring the data owner to maintain control on the data storage and accesses. In this paper, we address such a problem and propose a heuristic approach to minimize the number of keys to be maintained by the system and distributed to users. Like other proposals in the literature (Damiani et al., 2006, Damiani et al., 2007, De Capitani di Vimercati et al., 2007a), we base our solution on key derivation exploiting a key derivation tree that allows users to derive new keys from other keys they know. In Blundo et al. (2009) we presented an early version of our proposal that here is extended to consider alternative approaches for determining the minimal number of keys that correctly enforce an authorization policy defined by the data owner. In particular, we provide a new formulation of the problem in terms of an integer linear programming problem and present two new families of heuristics (i.e., leaves-based and mixed-based heuristics). We also formally prove that the problem of minimizing the number of keys is NP-Hard.

The remainder of the paper is organized as follows. Section 2 illustrates the basic concepts of access control systems based on selective encryption. Section 3 introduces our minimization problem. Section 4 formulates the minimization problem as a minimum weight problem. Section 5 illustrates the integer linear programming problem corresponding to the weight minimization problem. Section 6 presents three families of heuristic, which are based on the computation of a minimum spanning tree (MST) and on vertices factorization to improve the quality of the solution. Section 7 presents some experimental results showing that, compared with previous proposals, our heuristics prove efficient and effective in the computation of a key derivation graph. Section 8 discusses related work. Finally, Section 9 draws our conclusions.