Cryptographic Enforcement of Information Flow Policies Without Public Information

Abstract

The enforcement of access control policies using cryptographic primitives has been studied for over 30 years. When symmetric cryptographic primitives are used, each protected resource is encrypted and only authorized users are given the decryption key. Hence, users may require many keys. In most schemes in the literature, keys are derived from a single key explicitly assigned to the user and publicly available information. Recent work has challenged this design by developing schemes that do not require public information, the trade-off being that a user may require more than one key. However, these new schemes, which require a chain partition of the partially ordered set on which the access control policy is based, generally require more keys than necessary. Moreover, no algorithm is known for determining the best chain partition to use. In this paper we define the notion of a tree-based cryptographic enforcement scheme, which, like chain-based schemes, requires no public information but simultaneously has lower storage requirements. We formally establish that the strong security properties of recent chain-based schemes are preserved by tree-based schemes, and provide an efficient construction for deriving a tree-based enforcement scheme from a given policy that minimizes the number of keys required.

Optimal Constructions for Chain-Based Cryptographic Enforcement of Information Flow Policies

“…⊓ ⊔ Let (X, ) be an information flow policy and let y, z ∈ X with z < y. Then, following Crampton et al [10], we define…”

Cryptographic enforcement of information flow policies without public information via tree partitions1

“…We design and analyze an efficient algorithm for computing a forest that minimizes the total number of issued secrets. This work generalizes our previous work on tree-based enforcement schemes [16]. In addition, the more general framework enables us to simplify the techniques and formal exposition.…”

“…Crampton et al [16] made use of the fact that derivation paths are uniquely defined in trees (as well as in chains) to develop the idea of a tree-based cryptographic enforcement scheme. Their work established that it was possible to compute (in polynomial time) an optimal tree for the information flow policy.…”

“…In this section, we generalize the approach taken by Crampton et al [14] for chain-based enforcement schemes, and Crampton et al [16] for tree-based enforcement schemes. In particular, we introduce the concept of a tree partition of a poset (X, ) and show how such a partition may be used to construct a cryptographic enforcement scheme for an information flow policy defined by (X, ).…”

“…In Section 2, we provide the relevant background on cryptographic enforcement schemes, and formally identify the problem. We also discuss related work, including preliminary versions of the ideas presented in this paper [15,16]. Then, in Section 3, we formally define a tree partition and a forest-based cryptographic enforcement scheme for an information flow policy.…”