Efficient provably-secure hierarchical key assignment schemes

Santis, Alfredo De; Ferrara, Anna Lisa; Masucci, Barbara

doi:10.1016/j.tcs.2011.06.024

Cited by 37 publications

(31 citation statements)

References 31 publications

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“…Steiner TC-spanners of general d-dimensional posets. We continue the study of the number of edges in a sparsest Steiner k-TC-spanner of a poset as a function of its dimension, following [4] and [21]. Observe that the only poset of dimension 1 is the directed line H n,1 .…”

Section: Our Resultsmentioning

confidence: 99%

“…An access hierarchy is a partially ordered set G of access classes. Each user is entitled to access a certain class and all classes reachable from the corresponding node in G. One approach to enforcing the access hierarchy is to use a key management scheme of the following form [5,6,21,4]. Each edge (i, j) has an associated public key P (i, j), and each node i, an associated secret key k i .…”

Section: Applicationsmentioning

confidence: 99%

“…(See [19] for a survey.) In some applications of TC-spanners (in particular, to access control hierarchies [5,6,21,4]), the shortcuts can use Steiner vertices, that is, vertices not in the original graph G. The resulting spanner is called a Steiner TC-spanner. For some graphs, Steiner TC-spanners can be significantly sparser than ordinary TC-spanners.…”

Section: Introductionmentioning

confidence: 99%

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Steiner Transitive-Closure Spanners of Low-Dimensional Posets

Berman

Bhattacharyya

Grigorescu

et al. 2011

Automata, Languages and Programming

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Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TCspanner) of G is a directed graph H = (V, E H ) that has (1) the same transitive closure as G and (2) diameter at most k. In some applications, the shortcut paths added to the graph in order to obtain small diameter can use Steiner vertices, that is, vertices not in the original graph G. The resulting spanner is called a Steiner transitive-closure spanner (Steiner TC-spanner).Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners of directed acyclic graphs or, equivalently, partially ordered sets. In these applications, the goal is to find a sparsest Steiner k-TC-spanner of a poset G for a given k and G. The focus of this paper is the relationship between the dimension of a poset and the size of its sparsest Steiner TC-spanner. The dimension of a poset G is the smallest d such that G can be embedded into a d-dimensional directed hypergrid via an order-preserving embedding.We present a nearly tight lower bound on the size of Steiner 2-TC-spanners of d-dimensional directed hypergrids. It implies better lower bounds on the complexity of local reconstructors of monotone functions and functions with small Lipschitz constant. The lower bound is derived from an explicit dual solution to a linear programming relaxation of the Steiner 2-TC-spanner problem. We also give an efficient construction of Steiner 2-TC-spanners, of size matching the lower bound, for all low-dimensional posets. Finally, we present a lower bound on the size of Steiner k-TC-spanners of d-dimensional posets. It shows that the best-known construction, due to De Santis et al., cannot be improved significantly.

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Section: Our Resultsmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Steiner Transitive-Closure Spanners of Low-Dimensional Posets

Berman

Bhattacharyya

Grigorescu

et al. 2011

Automata, Languages and Programming

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“…This problem arises in content distribution, operating systems, and project development (see, e.g., the references in [8]). One approach to the access control problem [7,8,46] is to associate public information P (i, j) with each edge (i, j) ∈ G and a secret key k i with each node i. There is an efficient algorithm A which takes k i and P (i, j) and generates k j .…”

Section: Applications Of Tc-spannersmentioning

confidence: 99%

Transitive-Closure Spanners

Bhattacharyya¹,

Grigorescu²,

Jung³

et al. 2012

SIAM J. Comput.

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We define the notion of a transitive-closure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a k-transitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V, E H ) that has (1) the same transitive-closure as G and (2) diameter at most k. These spanners were studied implicitly in access control, property testing, and data structures, and properties of these spanners have been rediscovered over the span of 20 years. We bring these areas under the unifying framework of TC-spanners. We abstract the common task implicitly tackled in these diverse applications as the problem of constructing sparse TC-spanners.We study the approximability of the size of the sparsest k-TC-spanner for a given digraph. Our technical contributions fall into three categories: algorithms for general digraphs, inapproximability results, and structural bounds for a specific graph family which imply an efficient algorithm with a good approximation ratio for that family.Algorithms. We present two efficient deterministic algorithms that find k-TC-spanners of size approximating the optimum. The first algorithm gives anÕ(n 1−1/k )-approximation for k > 2. Our method, based on a combination of convex programming and sampling, yields the first sublinear approximation ratios for (1) DIRECTED k-SPANNER, a well-studied generalization of k-TC-SPANNER, and (2) its variants CLIENT/SERVER DIRECTED k-SPANNER, and the k-DIAMETER SPANNING SUBGRAPH. This resolves the main open question of Elkin and Peleg (IPCO, 2001). The second algorithm, specific to the k-TC-spanner problem, gives anÕ(n/k 2 )-approximation. It shows that for k = Ω( √ n), our problem has a provably better approximation ratio than DIRECTED k-SPANNER and its variants. This algorithm also resolves an open question of Hesse (SODA, 2003).Inapproximability. Our main technical contribution is a pair of strong inapproximability results. We resolve the approximability of 2-TC-spanners, showing that it is Θ(log n) unless P = N P . For constant k ≥ 3, we prove that the size of the sparsest k-TC-spanner is hard to approximate within 2 log 1− n , for any > 0, unless NP ⊆ DTIME(n polylog n ). Our hardness result helps explain the difficulty in designing general efficient solutions for the applications above, and it cannot be improved without resolving a longstanding open question in complexity theory. It uses an involved application of generalized butterfly and broom graphs, as well as noise-resilient transformations of hard problems, which may be of independent interest.Structural bounds. Finally, we study the size of the sparsest TC-spanner for H-minor-free digraphs, which include planar, bounded genus, and bounded tree-width graphs, explicitly investigated in applications above. We show that every H-minor-free digraph has an efficiently constructable k-TC-spanner of sizeÕ(n), which implies anÕ(1)-approximation algorithm for this family. Furthermore, using our insight that 2-TC-spanners yield property testers, we obtain a monotonicity tester with O(log 2 n...

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“…Another hierarchical scheme that was designed to increase efficiency can be found in [33]. Daza in [34] presented a BE approach for mobile ad-hoc networks.…”

Section: The Broadcast Encryption Schemesmentioning

confidence: 99%

One-Time Broadcast Encryption Schemes in Distributed Sensor Networks

Szałachowski

Kotulski

2012

International Journal of Distributed Sensor Networks

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Broadcasting is a message-transferring method characteristic for majority of sensor networks. Broadcast encryption (BE) is broadcasting encrypted messages in such a way that only legitimate nodes of a network can decrypt them. It has many potential applications in distributed wireless sensor networks (WSNs) but perfect deploying of that method is very difficult. This is because of a WSN is a very dynamic network which includes nodes with limited computational, storage, and communication capabilities. Furthermore, an attacker in this environment is powerful. He can eavesdrop, modify, and inject messages or even capture a large number of nodes, so the solutions must be both secure and efficient. This paper describes several BE schemes from the point of view of WSNs. We present in details the schemes called onetime, and we show how these methods can be applied in distributed sensor networks. We mainly focus on data origin authentication and rekeying processes, crucial for security in such a hostile environment. An analysis and evaluations of proposed schemes are also provided.

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Efficient provably-secure hierarchical key assignment schemes

Cited by 37 publications

References 31 publications

Steiner Transitive-Closure Spanners of Low-Dimensional Posets

Steiner Transitive-Closure Spanners of Low-Dimensional Posets

Transitive-Closure Spanners

One-Time Broadcast Encryption Schemes in Distributed Sensor Networks

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