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On the Applicability of Combinatorial Designs to key predistribution for wireless sensor networks. arXiv eprint Archive Report
, 2009
"... The constraints of lightweight distributed computing environments such as wireless sensor networks lend themselves to the use of symmetric cryptography to provide security services. The lack of central infrastructure after deployment of such networks requires the necessary symmetric keys to be predi ..."
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The constraints of lightweight distributed computing environments such as wireless sensor networks lend themselves to the use of symmetric cryptography to provide security services. The lack of central infrastructure after deployment of such networks requires the necessary symmetric keys to be predistributed to participating nodes. The rich mathematical structure of combinatorial designs has resulted in the proposal of several key predistribution schemes for wireless sensor networks based on designs. We review and examine the appropriateness of combinatorial designs as a tool for building key predistribution schemes suitable for such environments. 1
A Unified Approach to Combinatorial Key Predistribution Schemes for Sensor Networks
, 2012
"... There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified f ..."
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There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced tdesigns”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario. 1
Pairwise and Triple Key Distribution in Wireless Sensor Networks with Applications
"... mapped to a sensor network, where v represents the size of the key pool, b represents the maximum number of nodes that the network can support, and k represents the size of the key chain. Any pair (or tsubset) of keys occurs together uniquely in exactly nodes; 2 and 3 are used to establish unique ..."
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mapped to a sensor network, where v represents the size of the key pool, b represents the maximum number of nodes that the network can support, and k represents the size of the key chain. Any pair (or tsubset) of keys occurs together uniquely in exactly nodes; 2 and 3 are used to establish unique pairwise or triple keys. We use several known constructions of designs with 2, to predistribute keys in sensors. We also describe a new construction of a design called strong Steiner trade and use it for pairwise key establishment. To the best of our knowledge, this is the first paper on application of trades to key distribution. Our scheme is highly resilient against node capture attacks (achieved by key refreshing) and is applicable for mobile sensor networks (as key distribution is independent on the connectivity graph), while preserving low storage, computation and communication requirements. We introduce a novel concept of triple key distribution, in which three nodes share common keys, and discuss its application in secure forwarding, detecting malicious nodes and key management in clustered sensor networks. We present a polynomialbased and a combinatorial approach (using trades) for triple key distribution. We also extend our construction to simultaneously provide pairwise and triple key distribution scheme, and apply it to secure data aggregation.
Key predistribution techniques for gridbased wireless sensor networks, 2009. Available at ePrint Cryptology archive 2009/014
"... Abstract. We consider symmetric key predistribution in gridbased wireless sensor networks. Networks consisting of wireless sensor nodes arranged in a grid pattern have many useful applications, including environmental monitoring and agribusiness. The structured physical distribution of nodes in suc ..."
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Abstract. We consider symmetric key predistribution in gridbased wireless sensor networks. Networks consisting of wireless sensor nodes arranged in a grid pattern have many useful applications, including environmental monitoring and agribusiness. The structured physical distribution of nodes in such networks facilitates efficient distribution of keys to the nodes prior to deployment. It has been shown that combinatorial objects known as distinctdifference configurations (DDCs) can be used to construct effective key predistribution schemes (KPSs) for gridbased networks. In this paper we observe that the regular topology of a gridbased network enables an efficient tradeoff between the connectivity, resilience and storage requirements of a KPS, and we discuss the balancing of these properties to suit application requirements. We then show how recent results on the construction of DDCs can be used to produce KPSs that achieve the desired balance, and we provide explicit algorithms for the instantiation of these schemes. Key words: Key predistribution, wireless sensor networks; symmetric key management. 1
Key Predistribution in Wireless Sensor Networks When Sensors Are Within Communication Range
"... Abstract Wireless networks are more vulnerable to security threats than wired networks. Since sensors are resource constrained, the use of traditional cryptographic key management techniques is not practical. Hence keys are distributed in sensor nodes prior to their deployment. This method, called k ..."
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Abstract Wireless networks are more vulnerable to security threats than wired networks. Since sensors are resource constrained, the use of traditional cryptographic key management techniques is not practical. Hence keys are distributed in sensor nodes prior to their deployment. This method, called key predistribution, was investigated recently in a number of studies. This chapter restricts the discussion to singlehop networks, where any two sensors are within communication range of each other. The goal is to enable any two sensor nodes to exchange information using their common key, so that other sensors, or an adversary, are unable to decode the message. If two sensor nodes do not share a common key then a path between them, via other sensor nodes, is established, with sensors on the path being able to decode a message and forward it encrypted with a new key. We describe different types of key predistribution schemes for singlehop networks and discuss their merits and demerits in terms of resiliency (impact of node compromises), scalability, connectivity, and memory, computation, and communication resources. Sharedkey discovery process should minimize the use of communication bandwidth. We also
Key predistribution schemes using block designs in wireless sensor networks
 In Computational Science and Engineering, 2009. CSE ’09., 873878. DOI 10.1109/CSE.2009.35
, 2009
"... Key predistribution schemes using block designs in wireless sensor networks ..."
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Key predistribution schemes using block designs in wireless sensor networks
On the Inefficiency of the Resources Optimal Key PreDistribution Scheme for Wireless Sensor Network
"... Abstract — In this paper we reevaluate the resources requirements of the “resources optimal key predistribution (RKPD) scheme in wireless sensor networks”. Our evaluation shows that RKPD has excessive requirements in terms of memory, computation, and communication. Thees requirements are problem ..."
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Abstract — In this paper we reevaluate the resources requirements of the “resources optimal key predistribution (RKPD) scheme in wireless sensor networks”. Our evaluation shows that RKPD has excessive requirements in terms of memory, computation, and communication. Thees requirements are problematic for that they make RKPD less beneficial by violating the purpose that it was designed for. Furthermore, because RKPD is a hybrid scheme that uses two wellknown schemes in literature, we show that RKPD inherently have two security flows that challenge its chances of being deployment in real wireless sensor network. Detailed analysis, comparisons and examples are provided to evidence our arguments and conclusions. Key words: Key predistribution, sensor networks, resources reevaluation, security analysis. I.
1 Distinct Difference Configurations: Multihop Paths and Key Predistribution in Sensor Networks
, 811
"... Abstract — A distinct difference configuration is a set of points in Z 2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurat ..."
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Abstract — A distinct difference configuration is a set of points in Z 2 with the property that the vectors (difference vectors) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the khop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of k or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the khop coverage of a distinct difference configuration with m points, and exploit a connection with Bh sequences to construct configurations with maximal khop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application. I.
Folding, Tiling, and Multidimensional Coding
, 903
"... Abstract — Folding a sequence S into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence S can be folded into various shapes. The new definition of folding is based on lattice tiling and a ..."
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Abstract — Folding a sequence S into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence S can be folded into various shapes. The new definition of folding is based on lattice tiling and a direction in the Ddimensional grid. There are potentially 3D −1 2 different folding operations. Necessary and sufficient conditions that a lattice combined with a direction define a folding are given. The immediate and most impressive application is some new lower bounds on the number of dots in twodimensional synchronization patterns. This can be also generalized for multidimensional synchronization patterns. We show how folding can be used to construct multidimensional errorcorrecting codes and to generate multidimensional pseudorandom arrays. I.
1 TwoDimensional Patterns with Distinct Differences – Constructions, Bounds, and Maximal Anticodes
, 811
"... Abstract — A twodimensional grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and timep ..."
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Abstract — A twodimensional grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and timeposition synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various twodimensional shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid.