Maura B. Paterson

Efficient Key Predistribution for Grid-Based Wireless Sensor Networks

In this paper we propose a new key predistribution scheme for wireless sensor networks in which the sensors are arranged in a square grid. We describe how Costas arrays can be used for key predistribution in these networks, then define distinct difference configurations, a more general structure that provides a flexible choice of parameters in such schemes. We give examples of distinct difference configurations with good properties for key distribution, and demonstrate that the resulting schemes provide more efficient key predistribution on square grid networks than other schemes appearing in the literature.

An Application-Oriented Framework for Wireless Sensor Network Key Establishment

The term wireless sensor network is applied broadly to a range of significantly different networking environments. On the other hand there exists a substantial body of research on key establishment in wireless sensor networks, much of which does not pay heed to the variety of different application requirements. We set out a simple framework for classifying wireless sensor networks in terms of those properties that directly influence key distribution requirements. We fit a number of existing schemes within this framework and use this process to identify areas which require further attention from key management architects.

A unified approach to combinatorial key predistribution schemes for sensor networks

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 t-designs”, 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.

Key predistribution for homogeneous wireless sensor networks with group deployment of nodes

Recent literature contains proposals for key predistribution schemes for sensor networks in which nodes are deployed in separate groups. In this article we consider the implications of group deployment for the connectivity and resilience of a key predistribution scheme. We propose a flexible scheme, based on the structure of a resolvable transversal design. We demonstrate that this scheme permits effective trade-offs between resilience, connectivity and storage requirements within a group-deployed environment as compared with other schemes in the literature, and show that group deployment can be used to increase network connectivity, without increasing storage requirements or sacrificing resilience.

Ultra-Lightweight Key Predistribution in Wireless Sensor Networks for Monitoring Linear Infrastructure

One-dimensional wireless sensor networks are important for such security-critical applications as pipeline monitoring and perimeter surveillance. When considering the distribution of symmetric keys to secure the communication in such networks, the specific topology leads to security and performance requirements that are markedly distinct from those of the more widely-studied case of a planar network. We consider these requirements in detail, proposing a new measure for connectivity in one-dimensional environments. We show that, surprisingly, optimal results may be obtained through the use of extremely lightweight key predistribution schemes.

Distinct Difference Configurations: Multihop Paths and Key Predistribution in Sensor Networks

A distinct difference configuration is a set of points in Z2 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 k-hop 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 k-hop coverage of a distinct difference configuration with m points, and exploit a connection with Bh sequences to construct configurations with maximal k-hop 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.

Combinatorial characterizations of algebraic manipulation detection codes involving generalized difference families

This paper provides a mathematical analysis of optimal algebraic manipulation detection (AMD) codes. We prove several lower bounds on the success probability of an adversary and we then give some combinatorial characterizations of AMD codes that meet the bounds with equality. These characterizations involve various types of generalized difference families. Constructing these difference families is an interesting problem in its own right.

Two-Dimensional Patterns With Distinct Differences—Constructions, Bounds, and Maximal Anticodes

A two-dimensional (2-D) 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 time-position 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 2-D shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid.

Two attacks on a sensor network key distribution scheme of Cheng and Agrawal

Abstract A sensor network key distribution scheme for hierarchical sensor networks was recently proposed by Cheng and Agrawal. A feature of their scheme is that pairwise keys exist between any pair of high-level nodes (which are called cluster heads) and between any (low-level) sensor node and the nearest cluster head. We present two attacks on their scheme. The first attack can be applied for certain parameter sets. If it is applicable, then this attack can result in the compromise of most if not all of the sensor node keys after a small number of cluster heads are compromised. The second attack can always be applied, though it is weaker.

Error decodable secret sharing and one-round perfectly secure message transmission for general adversary structures

An error decodable secret-sharing scheme is a secret-sharing scheme with the additional property that the secret can be recovered from the set of all shares, even after a coalition of participants corrupts the shares they possess. In this paper, schemes that can tolerate corruption by sets of participants belonging to a monotone coalition structure are considered. This coalition structure may be unrelated to the authorised sets of the secret-sharing scheme. This is generalisation of both a related notion studied in the context of multiparty computation, and the well-known error-correction properties of threshold schemes based on Reed-Solomon codes. Necessary and sufficient conditions for the existence of such schemes are deduced, and methods for reducing the storage requirements of a technique of Kurosawa for constructing error-decodable secret-sharing schemes with efficient decoding algorithms are demonstrated. In addition, the connection between one-round perfectly secure message transmission (PSMT) schemes with general adversary structures and secret-sharing schemes is explored. We prove a theorem that explicitly shows the relation between these structures. In particular, an error decodable secret-sharing scheme yields a one-round PSMT, but the converse does not hold. Furthermore, we are able to show that some well-known results concerning one-round PSMT follow from known results on secret-sharing schemes. These connections are exploited to investigate factors affecting the performance of one-round PSMT schemes such as the number of channels required, the communication overhead, and the efficiency of message recovery.