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

Folding, Tiling, and Multidimensional Coding

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 $D$-dimensional grid. There are potentially $\frac{3^D-1}{2}$ 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 two-dimensional synchronization patterns. This can be also generalized for multidimensional synchronization patterns. We show how folding can be used to construct multidimensional error-correcting codes and to generate multidimensional pseudo-random arrays

A New Key Predistribution Scheme for Multiphase Sensor Networks Using a New Deployment Model

During the lifecycle of sensor networks, making use of the existing key predistribution schemes using deployment knowledge for pairwise key establishment and authentication between nodes, a new challenge is elevated. Either the resilience against node capture attacks or the global connectivity will significantly decrease with time. In this paper, a new deployment model is developed for multiphase deployment sensor networks, and then a new key management scheme is further proposed. Compared with the existing schemes using deployment knowledge, our scheme has better performance in global connectivity, resilience against node capture attacks throughout their lifecycle

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

BARI+: A Biometric Based Distributed Key Management Approach for Wireless Body Area Networks

Wireless body area networks (WBAN) consist of resource constrained sensing devices just like other wireless sensor networks (WSN). However, they differ from WSN in topology, scale and security requirements. Due to these differences, key management schemes designed for WSN are inefficient and unnecessarily complex when applied to WBAN. Considering the key management issue, WBAN are also different from WPAN because WBAN can use random biometric measurements as keys. We highlight the differences between WSN and WBAN and propose an efficient key management scheme, which makes use of biometrics and is specifically designed for WBAN domain

Resilient Wireless Sensor Networks Using Topology Control: A Review

Wireless sensor networks (WSNs) may be deployed in failure-prone environments, and WSNs nodes easily fail due to unreliable wireless connections, malicious attacks and resource-constrained features. Nevertheless, if WSNs can tolerate at most losing k − 1 nodes while the rest of nodes remain connected, the network is called k − connected. k is one of the most important indicators for WSNs’ self-healing capability. Following a WSN design flow, this paper surveys resilience issues from the topology control and multi-path routing point of view. This paper provides a discussion on transmission and failure models, which have an important impact on research results. Afterwards, this paper reviews theoretical results and representative topology control approaches to guarantee WSNs to be k − connected at three different network deployment stages: pre-deployment, post-deployment and re-deployment. Multi-path routing protocols are discussed, and many NP-complete or NP-hard problems regarding topology control are identified. The challenging open issues are discussed at the end. This paper can serve as a guideline to design resilient WSNs

Simple and flexible random key pre-distribution schemes for wireless sensor networks using deployment knowledge

Sensor nodes are tiny, low-power and battery constrained electromechanical devices that are usually deployed for sensing some type of data in different types of areas. Because of their memory and computational restrictions, public key cryptography (PKC) systems are not suited for sensor nodes to provide security. Instead, private key cryptography is preferred to be used with sensor networks and there has been considerable work in this area, but there still exist problems with private key cryptography because of memory restrictions of sensor nodes. Number of keys that can be deployed into a sensor node is determined by the available memory of that node which is limited even private key cryptographic techniques are applied. So, new key distribution mechanisms are required to decrease number of pairwise keys that are deployed into a sensor node. Random key pre-distribution mechanisms have been proposed to overcome memory restrictions of sensor nodes. These mechanisms are widely accepted for sensor network security. Simply, these schemes try do decrease the number of keys to be deployed in each sensor node in a sensor network and provide reasonable security for the sensor network. Random key pre-distribution schemes proposed until now have some deficiencies. Some of these schemes are too complicated and too difficult to be applied. Schemes that seem deployable involve unrealistic assumptions when real world scenarios are considered. In this thesis, we propose random key pre-distribution mechanisms that are simple and easily deployable. In this thesis, we first developed a generalized random key pre-distribution scheme. Then we proposed three random key pre-distribution mechanisms based on this generalized scheme and we provided their simulation results and their comparison to well-known random key pre-distribution schemes in the literature. Our generalized scheme allows different systems to be derived according to deployment needs. It offers simple, easily deployable distribution mechanisms and provides reasonable connectivity and resiliency with respect to its simplicity