Matrix grid-based key pre-distribution in sensor networks

Key pre-distribution in nodes is often employed to address the problems of security with a single secret key and management with pair-wise secret keys in ad hoc and sensor networks. Sensor nodes can establish secure links with their neighbors through shared key predistributed before node deployment. At the ends of the spectrum of key pre-distribution schemes are random and deployment based key pre-distribution. Random key pre-distribution suffers from a smaller probability of sharing keys with neighbors. Deployment based key pre-distribution has a near 100% probability of sharing keys with immediate neighbors but not with nodes that are further away. When a network is jammed and jamming coping techniques (such as increase in power, use of directional antennas, and spatial retreats) are used, the nodes that are new neighbors due to changes in physical connectivity may or may not share keys with a given node. In this paper, we examine the impact of increasing transmission power to cope with jamming on secure connectivity (provided by different key predistribution schemes) in ad hoc and sensor networks.

In order to provide security services in wireless sensor networks, a well-known task is to provide cryptographic keys to sensor nodes prior to deployment. It is difficult to assign secret keys for all pairs of sensor node when the number of nodes is large due to the large numbers of keys required and limited memory resources of sensor nodes. One possible solution is to randomly assign a few keys to sensor nodes and have nodes be able to connect to each other with some probability. This scheme has limitations in terms of the tradeoffs between connectivity and memory requirements. Recently, sensor deployment knowledge has been used to improve the level of connectivity while using lesser amounts of memory space. However, deployment based key predistribution schemes may cause a large number of nodes to be cryptographically isolated if nodes move after key pre-distribution. Mobility may be necessitated for reasons depending on applications or scenarios. In this paper, we consider mobility due to spatial retreat of nodes under jamming attacks as an example. Jamming attacks are easy and efficient means for disruption of the connectivity of sensors and thus the operation of a sensor network. One solution for mobile sensor nodes to overcome the impact of jamming is to perform spatial retreats by moving nodes away from jammed regions. Moved nodes may not be able to reconnect to the network because they do not have any shared secret with new neighbors at new locations if strict deployment knowledge based key predistribution is employed. In this paper, we propose a hybrid key predistribution scheme that supports spatial retreat strategies to cope with jamming attacks. Our scheme combines the properties of random and deployment knowledge based key predistribution schemes. In the presence of jamming attacks, our scheme provides high key connectivity (similar to deployment knowledge based schemes) while reducing the number of isolated nodes. We evaluate the performance of our scheme through simulations and analysis.

Owing to the security requirements of wireless sensor network, the background of Wireless Sensor Network (WSN) is to be analyzed with different threats and attack models. Physical compromising of sensor nodes by an adversary is an emerging problem in sensor network and accordingly, it is necessary to provide an environment with efficient key management techniques due to resource constraints on sensor network. It is obvious to evaluate the efficiency of symmetric key management schemes for WSN, since it is not feasible to use traditional key management techniques such as asymmetric key cryptosystem and Key Distribution Center (KDC). This survey paper aims to report an extensive study on classification of pairwise key pre-distribution techniques. Further a smaller portion of analysis and security issues using pairwise key management is pronounced. Analysed results shows that polynomial pool based method have higher probability of communication by non-compromised nodes when compared with other schemes. The proposed survey effectively track the merits and demerits of different key predistribution schemes, also the communication overhead and memory overhead is reduced in polynomial pool based method during execution.

Any key pre-distribution (KPD) scheme is inherently a trade-off between complexity and security. By sacrificing some security (KPD schemes need some assurance of the ability to limit sizes of attacker coalitions), KPD schemes gain many advantages. We argue that random KPD schemes, in general, perform an advantageous trade-off which renders them more suitable for practical large scale deployments of resource constrained nodes. We introduce a novel random KPD scheme, hashed random preloaded subsets (HARPS), which turns out to be a generalization of two other random KPD schemes, random preloaded subsets (RPS) and a scheme proposed by T. Leighton and S. Micali (LM). All three schemes have probabilistic measures for the merit of the system. We analyze and compare the performance of the three schemes. We show that HARPS has significant advantages over other KPD schemes, and in particular, over RPS and LM.

Pairwise key establishment is a fundamental security service in sensor networks; it enables sensor nodes to communicate securely with each other using cryptographic techniques. However, due to the resource constraints on sensors, it is infeasible to use traditional key management techniques such as public key cryptography and key distribution center (KDC). To facilitate the study of novel pairwise key predistribution techniques, this paper presents a general framework for establishing pairwise keys between sensors on the basis of a polynomial-based key predistribution protocol [2]. This paper then presents two efficient instantiations of the general framework: a random subset assignment key predistribution scheme and a grid-based key predistribution scheme. The analysis in this paper indicates that these two schemes have a number of nice properties, including high probability (or guarantee) to establish pairwise keys, tolerance of node captures, and low communication overhead. Finally, this paper presents a technique to reduce the computation at sensors required by these schemes.

Key agreement in sensor networks is a dif- ficult problem because of resource constraints of the sensors. The classical approaches used in general networks are impractical in sensor networks. Hence, several key pre-distribution schemes are proposed. In this paper, we propose a hypercube multivariate scheme (HMS) that is a threshold-based scheme. In the HMS, a hypercube in the multidimensional space is designed and a number of multivariate polynomials are assigned to every point on the hypercube. The points on the hypercube are uniquely assigned to the sensors. Using this technique, a direct key is established between any two sensors at Hamming distance of one from each other. Other sensors are also able to establish indirect keys. Our analysis shows an improvement in the security of HMS compared to other similar schemes. We also propose a location-aware scheme that takes advantage of the distribution information to boost the security. In the proposed scheme, the target field is divided into hexagonal cells because of their efficient coverage compared to square cells. The sensors are randomly distributed in every cell. An HMS scheme is employed to pre-distribute keys in every cell. For the communication between adjacent cells, we propose a grid- based scheme in which the sensors of every cell are divided into groups. Shares of bivariate polynomials are stored in the sensors of every group. As a result, every two sensor in two adjacent cells are able to establish a direct key. Our security analysis shows improvements over similar schemes.

Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by the application of key predistribution in wireless sensor networks (WSN), we initiate the study of preferential attachment with degree bound. Our paper has two important contributions to two different areas. The first is a contribution in the study of complex networks. We propose preferential attachment model with degree bound for the first time. In the normal preferential attachment model, the degree distribution follows a power law, with many nodes of low degree and a few nodes of high degree. In our scheme, the nodes can have a maximum degree $d_{\max}$, where $d_{\max}$ is an integer chosen according to the application. The second is in the security of wireless sensor networks. We propose a new key predistribution scheme based on the above model. The important features of this model are that the network is fully connected, it has fewer keys, has larger size of the giant component and lower average path length compared with traditional key predistribution schemes and comparable resilience to random node attacks. We argue that in many networks like key predistribution and Internet of Things, having nodes of very high degree will be a bottle-neck in communication. Thus, studying preferential attachment model with degree bound will open up new directions in the study of complex networks, and will have many applications in real world scenarios.

SummaryLow cost, decentralized architecture and ad hoc nature are a few desirable properties of wireless sensor networks that make them well suited for gathering sensitive information in hazardous deployment grounds. Existing security protocols exploit various cryptographic tools to strengthen their security. Not many works focus on constraints faced by an adversary. One such constraint being practical difficulties to trace a particular frequency band from a large range of unknown frequencies, specially in unharmonious geographical locations. Our research capitalizes on this weakness encountered by an adversary and preassigns nodes with multiple frequency bands from a wide range of frequencies allocated to the network. Deployed nodes can discover these bands during set network setup phase by a simple trick. Nodes are to internally switch their frequency bands depending on parametric variation that are caused by an (external) impulse. Experiments conducted using magneto optic sensors confirm that any variation of their parameter affects frequencies of emergent waves. Similar behavior is expected from application specific sensors. Frequency regulation (FR) concept is applied to combinatorial key predistribution schemes (KPS) having (regular) degree r. Depending on r and each node's capability to switch internal frequencies, nodes are preallocated with n frequency bands. This naturally partitions the (distributed) network and results in improved resilience. Combining our FR concept to a KPS where the number of shared key between a pair of nodes is at most one (γ ≤ 1) may yield best case scenario of an ideally resilient key predistribution. Our analysis of systems that combines FR idea with KPS where γ > 1 leads to an optimized key‐band distribution argument and drastic resilience improvements. Results of simulations conducted assuming real‐life scenario ascertain our analysis and establishes superior performance of our protocols as compared to prominent ones.

Many key pre-distribution (KPD) schemes based on combinatorial design were proposed for secure communication of wireless sensor networks (WSNs). Due to complexity of constructing the combinatorial design, it is infeasible to generate key rings using the corresponding combinatorial design in large scale deployment of WSNs. In this paper, we present a definition of new combinatorial design, termed “µ-partially balanced incomplete block design (µ-PBIBD)”, which is a refinement of partially balanced incomplete block design (PBIBD), and then describe a 2-D construction of µ-PBIBD which is mapped to KPD in WSNs. Our approach is of simple construction which provides a strong key connectivity and a poor network resilience. To improve the network resilience of KPD based on 2-D µ-PBIBD, we propose a KPD scheme based on 3-D Ex-µ-PBIBD which is a construction of µ-PBIBD from 2-D space to 3-D space. Ex-µ-PBIBD KPD scheme improves network scalability and resilience while has better key connectivity. Theoretical analysis and comparison with the related schemes show that key pre-distribution scheme based on Ex-µ-PBIBD provides high network resilience and better key scalability, while it achieves a trade-off between network resilience and network connectivity.

Despite much research on probabilistic key predistribution schemes for wireless sensor networks over the past decade, few formal analyses exist that define schemes' resilience to node-capture attacks precisely and under realistic conditions. In this paper, we analyze the resilience of the q-composite key predistribution scheme, which mitigates the node capture vulnerability of the Eschenauer-Gligor scheme in the neighbor discovery phase. We also show that this scheme can be easily enhanced to achieve the same "perfect resilience" property as in the random pairwise key pre-distribution for attacks launched after neighbor discovery. Despite considerable attention to this scheme, much prior work explicitly or implicitly uses an incorrect computation for the probability of link compromise under node-capture attacks. Based on our rigorous results, we provide guidelines on the design of secure sensor networks for resilience against node capture.

The establishment of shared keys between communicating neighbor nodes in wireless sensor networks is a challenge due to resource-constrained sensor networks. Several key pre-distribution schemes have been proposed in literatures to establish pairwise keys between sensor nodes. However, many of them are either too complicated to fit for wireless sensor networks or insecure for some common aggressions. In this paper, we propose a random key management scheme based on random key pre-distribution for wireless sensor networks. To achieve better performance and security, the proposed scheme employs two different phases to establish enhanced pairwise keys between neighboring nodes. Compared with other existing random key pre-distribution schemes, our scheme has better resilience against node capture and also performs better in terms of network connectivity and scalability with appropriate memory, computation and communication overheads.

Current key predistribution schemes for wireless sensor networks derive the merit of their performance based on the resilience of secure communication links to node-compromise attacks. As an adversarial entity gathers key information, it is able to mount attacks by spoofing or eavesdropping on networked communications with growing success. A powerful variety of attack is possible with a spoofed node, which is when the adversary is able to present itself as a legitimate identity in the network and not be detected. This work considers the security of wireless sensor networks with a priority on node-spoofing attacks. We propose node-spoofing attack models to classify various adversarial capabilities. We then propose two new key predistribution techniques as variants to random key predistribution, which provide improved resilience to node-spoofing attacks.

Key management has always remained a challenging problem for the entire security community. Standard practice in modern times is to agree on symmetric keys using public key protocols. However, public key protocols use heavy computations; rendering them inappropriate for application to low cost devices of Internet of Things (IoT). This led to proposals of various key management strategies for low cost networks; a prominent discovery being key predistribution technique for Wireless Sensor Network (WSN)–a prototype of IoT. Such schemes require several communicating nodes to share the same cryptographic key. This leads to interesting (combinatorial) graphical models and related optimality problems, that get intense for hierarchical architecture. Most protocols meant for hierarchical (low cost) networks employ separate designs for individual levels and/or clusters. Consequently only local optimal values can be computed. We develop a single universal platform using weighted signed graph (WSG) that designs the entire network for a hierarchical setup. This model can be used as itself or clubbed with a key predistribution scheme (KPS) to enhance the latter’s security when applied to a WSN. After generic presentation, we combine our universal model with prominent KPS to facilitate comparative study with existing protocols.

In wireless sensor network (WSN), a secure link in the key pre-distribution (KP) scheme may be compromised when sensor nodes are captured. Accordingly, the KP q- composite scheme was proposed to tackle this node-capture problem. Recently, Bechkit et al. proposed a hash chain based KP (HCKP) q-composite scheme to further enhance network resiliency against node capture. However, Bechkit et al.'s HCKP q-composite scheme has to perform too many hash operations to establish a secure link between two nodes for the case that the difference of node identifiers is large. This computational overhead is more serious for the large value of q. In this paper, we propose a computational overhead invariant HCKP q-composite scheme by storing one additional hashed value in sensor node. When compared with Bechkit et al.'s HCKP q-composite scheme, the proposed scheme reduces the number of hash operations, and meanwhile the storage overhead remains insignificant.

Security service is one of the fundamental elements required to realize the wireless sensor networks. To distribute key in WSNs, the predistribution technique is commonly used, because the traditional cryptography techniques such as public key cryptography and key distribution center (KDC) are impractical to be applied in the WSNs due to resource constraints of sensor node. The most common technique in famous predistribution schemes is random key predistribution scheme which use probability method. The random key predistribution scheme has a demerit that heavy overhead is occurred on establishing a path key. To reduce the overhead, the grid-based key predistribution scheme was proposed. They uses t-degree bivariate polynomial keys and 2-dimensional grid to provide good properties such as good resilience against the node compromise, high probability of establishing a pairwise key and the minimized overhead on establishing a path key. We extend the dimension of the grid-based key predistribution scheme which is more efficient than other existing schemes. Our scheme improves many properties, except the resilience, of the grid-based key predistribution scheme. So, we introduce n-dimensional grid-based key predistribution using group based deployment as one of methods which can enhance the resilience. Through a mathematical model, we show that our scheme is more efficient than other existing schemes including 2-dimensional grid-based scheme.