Key pre-distribution in wireless sensor networks using multivariate polynomials

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.

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.

Finding an optimal key assignment (subject to given constraints) for a key predistribution scheme in wireless sensor networks is a difficult task. Hence, most of the practical schemes are based on probabilistic key assignment, which leads to sub-optimal schemes requiring key storage linear in the total number of nodes. A graph theoretic framework is introduced to study the fundamental tradeoffs between key storage, average key path length (directly related to the battery consumption) and resilience (to compromised nodes) of key predistribution schemes for wireless sensor networks. Based on the proposed framework, a lower bound on key storage is derived for a given average key path length. An upper bound on the compromising probability is also given. This framework also leads to the design of key assignment schemes with a storage complexity of the same order as the lower bound.

Key establishment is the basic step for the wireless sensor network (WSN) security. The polynomial based key predistribution scheme of Blom and Blundo et al. has been the basic ingredient for the key establishment for WSNs. It is tempting to use many random and different instances of polynomial based key predistribution scheme for various parts of the WSN to enhance the efficiency of WSN key establishment protocols. This paper indicates that it is not secured in general to use many instances of Blom-Blundo et al. polynomial based key predistribution scheme in a WSN key establishment protocol. Thus the previously constructed group-based type WSN key predistribution schemes using polynomial based key predistribution scheme are insecure. We propose new generalized Blom-Blundo et al. key predistribution schemes. These new generalized Blom-Blundo et al. key predistribution schemes can be used many times in one WSN key establishment protocol with only a small increase of cost. The application to group-based WSN key predistribution schemes is given.

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.

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.

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.Keywordswireless sensor networkskey managementone-dimensional networks

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.

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.

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.

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.

To solve the security problem of wireless sensor networks, the concept of matrix pool and matrix grid were put forward, upon which our key pre-distribution scheme was built. And in the matrix grid based scheme, encryption was introduced into the process of key transfer. Using Blom's key pre-distribution for reference, an efficient key pre-distribution scheme was presented for sensor networks.

In this paper, the random key pre-distribution scheme introduced in ACM CCS'02 by Eschenauer and Gligor is reexamined, and a generalized form of key establishment is introduced. As the communication overhead is one of the most critical constraints of any successful protocol design, we introduce an alternative scheme in which the connectivity is maintained at the same level as in the original work, while the communication overhead is reduced by about 40% of the original overhead, for various carefully chosen parameters. The main modification relies on the use of a two-level key pool design and two round assignment/key establishment phases. Further analysis demonstrates the efficiency of our modification.

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.