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 @math , where @math 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.
Thereafter, many key predistribution schemes have been proposed, which trade-off storage with resilience and connectivity. Combinatorial schemes like @cite_15 @cite_6 @cite_13 are a class of deterministic schemes which were very popular because of their simplicity of construction and simple algorithms to find key sharing neighbors. However, such schemes do not scale well and have poor resilience. Camtepe and Yener @cite_15 were the first to propose such schemes using combinatorial designs called . Lee and Stinson @cite_6 proposed KPD schemes using transversal designs, while Ruj and Roy @cite_13 @cite_3 used partially balanced incomplete block designs and Reed-Solomon codes. In Section , we will show that the Lee-Stinson (LS) scheme @cite_6 has very poor resilience compared to random key predistribution schemes. A survey of such schemes appear in @cite_23 @cite_7 .
@cite_7 @cite_3 @cite_6 @cite_23 @cite_15 @cite_13
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We address pairwise and (for the first time) triple key establishment problems in wireless sensor networks (WSN). We use combinatorial designs to establish pairwise keys between nodes in a WSN. A BIBD(v; b; r; k; λ) (or t - (v; b; r; k; λ)) design can be 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, k represents the size of the key chain. Any pair (or t-subset) of keys occurs together uniquely in exactly λ nodes. λ = 2 and λ = 3 are used to establish unique pairwise or triple keys. Our pairwise key distribution is the first one that is fully secure (none of the links among uncompromised nodes is affected) and applicable for mobile sensor networks (as key distribution is independent on the connectivity graph), while preserving low storage, computation and communication requirements. We also use combinatorial trades to establish pairwise keys. This is the first time that trades are being applied to key management. We describe a new construction of Strong Steiner Trades. We introduce a novel concept of triple key distribution, in which a common key is established between three nodes. This allows secure passive monitoring of forwarding progress in routing tasks. We present a polynomial-based approach and a combinatorial approach (using trades) for triple key distribution. In this paper we propose novel deterministic key predistribution schemes using codes. In particular we use Reed Solomon codes to present key predistribution scheme, which is better than existing schemes in terms of connectivity. We show that selective node compromise attack cannot be launched, because there is no clever way of knowing which nodes to compromise. An important advantage of our scheme is that we can increase the scalability of the network without redistributing keys in the existing nodes. It is an important issue to establish pairwise keys in distributed sensor networks (DSNs). In this paper, we present two key predistribution schemes (KPSs) for DSNs, ID-based one-way function scheme (IOS) and deterministic multiple space Blom's scheme (DMBS). Our schemes are deterministic, while most existing schemes are based on randomized approach. We show that the performance of our schemes is better than other existing schemes in terms of resiliency against coalition attack. In addition we obtain perfectly resilient KPSs such that the maximum supportable network size is larger than random pairwise keys schemes. Wireless sensor networks have many applications, vary in size, and are deployed in a wide variety of areas. They are often deployed in potentially adverse or even hostile environment so that there are concerns on security issues in these networks. Sensor nodes used to form these networks are resource-constrained, which make security applications a challenging problem. Efficient key distribution and management mechanisms are needed besides lightweight ciphers. Many key establishment techniques have been designed to address the tradeoff between limited memory and security, but which scheme is the most effective is still debatable. In this paper, we provide a survey of key management schemes in wireless sensor networks. We notice that no key distribution technique is ideal to all the scenarios where sensor networks are used; therefore the techniques employed must depend upon the requirements of target applications and resources of each individual sensor network.