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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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 @math -composite key predistribution scheme, which mitigates the node capture vulnerability of the Eschenauer-Gligor scheme in the neighbor discovery phase. We derive scheme parameters to have a desired level of resiliency, and obtain optimal parameters that defend against different adversaries as much as possible. We also show that this scheme can be easily enhanced to achieve the same “perfect resilience” property as in the random pairwise key predistribution 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 and ignores the real-world transmission constraints of sensor nodes. Moreover, we derive the critical network parameters to ensure connectivity in both the absence and presence of node-capture attacks. We also investigate node replication attacks by analyzing the adversary’s optimal strategy. 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. This paper proposes a novel key management scheme for multi-dimensional scalable multimedia access control. We build up a collusion-attack model and prove that the proposed scheme is indeed resilient to collusion attack. The lower bound of number of the segment keys is also given in the analysis. We consider the key management problem on partially order set and propose a general approach consists of a poset decomposition step and an element projection step. Under the proposed framework, a novel hierarchical 3D poset decomposition approach is further developed. The proposed scheme is the first provable collusion resilient scheme in 3-dimension (and higher) scenario. It can be easily adapted to other scalable dependence structure and higher dimension. Analysis on the proposed scheme proves its collusion-resilient property.