Many basic key distribution schemes specifically tuned to wireless sensor networks have been proposed in the literature. Recently, several researchers have proposed schemes in which they have used group-based deployment models and assumed predeployment knowledge of the expected locations of nodes. They have shown that these schemes achieve better performance than the basic schemes, in terms of connectivity, resilience against node capture and storage requirements. But in many situations expected locations of nodes are not available. In this paper we propose a solution which uses the basic scheme, but does not use group-based deployment model and predeployment knowledge of the locations of nodes, and yet performs better than schemes which make the aforementioned assumptions. In our scheme, groups are formed after deployment of sensor nodes, on the basis of their physical locations, and the nodes sample keys from disjoint key pools. Compromise of a node affects secure links with other nodes that are part of its group only. Because of this reason, our scheme performs better than the basic schemes and the schemes using predeployment knowledge, in terms of connectivity, storage requirement, and security. Moreover, the post-deployment key generation process completes sooner than in schemes like LEAP+.
Du et. al. @cite_2 improve upon Blom's scheme by combining it with the random key distribution scheme. Similarly, Liu and Ning @cite_5 improve upon Blundo's @cite_9 scheme by combining it with random key distribution scheme. Both these schemes perform better than the EG scheme @cite_14 in terms of connectivity and resilience against node capture. But threshold schemes do not scale with the number of nodes in the network. For a fixed resilience against node capture, if the number of nodes is increased, then they require large memory.
@cite_5 @cite_9 @cite_14 @cite_2
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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. 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. In this paper, we propose the new (t i , n) threshold multi secret sharing scheme. In our scheme, each user keeps only one share and the secret vectors K i = k i , 1 ,…, k i , mi are shared according to independent (t i , n) threshold access structures (i = l,…, h). Here note that a (t i , n) threshold multi-secret sharing scheme has been proposed by [1]. Unfortunately, however, there is a serious attack on Shi's scheme that can reconstruct all elements of K i with only t 1 shares. In this paper, we shall give the solution to this problem by using one-way functions. Furthermore, Shi's scheme has a drawback such that the dimension of the secret vector K i cannot exceed t i . On the other hand, our scheme has no such a restriction. Finally, we demonstrate that our scheme is more efficient than Shi's scheme by showing that our scheme is more efficient than the three naive improvements on the protocol of The stochastic block model (SBM) with two communities, or equivalently the planted bisection model, is a popular model of random graph exhibiting a cluster behaviour. In the symmetric case, the graph has two equally sized clusters and vertices connect with probability @math within clusters and @math across clusters. In the past two decades, a large body of literature in statistics and computer science has focused on providing lower-bounds on the scaling of @math to ensure exact recovery. In this paper, we identify a sharp threshold phenomenon for exact recovery: if @math and @math are constant (with @math ), recovering the communities with high probability is possible if @math and impossible if @math . In particular, this improves the existing bounds. This also sets a new line of sight for efficient clustering algorithms. While maximum likelihood (ML) achieves the optimal threshold (by definition), it is in the worst-case NP-hard. This paper proposes an efficient algorithm based on a semidefinite programming relaxation of ML, which is proved to succeed in recovering the communities close to the threshold, while numerical experiments suggest it may achieve the threshold. An efficient algorithm which succeeds all the way down to the threshold is also obtained using a partial recovery algorithm combined with a local improvement procedure.