Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor (EG) under the assumption of full visibility. For this class of random graphs we establish a zero-one law for the existence of triangles, and identify the corresponding critical scaling. This zero-one law exhibits significant differences with the corresponding result in Erdős-Rényi grap...

Secure communication is a necessity for some wireless sensor network (WSN) applications. However, the resource constraints of a sensor render existing cryptographic systems for traditional network systems impractical for a WSN. Random key predistribution scheme has been proposed to overcome these limits. In this scheme, a ring of keys is randomly drawn from a large key pool and assigned to a se...

A secure scheme for heterogeneous wireless sensor networks is presented. The wireless sensor networks have some sensor nodes and heterogeneous sensor nodes that have greater power and transmission capability than other nodes have. All kinds of sensor nodes are evenly distributed respectively in entire sensing area that is divided into a number of same cells and logical groups evenly. The pairwi...

In this paper we propose a new key predistribution scheme for wireless sensor networks in which the sensors are arranged in a square grid. We describe how Costas arrays can be used for key predistribution in these networks, then define distinct difference configurations, a more general structure that provides a flexible choice of parameters in such schemes. We give examples of distinct differen...

We study the applicability of random graph theory in modeling secure connectivity of wireless sensor networks. Specifically, our work focuses on the highly influential random key predistribution scheme by Eschenauer and Gligor to examine the appropriateness of the modeling in finding system parameters for desired connectivity. We use extensive simulation and theoretical results to identify rang...

Key predistribution for wireless sensor networks has been a challenging field of research because stringent resource constraints make the key predistribution schemes difficult to implement. Despite this, key predistribution scheme is regarded as the best option for key management in wireless sensor networks. Here, the authors have proposed a new key predistribution scheme. This scheme exhibits ...

In WSNs, since the attacks, such as jamming or eavesdropping without physical access, easily occur, security is one of the important requirements for WSNs. The key pre-distribution scheme, recently being researched for advances of security in WSNs, distributes keys with probability with the use of qcomposite random key pre-distribution method, but there is a high probability that there is no ke...

We consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the absence of isolated nodes, and complement it by a Poisson convergence for the number of isolated nodes. Leveraging earlier results and analogies with Erdős-Renyi graphs, we explore similar results for the ...

In a key predistribution scheme (KPS), some secret information is distributed among a set of users. This secret information must enable every user in some specified privileged groups to compute a common key associated to that group. Besides, this common key must remain unknown to some coalitions of users outside the privileged group. The information rate, that is, the ratio between the length o...