We consider the network reliability problem in wireless sensor networks secured by the heterogeneous random key predistribution scheme. This scheme generalizes Eschenauer-Gligor scheme by considering the cases when the network comprises sensor nodes with varying level of resources; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted @math . We analyze the reliability of @math against random link failures. Namely, we consider @math formed by deleting each edge of @math independently with probability @math , and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on @math , @math , and @math such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We present numerical results to support these in the finite-node regime.
The reliability of secure WSNs was also studied in @cite_18 , but under the Eschenauer-Gligor scheme @cite_1 where all sensors receive the same number of keys. However, when the network consists of sensors with varying level of resources (e.g., computational, memory, power) and or with varying level of security and connectivity requirements, it may no longer be sensible to assign the same number of keys to all sensors. Our work addresses this issue by generalizing @cite_18 to the cases where nodes can be assigned different number of keys. When @math , i.e., when all nodes belong to the same class and receive the same number of keys, our result recovers the main result in @cite_18 .
@cite_18 @cite_1
2338794901 2056254754 1868819612 2011539652
We consider the network reliability problem in secure wireless sensor networks that employ a heterogeneous random key predistribution scheme. This scheme is introduced recently, as a generalization of the Eschenauer-Gligor scheme, to account for the cases when the network comprises sensors with varying level of resources or connectivity requirements; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted G(n;μ,K, P ), where each of the n nodes are independently assigned to one of r classes according to a probability distribution μ = (μ1, . . . , μr) and then a class-i node is assigned Ki keys uniformly at random from a pool of size P ; two nodes that share a key are then connected by an edge. We analyze the reliability of G(n;μ,K, P ) against random link failures. Namely, we consider G(n;μ,K, P, α) formed by deleting each edge of G(n;μ,K, P ) independently with probability 1 − α, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on K , P , and α such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime. Random key predistribution scheme of Eschenauer and Gligor (EG) is a typical solution for ensuring secure communications in a wireless sensor network (WSN). Connectivity of the WSNs under this scheme has received much interest over the last decade, and most of the existing work is based on the assumption of unconstrained sensor-to-sensor communications. In this paper, we study the k-connectivity of WSNs under the EG scheme with physical link constraints; k-connectivity is defined as the property that the network remains connected despite the failure of any (k - 1) sensors. We use a simple communication model, where unreliable wireless links are modeled as independent on off channels, and derive zero-one laws for the properties that i) the WSN is k-connected, and ii) each sensor is connected to at least k other sensors. These zero-one laws improve the previous results by Rybarczyk on the k-connectivity under a fully connected communication model. Moreover, under the on off channel model, we provide a stronger form of the zero-one law for the 1-connectivity as compared to that given by Yagan. Random key predistribution scheme of Eschenauer and Gligor (EG) is a typical solution for ensuring secure communications in a wireless sensor network (WSN). Connectivity of the WSNs under this scheme has received much interest over the last decade, and most of the existing work is based on the assumption of unconstrained sensor-to-sensor communications. In this paper, we study the k-connectivity of WSNs under the EG scheme with physical link constraints; k-connectivity is defined as the property that the network remains connected despite the failure of any (k - 1) sensors. We use a simple communication model, where unreliable wireless links are modeled as independent on off channels, and derive zero-one laws for the properties that i) the WSN is k-connected, and ii) each sensor is connected to at least k other sensors. These zero-one laws improve the previous results by Rybarczyk on the k-connectivity under a fully connected communication model. Moreover, under the on off channel model, we provide a stronger form of the zero-one law for the 1-connectivity as compared to that given by Ya g an. We also discuss the applicability of our results in a different network application, namely in a large-scale, distributed publish-subscribe service for online social networks. A major issue in many applications of Wireless Sensor Networks (WSNs) is ensuring security. Particularly, in military applications, sensors are usually deployed in hostile areas where they can be easily captured and operated by an adversary. Most of security attacks in WSNs are due to the lack of security guaranties in terms of authentication, integrity, and confidentiality. These services are often provided using cryptographic primitives where sensor nodes need to agree on a set of secret keys. Current key distribution schemes are not fully adapted to the tiny, low-cost, and fragile nature of sensors that are equipped with limited computation capability, reduced memory size, and battery-based power supply. This paper investigates the design of an efficient key distribution and management scheme for wireless sensor networks. The proposed scheme can ensure the generation and distribution of different encryption keys intended to secure individual and group communications. This is performed based on elliptic curve public key encryption using Diffie-Hellman like key exchange that is applied at different levels of the network topology. In addition, a re-keying procedure is performed using secret sharing techniques. This scheme is more efficient and less complex than existing approaches, due to the reduced number of messages and the less processing overhead required to accomplish key exchange. Furthermore, few number of encryption keys with reduced sizes are managed in sensor nodes, which optimizes memory usage and enhances scalability to large size networks.