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Secure and Energy-Efficient Geocasting Protocol for GPS-Free Hierarchical Wireless Sensor Networks with Obstacles

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Abstract

Wireless sensor networks (WSN) are nowadays a very promising field and are used in various types of applications requiring advanced and low-cost geocasting and security techniques. In this paper, we are interested in a secure clustering and fast geocasting protocol for a three-dimensional, hierarchical, GPS-free and low-density WSN. This spatial architecture has the advantage of being more realistic and more suitable for submarine and aerial applications. The new construction approach of this architecture is free of several previous limitations (need of a sink equipped with a powerful antenna, central position of the sink among the deployed sensors, a deployment zone obligatorily and homogeneously propitious to the propagation of the waves, ...). The protocol that we present here uses techniques of modulation of the radio’s power to be eco-energetic and reliable. It also uses elliptic curves as a generator of secret keys in the asymmetric process that secures communications.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, F.S., University of Dschang, B.P.: 67, Dschang, Cameroon

    Blaise Nana Paho & Vianney Kengne Tchendji

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  1. Blaise Nana Paho
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  2. Vianney Kengne Tchendji
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Correspondence to Vianney Kengne Tchendji.

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A Proof of \(R_c\)

A Proof of \(R_c\)

Proof

The notations of this proof are on Fig. 7 and the proof itself is based on the Alkashi’s theorem applied in a triangle.

$$\begin{aligned} L1=\sqrt{a^2+a^2-2 \times a^2 \times cos\theta } =a \sqrt{2 (1-cos\theta )} \end{aligned}$$

likewise \(L2=a \sqrt{2 (1-cos\varphi )}\) and \(L0 = a \sqrt{2 (1-cos\beta )}\)

$$\begin{aligned} L0^2= L1^2 + L2^2= 2a^2(1-cos\theta ) + 2a^2(1-cos\varphi )\\= 2a^2(1-cos\beta ) \\ \Longrightarrow cos \beta= 1-\frac{L_0^2}{2a^2} = 1-\frac{2a^2(1-cos\theta ) + 2a^2(1-cos\varphi )}{2a^2} \\ \Longrightarrow cos \beta= cos\theta + cos\varphi - 1 R_c^2=d1^2+d2^2-2 \times d1 \times d2 \times cos\beta \\= a^2c^2+a^2(c+1)^2-2 \times (ac) \times [a(c+1)] \times cos\beta \\= a^2c^2+a^2c^2+2a^2c+a^2-2a^2c(c+1) cos\beta \\= 2a^2c^2+2a^2c+a^2-2a^2c(c+1) cos\beta \\= 2a^2c[c+1-(c+1) cos\beta ] + a^2\\= 2a^2c(c+1)(1-cos\beta ) + a^2\\= 2a^2c(c+1)[1-(cos\theta + cos\varphi - 1)] + a^2\\ \Longrightarrow R_c= \left[ 2a^2c(c+1)(2- cos\theta - cos \varphi ) + a^2 \right] ^{\frac{1}{2}} \end{aligned}$$

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Paho, B.N., Tchendji, V.K. Secure and Energy-Efficient Geocasting Protocol for GPS-Free Hierarchical Wireless Sensor Networks with Obstacles. Int J Wireless Inf Networks 27, 60–76 (2020). https://doi.org/10.1007/s10776-019-00464-5

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