The eavesdropping attack is a serious security threat to a wireless sensor network (WSN) since the eavesdropping attack is a prerequisite for other attacks. Conventional WSNs consist of wireless nodes equipped with omnidirectional antennas, which broadcast radio signals in all directions and are consequently prone to the eavesdropping attacks. Different from omnidirectional antennas, directional antennas radiate radio signals on desired directions and potentially reduce the possibility of the eavesdropping attacks. In this paper, we propose a model to analyze the eavesdropping probability in both single-hop WSNs and multihop WSNs with omnidirectional antennas and directional antennas. We verify the correctness of our analytical model by conducting extensive simulations. We have found that using directional antennas in either single-hop WSNs or multihop WSNs can significantly reduce the eavesdropping probability. The reason of the improved security of WSNs with directional antennas lies in (i)
Recently, wireless sensor networks (WSNs) have received enormous interests from both industry and academia [
In WSNs, any wireless node residing in the
Conventional WSNs typically consist of nodes equipped with omnidirectional antennas which broadcast radio signals uniformly in all directions. Only a portion of these signals can reach the destinations and most of them are lost. This property of radiating signals omnidirectionally inevitably leads to
Compared with omnidirectional antennas, directional antennas can concentrate most of radio signals on desired directions. In other undesired directions, there are no radio signals or the weakened signals. Therefore, using directional antennas in WSNs can potentially reduce the interference [
In this paper, we only concentrate on the
The first contribution of this paper is to formally establish the eavesdropping model in WSNs with consideration of omnidirectional antennas and directional antennas. In particular, we propose
Secondly, we analyze the eavesdropping attacks in both single-hop networks and multihop networks with both omnidirectional antennas and directional antennas. We have found that a
Last, we conduct extensive simulations to verify the correctness of our analytical models. We show that the simulation results exactly agree with our analytical model in both single-hop
The remainder of the paper is organized as follows. Section
We adopt the notations shown in (Notation) throughout the paper. Sections
In this paper, we consider a directional antenna model that was used in previous studies [
We assume that a directional antenna gain
The antenna model.
The antenna gain of an omnidirectional antenna can be regarded as a special case in our model when the beamwidth
Note that a directional antenna generally has a beamwidth
We next describe the channel model. We denote the transmission power of node
The transmission from node
Note that there are only one transmitter and one receiver in a single-hop network and all other nodes are
In this paper, we consider the large-scale path loss in the channel model [
Note that the channel model also holds for both the normal transmission and the eavesdropping attack. When the channel model is used for the normal transmission,
We next formally propose our eavesdropping model. First, we map
Directional case and omnidirectional case.
Omnidirectional (I) | Directional (II) | |
---|---|---|
Transmitter | Omni | Directional |
Receiver | Omni | Omni |
Adversary | Omni | Omni |
In Case
Second, we analyze the channel model for the eavesdropping attacks. If an adversary node can correctly decode the information from the transmitter, the SINR at the adversary node must satisfy the condition given in Inequality (
We denote the right-hand side (RHS) of (
We then define the
The exposure region of a transmitter is an area that any adversary nodes within this area can potentially eavesdrop the transmission from the transmitter.
It is obvious that the area of the exposure region is determined by the geometric shape of the exposure region and the maximum radius
In Case
Note that both the receiver and the adversary nodes have the same minimum SINR (i.e.,
The exposure region of an omnidirectional antenna.
The exposure region of a directional antenna.
We then define the
An adversary node can successfully eavesdrop the information from the transmitter
To evaluate the seriousness of eavesdropping attacks, we define the
The eavesdropping probability
The eavesdropping probability of a multihop transmission is the probability that at least one-hop transmission is eavesdropped.
It is obvious that
The security improvement factor
When
Finally, we describe the node distribution. In this paper, we consider that both the adversary nodes and the good nodes are distributed in a two-dimensional plane. We use a Poisson point process to model the distribution of the nodes [
In this section, we analyze the eavesdropping probabilities of Omnidirectional case and Directional case in single-hop networks, in which all packets are transmitted through only one hop.
Generally, the eavesdropping probability of a single-hop WSN can be obtained by the following lemma.
The eavesdropping probability can be calculated by
From the definition of the eavesdropping probability, that is, Definition
Since the distribution of adversary nodes follows Poisson point process as defined in (
As shown in Lemma
In Omnidirectional case, the transmitter, the receiver, and the adversary nodes are equipped with omnidirectional antennas. The exposure region of an omnidirectional antenna is a circle with radius
In Directional case, the transmitter is equipped with a directional antenna while eavesdroppers are equipped with omnidirectional antennas. The exposure region of a directional antenna is a sector with radius
After replacing
The eavesdropping probability of the Omnidirectional case, denoted by
To simplify the analysis, we define the
We then have the following theorem to compare a
The security improvement factor of a WON over a DAWN is equal to
From the definition of security improvement factor, that is, Definition
Replacing
We then analyze the security improvement factor of a
DAWNs have the eavesdropping probability no higher than that of WONs under the same network settings. More precisely, one has the following. When the pass loss factor When the pass loss factor
We then calculate the security improvement factor
Security improvement factor of single-hop transmissions.
It is shown in Figures
Besides, it is also shown in Figure
Moreover, Figure
In this section, we extend our analysis from single-hop networks to multihop networks. We first derive the eavesdropping probability of multihop transmissions. Then, we analyze the security improvement factor of
To analyze the eavesdropping probability of multihop transmissions, we construct a simple routing scheme that chooses a route with the shortest distance to forward data packets. We first introduce the Source-Destination (S-D) Line model [
In the S-D Line model, we divide the unit-area plane into a lot of equal-sized square cells as shown in Figure
The S-D Line model.
In this S-D Line model, we directly draw a line to connect a source node S and its destination node D. Then, node S will send data packets to its destination D by multihop forwarding those packets along the cells lying on its S-D line. Figure
We then calculate the number of hops required to route a packet from S to D. Since calculating the exact number of hops is difficult, we are only concerned about the number of hops
We next calculate the number of hops
Similarly, the number of hops
In general, the eavesdropping probability of a multihop WSN (either
The eavesdropping probability of multihop networks can be calculated by
From the definition of the eavesdropping probability of multihop networks, that is, Definition
For a
For a
From (
We then have the following theorem to compare a
The security improvement factor of a WON over a DAWN under multihop networks is equal to
From the definition of security improvement factor, that is, Definition
After replacing
Note that when
We then calculate
The security improvement factor of multihop transmissions.
Two factors contribute to the increment of the security improvement of multihop transmissions:
Moreover, it is also shown in Figure
In addition, different from the single-hop networks, the security improvement
In this section, we conduct extensive simulations to evaluate the correctness and the accuracy of our proposed models in single-hop networks (Section
Figure
Eavesdropping probability versus node density
As shown in Figures
Moreover, we can see in Figure
Furthermore, we can also see that the eavesdropping probability of a
Tables
Eavesdropping probability versus node density
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Analytical | Simulation | Analytical | Simulation | Analytical | Simulation | Analytical | Simulation | |
0.05 | 0.727 | 0.624 | 0.338 | 0.360 | 0.231 | 0.255 | 0.144 | 0.187 |
0.10 | 0.925 | 0.851 | 0.562 | 0.605 | 0.408 | 0.444 | 0.268 | 0.346 |
0.15 | 0.979 | 0.944 | 0.710 | 0.751 | 0.544 | 0.589 | 0.374 | 0.439 |
0.20 | 0.994 | 0.988 | 0.808 | 0.866 | 0.649 | 0.714 | 0.464 | 0.544 |
0.25 | 0.998 | 0.989 | 0.873 | 0.915 | 0.730 | 0.790 | 0.542 | 0.607 |
0.30 | 0.999 | 0.996 | 0.916 | 0.943 | 0.792 | 0.835 | 0.608 | 0.685 |
0.35 | 0.999 | 0.996 | 0.944 | 0.953 | 0.840 | 0.890 | 0.664 | 0.746 |
0.40 | 0.999 | 0.999 | 0.963 | 0.973 | 0.877 | 0.884 | 0.713 | 0.818 |
0.45 | 0.999 | 0.998 | 0.976 | 0.990 | 0.905 | 0.928 | 0.754 | 0.829 |
0.50 | 0.999 | 0.999 | 0.984 | 0.990 | 0.927 | 0.941 | 0.790 | 0.863 |
Eavesdropping probability versus node density
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---|---|---|---|---|---|---|---|---|
Analytical | Simulation | Analytical | Simulation | Analytical | Simulation | Analytical | Simulation | |
0.05 | 0.683 | 0.570 | 0.264 | 0.300 | 0.171 | 0.176 | 0.106 | 0.120 |
0.10 | 0.899 | 0.801 | 0.458 | 0.488 | 0.313 | 0.374 | 0.201 | 0.236 |
0.15 | 0.968 | 0.903 | 0.601 | 0.663 | 0.431 | 0.482 | 0.286 | 0.305 |
0.20 | 0.989 | 0.963 | 0.706 | 0.756 | 0.528 | 0.554 | 0.362 | 0.399 |
0.25 | 0.996 | 0.980 | 0.784 | 0.818 | 0.609 | 0.655 | 0.430 | 0.483 |
0.30 | 0.998 | 0.993 | 0.841 | 0.878 | 0.676 | 0.712 | 0.490 | 0.554 |
0.35 | 0.999 | 0.999 | 0.883 | 0.909 | 0.731 | 0.766 | 0.544 | 0.604 |
0.40 | 0.999 | 0.999 | 0.913 | 0.933 | 0.777 | 0.820 | 0.593 | 0.651 |
0.45 | 0.999 | 0.999 | 0.936 | 0.959 | 0.815 | 0.828 | 0.636 | 0.671 |
0.50 | 0.999 | 0.999 | 0.953 | 0.961 | 0.847 | 0.873 | 0.674 | 0.752 |
Both Tables
As shown in Tables
Besides, Tables
There exist quite small gaps between the analytical values and the simulation results as shown in Tables
Wireless Sensor Networks (WSNs) are prone to the malicious attacks due to the shared wireless medium, the multihop transmissions, and the decentralized control scheme [
One of the malicious attacks, namely, the
There are a number of studies on investigating the passive eavesdropping attack [
There are a number of studies on using directional antennas in wireless ad hoc networks. The first category of them mainly focuses on the theoretical analysis on the network performance, for example, the network capacity and the transmission delay. In particular, studies [
Most of the above studies focus on improving the network performance by using directional antennas. However, there is little work on the security issue by using directional antennas. The study [
In this paper, we have explored using directional antennas in wireless sensor networks to improve the network security in terms of reducing the eavesdropping probability. In particular, we analyzed the eavesdropping probability of single-hop networks and that of multihop networks. We have found that using directional antennas in either a single-hop network or a multihop network can significantly reduce the eavesdropping probability. The security improvements of using directional antennas owe to the
There are some interesting topics in the eavesdropping activities of
Antenna gain of transmitters
Antenna gain of receivers
Directional antenna gain
Omnidirectional antenna gain
Antenna beamwidth, that is, the angle between the half-power points of the main lobe
The channel gain from node
Fixed transmission power of all nodes
Signal-to-Interference-Plus-Noise Ratio
Signal path loss factor
Minimum signal to interference and noise ratio
Fixed environmental noise power level
Maximum radius of the exposure region of directional antennas
Maximum radius of the exposure region of omnidirectional antennas
Node density
The average number of nodes in a circle with radius
Single-hop eavesdropping probability
Single-hop eavesdropping probability of a directional antenna
Single-hop eavesdropping probability of an omnidirectional antenna
Multihop eavesdropping probability
Multihop eavesdropping probability of a directional antenna
Multihop eavesdropping probability of an omnidirectional antenna
The security improvement factor of
The work described in this paper was supported by Macao Science and Technology Development Fund under Grant no. 036/2011/A and Grant no. 081/2012/A3. The authors would like to thank Guodong Han and Qinglin Zhao for their valuable comments.