After completing the judgment of mobile behavior, we will choose a new MAC address for the user uj whose updatej has been set to true. Then, we use a Spatio-Temporal Addressing [9] to generate a new MAC address for avoiding collision.
Basically, the main idea of Spatio-Temporal Addressing is based on the fact that two objects cannot exist at the same location at the same time. Therefore, we can achieve this goal of avoiding collision through an injection function .Finally, we send MAC-Update message to those users who need to update MAC address.
4. Evaluation
In this chapter, we mainly point out the improvement of our scheme on the two factors, unlinkable MAC address and useless update. Therefore, we will compare our proposed scheme with the prior arts [1, 2], and the remainder of this section is organized as follows. We first describe our simulation setup in section 4.1, and
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analyze the simulation result in section 4.2.
4.1 Simulation Setup
Our simulation environment is a 60m*60m 2-dimentional grid-area, and all mobile users move within this area by random walking model. The random walking model defines the patterns of moving direction [←, ↑, →, ↓], the probability of moving direction [p←, p↑, p→, p↓], velocity range [vmin, vmax] and the probability of changing velocity [p+, pno, p-] (i.e. [speed up, unchanged, slow down]). In our simulation, we set the parameters of random walking model as follows:
[p←, p↑, p→, p↓] = [0.15, 0.65, 0.15, 0.05]
[vmin, vmax] = [0 , 3] with unit (m/s)
[p+, pno, p-]= [0.1,0.8,0.1] with unit (1 m/s)
The values of these parameters take the mobile behavior of pedestrian into account.
In addition, in order to make our simulation analogous to real wireless propagation.
We actually measure the relation between signal strength and distance (1-meter interval) for the wireless interface of the mobile station and AP in an obstacle-less environment. We also log the signal-strength/distance information for later use.
Finally, we use a similar way [10] to obtain an empirical path loss model for both the mobile station and AP. Hence, when a node (ui) wants to send a frame, all the other nodes can obtain the signal strength by the log information. In other words, all the other nodes will randomly choose a signal-strength value from the log information according to the distance between ui and themselves. And then the PC translates the signal strength to distance by the empirical path loss model.
Next, we describe the tracking model used by attackers. First, the attackers will divide all the users into two type, target and disturber. Target is the user who the attackers are interested in, and Disturber is the user who will disturb the attackers to
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track target. In addition, the attackers utilize the same empirical path loss model to obtain the distance information, and track the targets by triangulation. Finally, when a target uj update its MAC address and doesn’t transmit any frame for a random period, the attackers will randomly pick an unobserved MAC address to track from the circle area,( i.e. the center of circle is the missing point of uj, and the circle area is tsp × vmax). We use Figure 4-1 to illustrate this situation. So the adversary will randomly pick from these users including uj, uk and um.
uj
uk
um
vmax tsp
node is updating MAC address and not transmitting node can be tracked by the same MACaddress
Figure 4-1 illustrating which users will be picked as target 4.2 Simulation Result and Analysis
Due to the prior works [1,2] analyzed the factor ,unlikable MAC address, through measuring how long a node can be tracked continuously. Therefore, we will use similar factor to evaluate the performance of our proposed scheme and realize the enhancement of “unlinkable MAC address”.
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Figure 4-2 CDF of tracking time
We show the simulation result of unlikable MAC address in Figure 4-2, which is plotted as a cumulative distribution function. The curve indicates the percentage of nodes (y-axis) that can be tracked for no more than a specified duration (x-axis). The
“Only Change MAC” curve indicates the system which only adopts disposable MAC address scheme [1]. Next, the “change MAC with 2s silent period” means the system will stop sending frames about 2 seconds after each update of MAC address [2].
Finally, the “My Scheme with 2s silent period” indicates the system adopts our proposed scheme. Now, consider the fifth tracking round of x-axis. In our scheme, there are only about 30% nodes can be tracked after the 5th tracking round. This value is smaller than both the disposable scheme (70%) and silent-period scheme (50%). Therefore, our scheme effectively reduces the duration of time that a user can be tracked.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 5 10 15 20 25 30
Only Change MAC
change MAC with 2s silent period My Scheme with 2s silent period
Tracking Round
Percentage of Nodes
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Figure 4-3 Comparison of maximal tracking round
Next, we show the comparison of maximal tracking round for each scheme in Figure 4-3. In our scheme the whole users can be traced at most 9 rounds. The value is far smaller than 27 rounds of disposal scheme and also smaller than 14 rounds of silent-period scheme. In other words, our scheme has the ability to obtain higher location privacy within less time.
Figure 4-4 Comparison of useless MAC address update
Finally, we analyze the improvement of useless MAC address update in Figure 4-4.
Figure 4-4(a) shows that we conserve 67% useless MAC address updates as compared our scheme with disposable scheme. In addition, compared with silent period scheme we also conserve about 35% useless MAC address updates (Figure 4-4
0
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(b)). This result substantially reduces the number of useless update and improves the performance of each user.