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Abstract

With the development of mobile smartphones equipped with a large number of sensor devices, mobile crowd computing has become the hotspot of current research. In the application, the publishers use the application platform to release the task and then select the appropriate users to participate in the task by bidding and collect their data, in which the users’ identity, location, and other private information face the risk of disclosure. To solve the problem of privacy disclosure in mobile crowd computing, we propose a privacy preserving method based on Voronoi Polygon (PP - Voronoi). The users construct the Voronoi diagram to form a cloaked region hiding users identity and then calculate the anchor point of the cloaked region, by which the users communicate with the task publisher to achieve privacy protection of the cloaked region and K anonymity. The experimental results show that compared with other privacy preserving methods, PP-Voronoi method has better effectiveness of privacy protection and lower network traffic.

Keywords

Mobile crowd computing privacy preserving Voronoi diagram cloaked region anonymity

Introduction

In the information era, with the popularity of smartphones equipped with a large number of sensor devices (such as GPS, camera, accelerometer, Wi-Fi/4G interface), mobile crowd computing (MCC) applications have developed rapidly. Mobile users can obtain complex data information (such as noise, weather, environment, traffic) at different locations by carrying mobile terminal devices. At present, a large number of MCC applications have been developed, including environmental testing,¹ traffic monitoring,^2,3 and noise monitoring.^4,5Figure 1 is the description of the MCC scenario. First, mobile users need to register as a candidate on the MCC platform. Task publishers release sensing tasks with certain requirements, including sensing locations, sensing times, sensing skills, and budget constraints. Candidate users acquire sensing tasks to calculate their own costs and upload bidding to the platform. The platform selects the winner of the bidding based on the criteria. After completing the sensing task, the selected users upload the sensing data and obtain the reward and evaluation.⁶ In this process, more users participating in the sensing task do not need to consider the cost of privacy as the users privacy is protected. This is an important research content on the current MCC.

Figure 1.

Description of the MCC scenario.

Related work

In MCC, taking into account that the privacy costs affect the users’ enthusiasm of participating in the sensing task, some privacy protection methods are proposed nowadays, which can be divided into four categories: (1) encryption method, (2) anonymous method, (3) sensitive location hiding method, and (4) cloaked region method. Some users may need other users’ bidding and sensing data to adjust their strategy, so as to obtain greater benefits. Even worse, the malicious user deduces the users’ location and activity trajectory by the obtained user-uploaded data. Further decrease in inference of privacy information can effectively encourage users to actively participate in the sensing task.

At present, the more direct way to solve the location disclosure is the anonymous method and is to hide the users’ true identity and related location information. However, the opponent can infer the users identity and location information by obtaining sufficient sensing data. To further reduce the opponents’ inference, Chen et al.⁷ used K-anonymous mechanisms to overcome the exposure of real identity information caused by low user density. Beresford and Stajano⁸ proposed the method of hiding the identity information by frequently changing the anonymous information. However, if the opponent obtains a large amount of spatiotemporal correlation sensing data, he can also associate the user to transform the anonymous information to acquire the users’ identity and location. Yang et al.⁹ proposed a K-anonymous location privacy protection mechanism to solve the above problem. However, in sparse environment, the attacker can still infer the users’ information. Freudiger et al.¹⁰ proposed to add anonymous users to a mixed area to protect their location information. However, as this method assumes that the users of the mixed area are trustworthy, it cannot prevent the attack of the bad users. In addition, the mixed area is regular, so the attacker can infer the relevant information by repeatedly inferring. This work mainly focuses on the following problems:

The malicious user can analyze the users’ identity and location information by obtaining enough data with spatiotemporal correlation and further deduce the users’ trajectory information.

How to establish an irregular cloaked region so that it would be difficult for attackers to infer the users’ activity range;

How to prevent the untrusted users in the cloaked region from attacking user information.

To solve the above problem, we propose a privacy preserving method based on Voronoi diagram. First of all, the users build their own Voronoi cell and then band with other users to establish a K-anonymous cloaked region. To further prevent the attacker from inferring the users’ location information, in the cloaked region, we calculate an anchor to communicate with the task publisher. In addition, to prevent untrusted users from attacking, the users utilize anonymous method to transmit only anonymous information and Voronoi cell area to the neighbors. The major contributions of this article are summarized in the following:

To the best of our knowledge, we are the first to apply Voronoi diagram to protect participants’ privacy in MCC, where users can hide their specific location in irregular region. We construct Voronoi cell by the setting of users’ activity range and sensing range threshold to reduce computational complexity using geometric method.

We propose an establishment method of the cloaked region to further protect the participants’ privacy, which utilizes a distributed mechanism to broadcast requests and communicates among users by cache contact list to overcome many unique limitations in mobile environment. In addition, we design a calculation method of the anchor to reduce the communication overhead.

To verify the performance of the $PP - Voronoi$ method, we compare our proposed method with two typical algorithms through simulations. The experimental results show that our proposed method has better effectiveness of privacy protection and lower network overhead.

The rest of the article is organized as follows: section “Privacy preserving method based on Voronoi diagram” describes in detail the privacy preserving method based on Voronoi diagram. Section “Performance evaluation” evaluates the performance of our proposed method by extensive simulations, along with the related parameters setting, followed by the result discussions and analysis. Section “Conclusion” concludes the article.

Privacy preserving method based on Voronoi diagram

In MCC, due to the problems of privacy disclosure, the users do not want to upload too much information to the platform. Even if the users hide their location information, it is also very easy to infer the users’ location due to the users’ motion or the sparse network environment.¹¹ To better protect the users’ privacy, we introduce our approach step by step in the following part.

Establishment of the Voronoi diagram

To prevent privacy disclosure, users hide their position by the establishment of the Voronoi diagram, which is a geometric structure in computational geometry and a spatial segmentation method which can form some irregular area. Polygons in the Voronoi diagram on a two-dimensional (2D) plane are often called Voronoi cell. In the geometric space, the Voronoi cell represents the corresponding spatial description or range of action for each user. Figure 2 is a description of the Voronoi diagram generation. The specific Voronoi diagram is defined in the figure

Figure 2.

Establishment of the Voronoi diagram.

Definition 1

Assume that the user set $S = {s_{1}, s_{2}, \dots, s_{n}}, n > 3$ is a set of points on the Euclidean plane R. These points are not collinear, and any four points are not in a circle. $d (v_{i}, v_{j})$ represents the Euclidean distance between $v_{i}$ and $v_{j}$ . E(P,S) indicates the environment including the sensing nodes and the user set. Suppose $\forall p \in E$ , region $V_{i} = {p \in R^{2} | d (p, s_{i}) \leq d (p, s_{j}), i, j = 1, 2, \dots, n, i \neq j}$ is called Voronoi cell of $s_{i}$ , which of each user forms together the Voronoi diagram.

In the user set S, each point which is viewed as a growth kernel expands outward at the same rate until each other encounters to form the Voronoi diagram on a plane. Some outermost points form the open area, and the rest form a convex polygon (Voronoi cell). In the Voronoi diagram, the distance from any point of the Voronoi cells to the control point $s_{i}$ is less than that from this point to any other control point $s_{j}$ . The Voronoi cell is usually used to generate “territory” or control area. Because each control point is uniquely contained by a Voronoi cell, the space adjacency between the control points can be clearly expressed by the Voronoi diagram. Combining human behavior with social activity criteria, people usually choose the shortest time, the nearest distance, the lowest cost, and the optimal route to solve the problems encountered in life, which reflects that the human follows spatial conduct code. At this level, if the seed points in the Voronoi diagram are considered as the starting or destination point of human daily behavior or activity, then the Voronoi cell reflects the spatial reference of their corresponding behavioral activity or the influence scope.

The sensing platform forwards all the sensing tasks in the Voronoi cell to the corresponding user $s_{i}$ . Since the sensing nodes in the Voronoi cell are closest to $s_{i}$ , the user can better accomplish the task and obtain high-quality sensing data. However, the users are not willing to send their location to the sensing platform based on privacy consideration. We need to deal with the users’ privacy preserving issues so that users can upload their data to the platform without reservation.

Privacy preserving method

The Voronoi cell, which is calculated by the sensing platform, has a large degree of privacy disclosure. So the users can contact his neighbors to establish their own Voronoi cell. But the platform is still able to infer the users’ activity range, so the user cannot fully realize the privacy protection by only relying on the establishment of Voronoi cell. To overcome this problem, we design to establish a cloaked region on the basis of Voronoi diagram, by which user can further protect the privacy. The users’ privacy preserving level is determined by the privacy protection value $(K, A_{\min})$ , where K represents at least K users contained in the cloaked region, and $A_{\min}$ represents the minimum area of the cloaked region. Algorithm is divided into three steps. The first step utilizes a distributed method for each user to establish their own Voronoi cell $V_{i}$ . The second forms a cloaked region $C_{i}$ between adjacent users and the third selects an anchor point for the cloaked region. Next, we describe in details in the following.

The first step is to build a users’ Voronoi diagram. In the literatures,^12–14 the authors proposed some algorithms to calculate the Voronoi diagram. However, these geometry algorithms have high computational complexity and are not suitable for mobile environments. In this article, we improve the generation method of original Voronoi diagrams to construct a Voronoi cell by the distribution area of user $s_{i}$ and sensing nodes. The distance from any sensing nodes in this cell to $s_{i}$ is smaller than those to other user $s_{j}$ . In other words, $d (s_{i}, p) < d (s_{j}, p)$ , where $d (\cdot, \cdot)$ is the Euclidean distance between user and sensing node, and p is sensing node. In traditional method, the construction of Voronoi diagrams of n nodes takes $O (nlogn)$ . In our proposed method, the Voronoi cells are constructed by the setting of users’ activity range and sensing range threshold. In addition, it can be updated in real time and newly added to Voronoi cells. Constructing Voronoi diagrams of n nodes takes O(n) time. The method is divided into two steps. First, according to the threshold of user activity range and sensing range, we look for the neighbors of the user. Second, the boundary of the Voronoi cell is calculated by the intersection of sensing range between the users and the neighbors. The users discover the respective neighbors by mutual notification. After receiving the confirmation information of the neighbors, the users establish the interactive Voronoi cell and calculate their area $A_{i}$ .

To further protect the users’ privacy, when each user establishes their own Voronoi cell, the second step is to establish a cloaked region among adjacent users in mobile environment, which have a lot of unique limitations, scarce bandwidth resources, limited transmission range, user mobility, and multi-hop communication.¹⁵ To overcome these limitations, we utilize the historical non-sensitive information sharing scheme and the establishment of cache contact list to reduce the limited communication overhead. In addition, we build a cloaked region of limited number users by the broadcasting method to overcome the problem of limited transmission range. Finally, due to the users’ mobility, the cloaked area adjustment scheme can remove and add users in real time. The following is a specific method. The user first broadcasts a request to his or her neighbors through a single-hop route to look for neighbors to join. If he does not find enough neighbors, he or she will continue through the multi-hop route until he finds K − 1 neighbors. To decrease the users’ distrust in the cloaked region, the user $s_{i}$ communicates with the neighbor by anonymous way. If the neighbor agrees to join the cloaked region after receiving the request, the user sends only his or her anonymous information and the area $A_{i}$ of the Voronoi cell to $s_{i}$ . Searching neighbors need to spend a long time and multiple broadcast requests need to consume network resources. To save time and network overhead, when the neighbors join the cloaked region, they can also broadcast the request to find their neighbors to join. And we establish a cache contact list for each user. The system preferentially looks for the neighbors in the cache list and then it updates the cache list after finding the new neighbors. In MCC, the user is dynamically moving. In fact, the users’ activity has a certain periodicity. At a certain time, it does not exceed the scope of the Voronoi cell, especially during the task receiving period. In view of the worst case, when the users of the cloaked region leave the current location, we can also dynamically join the new neighbors into the cloaked region. In Figure 3, the blue area represents the established cloaked region $C = {s_{8}, s_{15}, s_{16}, s_{21}, s_{25}}$ , where the privacy protection level K = 5. The specific establishment process of the cloaked region is shown in Algorithm 1.

Figure 3.

Establishment of the cloaked region.

Algorithm 1. Establishment of the cloaked region.
Input: $S = {s_{1}, s_{2}, \dots, s_{n}}$ , K Output: the set A of cloaked region area, the anchor user $s_{r}$ 1: $C \leftarrow {\emptyset}; V \leftarrow {\emptyset}; A \leftarrow {\emptyset}; h \leftarrow 1$ //V represents the Voronoi diagram and $V_{i}$ represents the Voronoi cell //step 1: Establishment of the Voronoi diagram 2: for i from 1 to n do 3: Constructing Voronoi cell $V_{i}$ for every user $s_{i}$ 4: $V \leftarrow {V_{i}}$ 5: end //step 2: Establishment of the cloaked region 6: $A \leftarrow A \cup {area (V_{i})}$ //Calculating the area of arbitrary users’ Voronoi cell 7: while $\| C \| < K$ do // $\| C \|$ indicates the user number of cloaked region 8: Broadcasting request to the user in cache contact list of the h-hop neighbor. 9: $C \leftarrow C \cup {s_{j}}$ //If the P2P neighbor $s_{j}$ agrees to join, we add $s_{j}$ into the set C 10: $A \leftarrow A \cup {area (V_{j})}$ 11: $h \leftarrow h + 1$ 12: end 13: if users leave or join in cloaked region 14: Removing users from C and going to line 7 //step 3: The calculation of the anchor 15: for $s_{i}$ in C do 16: Calculating the average of the distance $d_{i}$ from $s_{i}$ to other users 17: $D \leftarrow D \cup {d_{i}}$ 18: end 19: Finding the user of smallest distance as anchor $s_{r}$ 20: return ${A; s_{r}}$

Algorithm 1. Establishment of the cloaked region.

Input:

S = {s_{1}, s_{2}, \dots, s_{n}}

, K
Output: the set A of cloaked region area, the anchor user

s_{r}

C \leftarrow {\emptyset}; V \leftarrow {\emptyset}; A \leftarrow {\emptyset}; h \leftarrow 1

//V represents the Voronoi diagram and

V_{i}

represents the Voronoi cell
//step 1: Establishment of the Voronoi diagram
2: for i from 1 to n do
3: Constructing Voronoi cell

V_{i}

for every user

s_{i}

V \leftarrow {V_{i}}

5: end
//step 2: Establishment of the cloaked region
6:

A \leftarrow A \cup {area (V_{i})}

//Calculating the area of arbitrary users’ Voronoi cell
7: while

| C | < K

do
//

| C |

indicates the user number of cloaked region
8: Broadcasting request to the user in cache contact list of the h-hop neighbor.
9:

C \leftarrow C \cup {s_{j}}

//If the P2P neighbor

s_{j}

agrees to join, we add

s_{j}

into the set C
10:

A \leftarrow A \cup {area (V_{j})}

11:

h \leftarrow h + 1

12: end
13: if users leave or join in cloaked region
14: Removing users from C and going to line 7
//step 3: The calculation of the anchor
15: for

s_{i}

in C do
16: Calculating the average of the distance

d_{i}

from

s_{i}

to other users
17:

D \leftarrow D \cup {d_{i}}

18: end
19: Finding the user of smallest distance as anchor

s_{r}

20: return

{A; s_{r}}

After the cloaked region is constructed, the third step is to select an anchor point $s_{r}$ to communicate with the platform so that the user of the cloaked region is hidden in this area. It is difficult for the malicious user to infer the users’ privacy from the anchor. There are many ways to calculate an anchor, such as the greedy algorithm in Kleinberg and Tardos,¹⁶ which selects the Voronoi cell users with the largest number of sensing nodes as the anchor point. The method is applied only to the centralized structure. However, in the distributed structure, the users do not know the number of sensing nodes covered in the respective Voronoi cell. In Kazemi and Shahabi,¹⁴ according to the neighbors vote, the system determines the users’ anchor point. The method is too complicated to calculate in a complex network environment and the network cost is large. To reduce the communication overhead, we choose a nearest user from the other users of the cloaked region as an anchor. And the calculation of the anchor should avoid the participation of the sensing platform to prevent the privacy of the anchor user. Thus, the users of cloaked region calculate the average of the distances to other users. Then, the smallest distance user is selected as anchor of cloaked region.

To prevent malicious users from attacking, the user first builds their own Voronoi cell, and then K users form a cloaked region, where the users only transmit Voronoi cell area with the neighbors anonymously. It prevents the attack of the untrusted user. In addition, the Voronoi cells and cloaked region are both irregular in our proposed method, so it is difficult to deduce the identity information and the specific location of the users for a malicious attacker. Due to the dynamic nature of mobile users, when users leave the cloaked region, to ensure the privacy level, we can dynamically invite new users to join.

Performance evaluation

To evaluate the performance of the $PP - Voronoi$ method, we choose $Coprivacy$ method¹⁷ and the $privacy_l_k$ method¹⁸ to carry on the contrast experiment. The main performance values to be compared include cloaked success rate, average response time, and average traffic. The cloaked success rate refers to the proportion of users who can successfully disguise the location under a malicious user attack. In this article, the attack method mentioned in Pan et al.¹⁹ is used to test the cloaked success rate. The higher the value of the cloaked success rate, the better the effect of the privacy protection is. The smaller the average response time and the lower the average traffic, the higher the efficiency of the privacy protection is. We mainly compare the above three performance values through the number of different users and different K value of privacy protection levels, where K value refers to the number of anonymous users in the cloaked area.

Experimental setup

All the simulations are run on laptop with Intel Core i7-5557U CPU 3.10 GHZ, 8 GB memory, and Windows 8.1 operating system. We utilize Dev-cpp 5.4 as simulation platform to compile the three privacy preserving methods and carry out a simple wireless network node simulation, setting 4G network communication with the 20 Mbps bandwidth between users in NS2. The experimental data are generated using the Thomas Brinkhoff network data generator in Chen et al.¹⁸ This method is a commonly used method of moving data research, which uses the urban Oldenburg traffic network as input to generate simulated mobile user data. Table 1 lists the parameters used in the experiment. All experimental results are the average values of at least 100 rounds of experiments.

Table 1.

The settings of parameters.

Parameter name	Value
Number of mobile users	1000–10,000
Privacy protection level K value	1–10
Radius of privacy protection zone of $Coprivacy$ method	500 m

Experimental analysis

We consider the experimental environment and parameters with the same scenario as Huang et al.¹⁷ We first compare the cloaked success rate of different privacy protection methods. When the number of users changes, we set the K value as 5. The number of untrusted users increases as the users’ number goes up. Because our proposed method and $Coprivacy$ method all consider the privacy protection against the untrustworthy users, the cloaked success rate is basically stable, and that of $privacy_l_k$ method fall more obviously, as shown in Figure 4(a). In Figure 4(b), we can observe that when the number of users is fixed at 5000 and the K value increases, the cloaked success rates of the three methods all go up. Our proposed method has larger and more irregular cloaked area compared to others, so the cloaked success rate is higher.

Figure 4.

The comparative results of cloaked success rate: (a) under different number of users and (b) under different privacy protection level K.

From Figure 5(a), we can observe that the average response time of three privacy protection methods decreases with the increasing of users’ number because it is easier to construct cloaked region of anonymous user. However, the $Coprivacy$ method assumes that all users are trusted and the location of the anchor point is known in advance when the anonymous ring is built, so its average response time is the lowest. The $privacy_l_k$ method takes more time to construct a trusted environment, so the average response time is the highest. While our proposed method takes more time to build a Voronoi diagram and cloaked region, it saves time to establish a trusted environment, so the average response time is lower than that of the $privacy_l_k$ method. As shown in Figure 5(b), when the cloaked region needs more anonymous users, the average response time of three methods increases. The average response time grows faster when $K > 8$ . During the whole process, the average response time of our proposed method is lower than that of the $privacy_l_k$ method, but higher than that of the $Coprivacy$ method.

Figure 5.

The comparative results of mean response time: (a) under different number of users and (b) under different privacy protection level K.

The average traffic refers to the average mutual communication times from the setting up of the cloaked area to the task ending. From Figure 6(a), we can observe that when the number of users is limited, it takes more communication times to build a cloaked area so that the average traffic of the three methods is all higher. As the number of users goes up, the untrusted users number increases, too. The calculation of anchor point in the $privacy_l_k$ method requires further cooperative communication. Thus, the average traffic is slowing down. Since the $Coprivacy$ method assumes that the number of untrustworthy users is zero, the anchor point is calculated in a completely trusted environment, so it has the lowest traffic. Our proposed method achieves the communication between users by the neighbor’s cache list. In the process of cloaked region establishment, we can calculate the anchor point, so the average traffic is lower than that of the $privacy_l_k$ method. In Figure 6(b), when the privacy protection level K increases, the cloaked region needs more anonymous users, so the average traffic grows correspondingly. The $Coprivacy$ method assumes that the user is fully trusted; therefore, it has the least average traffic. Our proposed method does not need to spend additional communication to construct a trusted environment, but it requires the Voronoi diagram and the cloaked region to be built, so the average traffic of our proposed method is lower than that of the $privacy_l_k$ method and gradually closer to that of $Coprivacy$ method.

Figure 6.

The comparative results of average traffic: (a) under different number of users and (b) under different privacy protection level K.

Conclusion

In MCC, the users participating in the sensing task face the risk of privacy disclosure, which seriously impedes the participation of massive users. In this article, we propose a privacy preserving method based on Voronoi diagram. The users create a Voronoi cell and cloaked region among them and then choose an anchor point to communicate with the platform. By this method, it is difficult for a malicious attacker to infer the users’ private information. The experimental results show that our privacy protection method can effectively protect the users’ privacy. Compared to other methods, the average response time and the average traffic have greatly improved. In further research work, we mainly consider the dynamic updating of the anonymous users in the cloaked area and how to apply the lightweight encryption algorithm to the users’ privacy protection.

Footnotes

Handling Editor: Yanping Zhang

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by National Natural Science Foundation of China under grant nos 61070169, 61201212, Natural Science Foundation of Jiangsu Province under grant no. BK2011376, Production-Teaching-Research Prospective of Jiangsu Province under grant no. BY2012114, and Suzhou Key Laboratory of Converged Communication under grant no. SKLCC 2013XX.

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