A privacy preserving-location_monitoring_system_for_wireless_sensor_networks
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1 A Privacy-Preserving Location Monitoring System for Wireless Sensor NetworksChi-Yin Chow, Student Member, IEEE, Mohamed F. Mokbel, Member, IEEE, and Tian He, Member, IEEE Abstract—Monitoring personal locations with a potentially untrusted server poses privacy threats to the monitored individuals. To this end, we propose a privacy-preserving location monitoring system for wireless sensor networks. In our system, we design two in- network location anonymization algorithms, namely, resource- and quality-aware algorithms, that aim to enable the system to provide high quality location monitoring services for system users, while preserving personal location privacy. Both algorithms rely on the well established k-anonymity privacy concept, that is, a person is indistinguishable among k persons, to enable trusted sensor nodes to provide the aggregate location information of monitored persons for our system. Each aggregate location is in a form of a monitored area A along with the number of monitored persons residing in A, where A contains at least k persons. The resource-aware algorithm aims to minimize communication and computational cost, while the quality-aware algorithm aims to maximize the accuracy of the aggregate locations by minimizing their monitored areas. To utilize the aggregate location information to provide location monitoring services, we use a spatial histogram approach that estimates the distribution of the monitored persons based on the gathered aggregate location information. Then the estimated distribution is used to provide location monitoring services through answering range queries. We evaluate our system through simulated experiments. The results show that our system provides high quality location monitoring services for system users and guarantees the location privacy of the monitored persons. Index Terms—Location privacy, wireless sensor networks, location monitoring system, aggregate query processing, spatial histogram !1 I NTRODUCTION tackle such a privacy breach, the concept of aggregate location information, that is, a collection of location dataThe advance in wireless sensor technologies has resulted relating to a group or category of persons from whichin many new applications for military and/or civilian individual identities have been removed [8], [9], has beenpurposes. Many cases of these applications rely on the suggested as an effective approach to preserve locationinformation of personal locations, for example, surveil- privacy [6], [8], [9]. Although the counting sensors by na-lance and location systems. These location-dependent ture provide aggregate location information, they wouldsystems are realized by using either identity sensors also pose privacy breaches.or counting sensors. For identity sensors, for example,Bat [1] and Cricket [2], each individual has to carry Figure 1 gives an example of a privacy breach in aa signal sender/receiver unit with a globally unique location monitoring system with counting sensors. Thereidentiﬁer. With identity sensors, the system can pinpoint are 11 counting sensor nodes installed in nine rooms R1the exact location of each monitored person. On the to R9 , and two hallways C1 and C2 (Figure 1a). The non-other hand, counting sensors, for example, photoelectric zero number of persons detected by each sensor node issensors [3], [4], and thermal sensors [5], are deployed depicted as a number in parentheses. Figures 1b and 1cto report the number of persons located in their sensingareas to a server. Unfortunately, monitoring personal locations with apotentially untrusted system poses privacy threats tothe monitored individuals, because an adversary couldabuse the location information gathered by the system toinfer personal sensitive information [2], [6], [7], [8]. Forthe location monitoring system using identity sensors,the sensor nodes report the exact location information ofthe monitored persons to the server; thus using identitysensors immediately poses a major privacy breach. To• Chi-Yin Chow, Mohamed F. Mokbel, and Tian He are with the Department of Computer Science and Engineering, University of Minnesota, Min- neapolis, MN 55455, USA, email: {cchow, mokbel, tianhe}@cs.umn.edu. (a) At time ti (b) At time ti+1 (c) At time ti+2• This research was partially supported by NSF Grants IIS-0811998, IIS- 0811935, CNS-0708604, CNS-0720465, and CNS-0626614, and a Mi- Fig. 1: A location monitoring system using counting crosoft Research Gift. sensors.
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2give the numbers reported by the same set of sensor cloaked area. On the other hand, the quality-aware algo-nodes at two consecutive time instances ti+1 and ti+2 , rithm starts from a cloaked area A, which is computed byrespectively. If R3 is Alice’s ofﬁce room, an adversary the resource-aware algorithm. Then A will be iterativelyknows that Alice is in room R3 at time ti . Then the reﬁned based on extra communication among the sensoradversary knows that Alice left R3 at time ti+1 and went nodes until its area reaches the minimal possible size. Forto C2 by knowing the number of persons detected by both algorithms, the sensor node reports its cloaked areathe sensor nodes in R3 and C2 . Likewise, the adversary with the number of monitored persons in the area as ancan infer that Alice left C2 at time ti+2 and went to R7 . aggregate location to the server.Such knowledge leakage may lead to several privacy Although our system only knows the aggregate lo-threats. For example, knowing that a person has visited cation information about the monitored persons, it cancertain clinical rooms may lead to knowing the her still provide monitoring services through answering ag-health records. Also, knowing that a person has visited gregate queries, for example, “What is the number ofa certain bar or restaurant in a mall building may reveal persons in a certain area?” To support these monitoringconﬁdential personal information. services, we propose a spatial histogram that analyzes the This paper proposes a privacy-preserving location gathered aggregate locations to estimate the distributionmonitoring system for wireless sensor networks to pro- of the monitored persons in the system. The estimatedvide monitoring services. Our system relies on the well distribution is used to answer aggregate queries.established k-anonymity privacy concept, which requires We evaluate our system through simulated experi-each person is indistinguishable among k persons. In our ments. The results show that the communication andsystem, each sensor node blurs its sensing area into a computational cost of the resource-aware algorithmcloaked area, in which at least k persons are residing. Each is lower than the quality-aware algorithm, while thesensor node reports only aggregate location information, quality-aware algorithm provides more accurate moni-which is in a form of a cloaked area, A, along with the toring services (the average accuracy is about 90%) thannumber of persons, N , located in A, where N ≥ k, to the the resource-aware algorithm (the average accuracy isserver. It is important to note that the value of k achieves about 75%). Both algorithms only reveal k-anonymousa trade-off between the strictness of privacy protection aggregate location information to the server, but they areand the quality of monitoring services. A smaller k indi- suitable for different system settings. The resource-awarecates less privacy protection, because a smaller cloaked algorithm is suitable for the system, where the sensorarea will be reported from the sensor node; hence better nodes have scarce communication and computationalmonitoring services. However, a larger k results in a resources, while the quality-aware algorithm is favorablelarger cloaked area, which will reduce the quality of for the system, where accuracy is the most importantmonitoring services, but it provides better privacy pro- factor in monitoring services.tection. Our system can avoid the privacy leakage in The rest of this paper is organized as follows. Ourthe example given in Figure 1 by providing low quality system model is outlined in Section 2. Section 3 presentslocation monitoring services for small areas that the the resource- and quality-aware location anonymizationadversary could use to track users, while providing high algorithms. Section 4 describes the aggregate query pro-quality services for larger areas. The deﬁnition of a small cessing. We describe an attacker model and the experi-area is relative to the required anonymity level, because ment setting of our system in Section 5. The experimentalour system provides better quality services for the same results are given in Section 6. Section 7 highlights thearea if we relax the required anonymity level. Thus the related work. Finally, Section 8 concludes the paper.adversary cannot infer the number of persons currentlyresiding in a small area from our system output withany ﬁdelity; therefore the adversary cannot know that 2 S YSTEM M ODELAlice is in room R3 . Figure 2 depicts the architecture of our system, where To preserve personal location privacy, we propose there are three major entities, sensor nodes, server, andtwo in-network aggregate location anonymization algo- system users. We will deﬁne the problem addressed byrithms, namely, resource- and quality-aware algorithms. our system, and then describe the detail of each entityBoth algorithms require the sensor nodes to collaborate and the privacy model of our system.with each other to blur their sensing areas into cloaked Problem deﬁnition. Given a set of sensor nodes s1 , s2 ,areas, such that each cloaked area contains at least k . . . , sn with sensing areas a1 , a2 , . . . , an , respectively,persons to constitute a k-anonymous cloaked area. The a set of moving objects o1 , o2 , . . . , om , and a requiredresource-aware algorithm aims to minimize communi- anonymity level k, (1) we ﬁnd an aggregate locationcation and computational cost, while the quality-aware for each sensor node si in a form of Ri = (Areai , Ni ),algorithm aims to minimize the size of the cloaked areas, where Areai is a rectangular area containing the sensingin order to maximize the accuracy of the aggregate area of a set of sensor nodes Si and Ni is the numberlocations reported to the server. In the resource-aware of objects residing in the sensing areas of the sensoralgorithm, each sensor node ﬁnds an adequate number nodes in Si , such that Ni ≥ k, Ni = | ∪sj ∈Si Oj | ≥ k,of persons, and then it uses a greedy approach to ﬁnd a Oj = {ol |ol ∈ aj }, 1 ≤ i ≤ n, and 1 ≤ l ≤ m; and (2) we
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3 to get more accurate aggregate locations from the sensor nodes, or even set it to zero to disable our algorithm to get the original readings from the sensor nodes, in order to get the best services from the system. Since the server and the system user are outside the trusted zone, they are untrusted. We now discuss the privacy threat in existing location monitoring systems. In an identity-sensor location mon- itoring system, since each sensor node reports the exact location information of each monitored object to the Fig. 2: System architecture. server, the adversary can pinpoint each object’s exact lo- cation. On the other hand, in a counting-sensor location monitoring system, each sensor node reports the numberbuild a spatial histogram to answer an aggregate query of objects in its sensing area to the server. The adversaryQ that asks about the number of objects in a certain area can map the monitored areas of the sensor nodes to theQ.Area based on the aggregate locations reported from system layout. If the object count of a monitored area isthe sensor nodes. very small or equal to one, the adversary can infer the Sensor nodes. Each sensor node is responsible for deter- identity of the monitored objects based on the mappedmining the number of objects in its sensing area, blurring monitored area, for example, Alice is in her ofﬁce roomits sensing area into a cloaked area A, which includes at time instance ti in Figure 1.at least k objects, and reporting A with the number of Since our system only allows each sensor node toobjects located in A as aggregate location information report a k-anonymous aggregate location to the server,to the server. We do not have any assumption about the adversary cannot infer an object’s exact location withthe network topology, as our system only requires a any ﬁdelity. The larger the anonymity level, k, the morecommunication path from each sensor node to the server difﬁcult for the adversary to infer the object’s exactthrough a distributed tree [10]. Each sensor node is also location. With the k-anonymized aggregate locationsaware of its location and sensing area. reported from the sensor nodes, the underlying spatial Server. The server is responsible for collecting the ag- histogram at the server provides low quality locationgregate locations reported from the sensor nodes, using monitoring services for a small area, and better qualitya spatial histogram to estimate the distribution of the services for larger areas. This is a nice privacy-preservingmonitored objects, and answering range queries based feature, because the object count of a small area ison the estimated object distribution. Furthermore, the more likely to reveal personal location information. Theadministrator can change the anonymized level k of the deﬁnition of a small area is relative to the requiredsystem at anytime by disseminating a message with a anonymity level, because our system provides lowernew value of k to all the sensor nodes. quality services for the same area if the anonymized System users. Authenticated administrators and users level gets stricter. We will also describe an attack model,can issue range queries to our system through either the where we stimulate an attacker that could be a systemserver or the sensor nodes, as depicted in Figure 2. The user or the server attempting to infer the object count ofserver uses the spatial histogram to answer their queries. a particular sensor node in Section 5.1. We evaluate our Privacy model. In our system, the sensor nodes con- system’s resilience to the attack model and its privacystitute a trusted zone, where they behave as deﬁned in protection in Section 6.our algorithm and communicate with each other througha secure network channel to avoid internal network 3 L OCATION A NONYMIZATION A LGORITHMSattacks, for example, eavesdropping, trafﬁc analysis, and In this section, we present our in-network resource- andmalicious nodes [6], [11]. Since establishing such a secure quality-aware location anonymization algorithms that isnetwork channel has been studied in the literature [6], periodically executed by the sensor nodes to report their[11], the discussion of how to get this network channel is k-anonymous aggregate locations to the server for everybeyond the scope of this paper. However, the solutions reporting period.that have been used in previous works can be appliedto our system. Our system also provides anonymouscommunication between the sensor nodes and the server 3.1 The Resource-Aware Algorithmby employing existing anonymous communication tech- Algorithm 1 outlines the resource-aware locationniques [12], [13]. Thus given an aggregate location R, anonymization algorithm. Figure 3 gives an example tothe server only knows that the sender of R is one of the illustrate the resource-aware algorithm, where there aresensor nodes within R. Furthermore, only authenticated seven sensor nodes, A to G, and the required anonymityadministrators can change the k-anonymity level and the level is ﬁve, k = 5. The dotted circles represent thespatial histogram size. In emergency cases, the admin- sensing area of the sensor nodes, and a line betweenistrators can set the k-anonymity level to a small value two sensor nodes indicates that these two sensor nodes
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4 (a) PeerLists after the ﬁrst broadcast (b) Rebroadcast from sensor node F (c) Resource-aware cloaked area of sensor node A Fig. 3: The resource-aware location anonymization algorithm (k = 5).can communicate directly with each other. In general, Algorithm 1 Resource-aware location anonymizationthe algorithm has three steps. 1: function R ESOURCE AWARE (Integer k, Sensor m, List R) 2: PeerList ← {∅} Step 1: The broadcast step. The objective of this step is // Step 1: The broadcast stepto guarantee that each sensor node knows an adequate 3: Send a message with m’s identity m.ID, sensing area m.Area, and object count m.Count to m’s neighbor peersnumber of objects to compute a cloaked area. To reduce 4: if Receive a message from a peer p, i.e., (p.ID, p.Area, p.count) thencommunication cost, this step relies on a heuristic that 5: Add the message to PeerList 6: if m has found an adequate number of objects thena sensor node only forwards its received messages to 7: Send a notiﬁcation message to m’s neighborsits neighbors when some of them have not yet found 8: end if 9: if Some m’s neighbor has not found an adequate number of objects thenan adequate number of objects. In this step, after each 10: Forward the message to m’s neighborssensor node m initializes an empty list PeerList (Line 2 11: end if 12: end ifin Algorithm 1), m sends a message with its identity // Step 2: The cloaked area stepm.ID, sensing area m.Area, and the number of objects 13: S ← {m} 14: Compute a score for each peer in PeerListlocated in its sensing area m.Count, to its neighbors 15: Repeatedly select the peer with the highest score from PeerList to S until the(Line 3). When m receives a message from a peer p, total number of objects in S is at least k 16: Area ← a minimum bounding rectangle of the senor nodes in Si.e., (p.ID, p.Area, p.Count), m stores the message in its 17: N ← the total number of objects in SPeerList (Line 5). Whenever m ﬁnds an adequate number // Step 3: The validation step 18: if No containment relationship with Area and R ∈ R thenof objects, m sends a notiﬁcation message to its neighbors 19: Send (Area, N ) to the peers within Area and the server(Line 7). If m has not received the notiﬁcation message 20: else if m’s sensing area is contained by some R ∈ R then 21: Randomly select a R ∈ R such that R .Area contains m’s sensing areafrom all its neighbors, some neighbor has not found an 22: Send R to the peers within R .Area and the serveradequate number of objects; therefore m forwards the 23: else 24: Send Area with a cloaked N to the peers within Area and the serverreceived message to its neighbors (Line 10). 25: end if Figures 3a and 3b illustrate the broadcast step. Whena reporting period starts, each sensor node sends amessage with its identity, sensing area, and the number approach to ﬁnd a cloaked area based on the informationof objects located in its sensing area to its neighbors. stored in PeerList. For each sensor node m, m initializesAfter the ﬁrst broadcast, sensor nodes A to F have found a set S = {m}, and then determines a score for each peeran adequate number of objects (represented by black in its PeerList (Lines 13 to 14 in Algorithm 1). The scorecircles), as depicted in Figure 3a. Thus sensor nodes A to is deﬁned as a ratio of the object count of the peer to theF send a notiﬁcation message to their neighbors. Since Euclidean distance between the peer and m. The ideasensor node F has not received a notiﬁcation message behind the score is to select a set of peers from PeerListfrom its neighbor G, F forwards its received messages, to S to form a cloaked area that includes at least k objectswhich include the information about sensor nodes D and and has an area as small as possible. Then we repeatedlyE, to G (Figures 3b). Finally, sensor node G has found select the peer with the highest score from the PeerListan adequate number of objects, so it sends a notiﬁcation to S until S contains at least k objects (Line 15). Finally,message to its neighbor, F . As all the sensor nodes have m determines the cloaked area (Area) that is a minimumfound an adequate number of objects, they proceed to bounding rectangle (MBR) that covers the sensing area ofthe next step. the sensor nodes in S, and the total number of objects Step 2: The cloaked area step. The basic idea of this in S (N ) (Lines 16 to 17).step is that each sensor node blurs its sensing area An MBR is a rectangle with the minimum area (whichinto a cloaked area that includes at least k objects, in is parallel to the axes) that completely contains allorder to satisfy the k-anonymity privacy requirement. desired regions, as illustrated in Figure 3c, where theTo minimize computational cost, this step uses a greedy dotted rectangle is the MBR of the sensing area of sensor
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5nodes A and B. The major reasons of our algorithms Algorithm 2 Quality-aware location anonymizationaligning with MBRs rather than other polygons are that 1: function Q UALITYAWARE (Integer k, Sensor m, Set init solution, List R) 2: current min cloaked area ← init solutionthe concept of MBRs have been widely adopted by // Step 1: The search space stepexisting query processing algorithms and most database 3: Determine a search space S based on init solution 4: Collect the information of the peers located in Smanagement systems have the ability to manipulate // Step 2: The minimal cloaked area stepMBRs efﬁciently. 5: Add each peer located in S to C[1] as an item 6: Add m to each itemset in C[1] as the ﬁrst item Figure 3c illustrates the cloaked area step. The PeerList 7: for i = 1; i ≤ 4; i ++ doof sensor node A contains the information of three peers, 8: for each itemset X = {a1 , . . . , ai+1 } in C[i] do 9: if Area(M BR(X)) < Area(current min cloaked area) thenB, D, and E. The object count of sensor nodes B, D, and 10: if N (M BR(X)) ≥ k thenE is 3, 1, and 2, respectively. We assume that the distance 11: current min cloaked area ← {X} 12: Remove X from C[i]from sensor node A to sensor nodes B, D, and E is 17, 13: end if18, and 16, respectively. The score of B, D, and E is 14: else 15: Remove X from C[i]3/17 = 0.18, 1/18 = 0.06, and 2/16 = 0.13, respectively. 16: end ifSince B has the highest score, we select B. The sum of 17: end for 18: if i < 4 thenthe object counts of A and B is six which is larger than 19: for each itemset pair X={x1 ,. . . ,xi+1 }, Y ={y1 ,. . . ,yi+1 } in C[i]the required anonymity level k = 5, so we return the do 20: if x1 = y1 , . . . , xi = yi and xi+1 = yi+1 thenMBR of the sensing area of the sensor nodes in S, i.e., A 21: Add an itemset {x1 , . . . , xi+1 , yi+1 } to C[i + 1]and B, as the resource-aware cloaked area of A, which 22: end if 23: end foris represented by a dotted rectangle. 24: end if Step 3: The validation step. The objective of this step 25: end for 26: Area ← a minimum bounding rectangle of current min cloaked areais to avoid reporting aggregate locations with a con- 27: N ← the total number of objects in current min cloaked areatainment relationship to the server. Let Ri and Rj be // Step 3: The validation step 28: Lines 18 to 25 in Algorithm 1two aggregate locations reported from sensor nodes iand j, respectively. If Ri ’s monitored area is included inRj ’s monitored area, Ri .Area ⊂ Rj .Area or Rj .Area ⊂Ri .Area, they have a containment relationship. We do therefore m sends Rm to the peers within Rm .Area andnot allow the sensor nodes to report their aggregate the server. However, if N < k, m cloaks the number oflocations with the containment relationship to the server, monitored persons of Rm , Rm .N , by increasing it by anbecause combining these aggregate locations may pose integer uniformly selected between k and 2k, and sendsprivacy leakage. For example, if Ri .Area ⊂ Rj .Area Rm to the peers within Rm .Area and the server (Line 24).and Ri .Area = Rj .Area, an adversary can infer that Since the server receives an aggregate location from eachthe number of objects residing in the non-overlapping sensor node for every reporting period, it cannot tellarea, Rj .Area − Ri .Area, is Rj .N − Ri .N . In case that whether any containment relationship takes place amongRj .N − Ri .N < k, the adversary knows that the number the actual aggregate locations of the sensor nodes.of objects in the non-overlapping is less than k, whichviolates the k-anonymity privacy requirement. As thisstep ensures that no aggregate location with the contain- 3.2 The Quality-Aware Algorithmment relationship is reported to the server, the adversary Algorithm 2 outlines the quality-aware algorithm thatcannot obtain any deterministic information from the takes the cloaked area computed by the resource-awareaggregate locations. algorithm as an initial solution, and then reﬁnes it until In this step, each sensor node m maintains a list R to the cloaked area reaches the minimal possible area,store the aggregate locations sent by other peers. When which still satisﬁes the k-anonymity privacy require-a reporting period starts, m nulliﬁes R. After m ﬁnds ment, based on extra communication between otherits aggregate location Rm , m checks the containment peers. The quality-aware algorithm initializes a variablerelationship between Rm and the aggregate locations current minimal cloaked area by the input initial solutionstored in R. If there is no containment relationship (Line 2 in Algorithm 2). When the algorithm terminates,between Rm and the aggregate locations in R, m sends the current minimal cloaked area contains the set of sen-Rm to the peers within Rm .Area and the server (Line 19 sor nodes that constitutes the minimal cloaked area. Inin Algorithm 1). Otherwise, m randomly selects an ag- general, the algorithm has three steps.gregate location Rp from the set of aggregate locations in Step 1: The search space step. Since a typical sensorR that contain m’s sensing area, and m sends Rp to the network has a large number of sensor nodes, it is toopeers within Rp .Area and the server (Lines 21 to 22). In costly for a sensor node m to gather the informationcase that no aggregate location in R contains m’s sensing of all the sensor nodes to compute its minimal cloakedarea, we ﬁnd a set of aggregate locations in R that are area. To reduce communication and computational cost,contained by Rm , R , and N is the number of monitored m determines a search space, S, based on the inputpersons in Rm that is not covered by any aggregate initial solution, which is the cloaked area computedlocation in R . If N ≥ k, the containment relationship by the resource-aware algorithm, such that the sensordoes not violate the k-anonymity privacy requirement; nodes outside S cannot be part of the minimal cloaked
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6(a) The MBR of A’s sensing area (b) The extended MBR1 of the edge e1 (c) The extended MBRi (1 ≤ i ≤ 4) (d) The search space S Fig. 4: The search space S of sensor node A. area (Line 3 in Algorithm 2). We will describe how to determine S based on the example given in Figure 4. Thus gathering the information of the peers residing in S is enough for m to compute the minimal cloaked area for m (Line 4). Figure 4 illustrates the search space step, in which we compute S for sensor node A. Let Area be the area of the input initial solution. We assume that Area = 1000. We determine S for A by two steps. (1) We ﬁnd the minimum bounding rectangle (MBR) of the sensing area of A. It is important to note that the sensing area can be in any polygon or irregular shape. In Figure 4a, the Fig. 5: The lattice structure of a set of four items. MBR of the sensing area of A is represented by a dotted rectangle, where the edges of the MBR are labeled by e1 to e4 . (2) For each edge ei of the MBR, we compute nodes deﬁne the width of the MBR (parallel to the an MBRi by extending the opposite edge such that the x-axis) while at most two other sensor nodes deﬁne area of the extended MBRi is equal to Area. S is the the height of the MBR (parallel to the y-axis). Thus MBR of the four extended MBRi . Figure 4b depicts this optimization mainly reduces computational cost by the extended MBR1 of the edge e1 by extending the reducing the number of MBR computations among the opposite edge e3 , where MBR1 .x is the length of MBR1 , peers in S. The correctness of this optimization technique MBR1 .y = Area/MBR1 .x and Area = 1000. Figure 4c will be discussed in Section 3.2.2. shows the four extended MBRs, MBR1 to MBR4 , which The second optimization technique has two properties, are represented by dotted rectangles. The MBR of the lattice structure and monotonicity property. We ﬁrst de- four extended MBRs constitutes S, which is represented scribe these two properties, and then present a progressive by a rectangle (Figure 4d). Finally, the sensor node only reﬁnement approach for ﬁnding a minimal cloaked area. needs the information of the peers within S. A. Lattice structure. In a lattice structure, a data set that Step 2: The minimal cloaked area step. This step takes a contains n items can generate 2n−1 itemsets excluding a set of peers residing in the search space, S, as an input null set. In the sequel, since the null set is meaningless and computes the minimal cloaked area for the sensor to our problem, it will be neglected. Figure 5 shows the node m. Although the search space step already prunes lattice structure of a set of four items S = {s1 , s2 , s3 , s4 }, the entire system space into S, exhaustively searching where each black line between two itemsets indicates the minimal cloaked area among the peers residing in that an itemset at a lower level is a subset of an itemset S, which needs to search all the possible combinations at a higher level. For our problem, given a set of sensor of these peers, could still be costly. Thus we propose two nodes S = {s1 , s2 , . . . , sn }, all the possible combinations optimization techniques to reduce computational cost. of these sensor nodes are the non-empty subsets of The basic idea of the ﬁrst optimization technique is S; thus we can use a lattice structure to generate the that we do not need to examine all the combinations combinations of the sensor nodes in S. In the lattice of the peers in S; instead, we only need to consider structure, since each itemset at level i has i items in S, the combinations of at most four peers. The rationale each combination at the lowest level, level 1, contains a behind this optimization is that an MBR is deﬁned by distinct item in S; therefore there are n itemsets at the at most four sensor nodes because at most two sensor lowest level. We generate the lattice structure from the
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7 (a) The full lattice structure (b) Pruning itemset {A, B} (c) Pruning itemset {A, D} (d) The minimal cloaked area Fig. 6: The quality-aware cloaked area of sensor node A.lowest level based on a simple generation rule: given two computational and storage overhead. To compute thesorted itemsets X = {x1 , . . . , xi } and Y = {y1 , . . . , yi } in minimal cloaked area for the sensor node m, we ﬁrstincreasing order, where each itemset has i items (1 ≤ i < generate an itemset for each peer in S at the lowest leveln), if all item pairs but the last one in X and Y are the of the lattice structure, C[1] (Line 5 in Algorithm 2). Tosame, x1 = y1 , x2 = y2 , . . ., xi−1 = yi−1 , and xi = yi , we accommodate with our problem, we add m to each item-generate a new itemset with i + 1 items, {x1 , . . . , xi , yi }. set in C[1] as the ﬁrst item (Line 6). Such accommodationIn the example, we use bold lines to illustrate the con- does not affect the generation of the lattice structure, butstruction of the lattice structure based on the generation each itemset has an extra item, m. For each itemset Xrule. For example, the itemset {s1 , s2 , s3 , s4 } at level 4 in C[1], we determine the MBR of X, M BR(X). If theis combined by the itemsets {s1 , s2 , s3 } and {s1 , s2 , s4 } area of M BR(X) is less than the current minimal cloakedat level 3, so there is a bold line from {s1 , s2 , s3 , s4 } to area and the total number of objects in M BR(X) is at{s1 , s2 , s3 } and another one to {s1 , s2 , s4 }. least k, we set X to the current minimal cloaked area, and B. Monotonicity property. Let S be a set of items, and P remove X from C[1] based on the ﬁrst pruning conditionbe the power set of S, 2S . The monotonicity property of of the monotonicity property (Lines 11 to 12). However,a function f indicates that if X is a subset of Y , then if the area of M BR(X) is equal to or larger than thef (X) must not exceed f (Y ), i.e., ∀X, Y ∈ P : (X ⊆ area of the current minimal cloaked area, we also remove XY ) → f (X) ≤ f (Y ). For our problem, the MBR of a from C[1] based on the second pruning condition of theset of sensor nodes S has the monotonicity property, monotonicity property (Line 15). Then we generate thebecause adding sensor nodes to S must not decrease the itemsets, where each itemset contains two items, at thearea of the MBR of S or the number of objects within second lowest level of the lattice structure, C[2], based onthe MBR of S. Let Area(M BR(X)) and N (M BR(X)) the remaining itemsets in C[1] based on the generationbe two functions that return the area of the MBR of an rule of the lattice structure. We repeat this procedureitemset X and the number of monitored objects located until we produce the itemsets at the highest level of thein the MBR, respectively. Thus, given two itemsets X and lattice structure, C[4], or all the itemsets at the currentY , if X ⊆ Y , then Area(M BR(X)) ≤ Area(M BR(Y )) level are pruned (Lines 19 to 23). After we examine alland N (M BR(X)) ≤ N (M BR(Y )). By this property, we non-pruned itemsets in the lattice structure, the currentpropose two pruning conditions in the lattice structure. minimal cloaked area stores the combination giving the(1) If a combination C gives the current minimal cloaked minimal cloaked area (Lines 26 to 27).area, other combinations that contain C at the higher Figure 6 illustrates the minimal cloaked area step thatlevels of the lattice structure should be pruned. This computes the minimal cloaked area for sensor node A.is because the monotonicity property indicates that the The set of peers residing in the search space is S =pruned combinations cannot constitute a cloaked area {B, D, E}. We assume that the area of the MBR of {A, B},smaller than the current minimal cloaked area. (2) Similarly, {A, D}, and {A, E} is 1000, 1200, and 900, respectively.if a combination C constitutes a cloaked area that is the The number of objects residing in the MBR of {A, B},same or larger than the current minimal cloaked area, other {A, D}, and {A, E} is six, four, and ﬁve, respectively, ascombinations that contain C at the higher levels of the depicted in Figure 3. Figure 6a depicts the full latticelattice structure should be pruned. structure of S where A is added to each itemset as C. Progressive reﬁnement. Since the monotonicity prop- the ﬁrst item. Initially, the current minimal cloaked areaerty shows that we would not need to generate a com- is set to the initial solution, which is the MBR of {A, B}plete lattice structure to compute a minimal cloaked area, ’computed by the resource-aware algorithm. The area ofwe generate the lattice structure of the peers in the search the MBR of {A, B}, Area(M BR({A, B})), is 1000 andspace, S, progressively from the lowest level of the lattice the total number of monitored objects in M BR({A, B}),structure to its higher levels, in order to minimize the N (M BR({A, B})), is six. It is important to note that
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8the progressive reﬁnement approach may not require algorithm reduces over 95% computational cost of theour algorithm to compute the full lattice structure. As brute-force approach, as it reduces the number of MBRdepicted in Figure 6b, we construct the lowest level computations from 63 to 3.of the lattice structure, where each itemset contains apeer in S. Since the area of M BR({A, B}) is the current 3.2.2 Proof of Correctnessminimal cloaked area, we remove {A, B} from the lattice In this section, we show the correctness of the quality-structure; hence the itemsets at the higher levels that aware location anonymization algorithm.contain {A, B}, {A, B, D}, {A, B, E}, and {A, B, D, E} Theorem 1: Given a resource-aware cloaked area of(enclosed by a dotted oval), will not be considered by the size Area of a sensor node s, a search space, S, computedalgorithm. Then, we consider the next itemset {A, D}. by the quality-aware algorithm contains the minimalSince the area of M BR({A, D}) is larger than the current cloaked area.minimal cloaked area, this itemset is removed from the Proof: Let X be the minimal cloaked area of sizelattice structure. After pruning {A, D}, the itemsets at equal to or less than Area. We know that X must totallythe higher levels that contain {A, D}, {A, D, E} (enclosed cover the sensing area of s. Suppose X is not totallyby a dotted oval), will not be considered (Figure 6c). covered by S, X must contain at least one extendedWe can see that all itemsets beyond the lowest level of MBR, MBRi , where 1 ≤ i ≤ 4 (Figure 4c). This meansthe lattice structure will not be considered by the algo- that the area of X is larger than the area of an extendedrithm. Finally, we consider the last itemset {A, E}. Since MBR, Area. This contradicts to the assumption that X isthe area of M BR({A, E}) is less than current minimal the minimal cloaked area; thus X is included in S.cloaked area and the total number of monitored objects Theorem 2: A minimum bounding rectangle (MBR) canin M BR({A, E}) is k = 5, we set {A, E} to the current be deﬁned by at most four sensor nodes.minimal cloaked area (Figure 6d). As the algorithm cannot Proof: By deﬁnition, given an MBR, each edge of thegenerate any itemsets at the higher level of the lattice MBR touches the sensing area of some sensor node. Instructure, it terminates. Thus the minimal cloaked area an extreme case, there is a distinct sensor node touchingis the MBR of sensor nodes A and E, and the number each edge of the MBR but not other edges. The MBRof monitored objects in this area is ﬁve. is deﬁned by four sensor nodes, which touch different Step 3: The validation step. This step is exactly the same edges of the MBR. For any edge e of the MBR, if multipleas in the resource-aware algorithm (Section 3.1). sensor nodes touch e but not other edges, we can simply pick one of these sensor nodes, because any one of these3.2.1 Analysis sensor nodes gives the same e. Thus an MBR is deﬁnedA brute-force approach of ﬁnding the minimal cloaked by at most four sensor nodes.area of a sensor node has to examine all the combinationsof its peers. Let N be the number of sensor nodes in 4 S PATIAL H ISTOGRAMthe system. Since each sensor node has N − 1 peers, In this section, we present a spatial histogram that is N −1 N −1we have to consider i=1 Ci = 2N −1 − 1 MBRs embedded inside the server to estimate the distributionto ﬁnd the minimal cloaked area. In our algorithm, the of the monitored objects based on the aggregate locationssearch space step determines a search space, S, and reported from the sensor nodes. Our spatial histogramprunes the peers outside S. Let M be the number of is represented by a two-dimensional array that modelspeers in S, where M ≤ N − 1. Thus the computational a grid structure G of NR rows and NC columns; hence, Mcost is reduced to i=1 Ci = 2M − 1. In the minimal M the system space is divided into NR × NC disjoint equal-cloaked area step, the ﬁrst optimization technique in- sized grid cells. In each grid cell G(i, j), we maintain adicates that an MBR can be deﬁned by at most four ﬂoat value that acts as an estimator H[i, j] (1 ≤ i ≤ NC ,peers. As we need to consider the combinations of at 1 ≤ j ≤ NR ) of the number of objects within its area.most four peers, the computational cost is reduced to We assume that the system has the ability to know 4 M i=1 Ci = (M 4 − 2M 3 + 11M 2 + 14M )/24 = O(M 4 ). the total number of moving objects M in the system.Furthermore, the second optimization technique uses the The value of M will be used to initialize the spatialmonotonicity property to prune the combinations, which histogram. In practice, M can be computed online forcannot give the minimal cloaked area. In our example, both indoor and outdoor dynamic environments. For thethe brute-force approach considers all the combinations indoor environment, the sensor nodes can be deployedof six peers; hence this approach computes 26 − 1 = 63 at each entrance and exit to count the number of usersMBRs to ﬁnd the minimal cloaked area of sensor node entering or leaving the system [4], [5]. For the outdoorA. In our algorithm, the search space step reduces the environment, the sensor nodes have been already usedentire space into S, which contains only three peers; to count the number of people in a predeﬁned area [3].hence this step needs to compute 23 − 1 = 7 MBRs. We use the spatial histogram to provide approximateAfter examining the three itemsets at the lowest level location monitoring services. The accuracy of the spa-of the lattice structure, all other itemsets at the higher tial histogram that indicates the utility of our privacy-levels are pruned. Thus the progressive reﬁnement ap- preserving location monitoring system will be evaluatedproach considers only three combinations. Therefore our in Section 6.
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9Algorithm 3 Spatial histogram maintenance 5.1 Attacker Model 1: function H ISTOGRAM M AINTENANCE (AggregateLocationSet R) 2: for each aggregate location R ∈ R do To evaluate the privacy protection of our system, we 3: if there is an existing partition P = {R1 , . . . , R|P | } such that R.Area∩ simulate an attacker attempting to infer the number of Rk .Area = ∅ for every Rk ∈ P then 4: Add R to P objects residing in a sensor node’s sensing area. We will 5: else analyze the evaluation result in Section 6.1. The key 6: Create a new partition for R 7: end if idea of the attacker model is that if the attacker cannot 8: end for infer the exact object count of the sensor node from 9: for each partition P do10: for each aggregate location Rk ∈ P do our system output, the attacker cannot infer the location11: R k .N ← H[i, j] information corresponding to an individual object. We G[i,j]∈Rk .Area12: For every cell G(i, j) ∈ Rk .Area, H[i, j] ← Rk .N consider the worst-case scenario where the attacker has No. of cells within Rk .Area13: end for the background knowledge about the system, i.e., the14:15: P.Area ← R1 .Area ∪ . . . ∪ R|P | .Area For every cell G(i, j) ∈ P.Area, / map layout of the system, the location of each sensor Rk .N−Rk .N node, the sensing area of each sensor node, the total Rk ∈P H[i, j] = H[i, j] + No. of cells outside P.Area number of objects currently residing in the system, and16: end for the aggregate locations reported from the sensor nodes. In general, the attacker model is deﬁned as: Given an area A (that corresponds to the monitored area of a sensor node) Algorithm 3 outlines our spatial histogram approach. and a set of aggregate locations R = {R1 , R2 , . . . , R|R| }Initially, we assume that the objects are evenly dis- overlapping with A, the attacker estimates the number oftributed in the system, so the estimated number of persons within A. Since the validation step in our locationobjects within each grid cell is H[i, j] = M/(NR × NC ). anonymization algorithms does not allow the aggregateThe input of the histogram is a set of aggregate loca- locations with the containment relationship to be re-tions R reported from the sensor nodes. Each aggregate ported to the server, no aggregate location is includedlocation R in R contains a cloaked area, R.Area, and in other aggregate locations in R.the number of monitored objects within R.Area, R.N . Without loss of generality, we use the Poisson distribu-First, the aggregate locations in R are grouped into the tion as a concrete exemplary distribution for the attackersame partition P = {R1 , R2 , . . . , R|P | } if their cloaked model [14]. Under the Poisson distribution, objects areareas are not overlapping with each other, which means uniformly distributed in an area within intensity of λ.that for every pair of aggregate locations Ri and Rj The probability of n distinct objects in a region S of sizein P , Ri .Area ∩ Rj .Area = ∅ (Lines 2 to 8. Then, for −λs (λs)neach partition P , we update its entire set of aggregate s is: P (N (S) = n) = e n! , where λ is computed aslocations to the spatial histogram at the same time. For the number of objects in the system divided by the areaeach aggregate location R in P , we record the estimation of the system.error, which is the difference between the sum of the Suppose that the object count of each aggregate lo-estimators within R.Area, R.N , and R.N , and then R.N cation Ri is ni , where 1 ≤ i ≤ |R|, and the aggregateis uniformly distributed among the estimators within locations in R and A constitute m non-overlappingR.Area; hence, each estimator within R.Area is set to subregions Sj , where 1 ≤ j ≤ m; hence, N (Ri ) =R.N divided by the total number of grid cells within Sj ∈Ri N (Sj ) = ni . Each subregion must either intersectR.Area (Lines 10 to 13). After processing all the aggre- or not intersect A, and it intersects one or more aggregategate locations in P , we sum up the estimation error of locations. If a subregion Sk intersects A, but none of the |P | aggregate locations in R, then N (Sk ) = 0. The probabil-each aggregate location in P , k=1 Rk .N − Rk .N , that ity mass function of the number of distinct objects in Ais uniformly distributed among the estimators outside being equal to na , N = na , given the aggregate locationsP.Area, where P.Area is the area covered by some ag- in R can be expressed as follows:gregate location in P , P.Area = ∪Rk ∈P Rk .Area (Line 15).Formally, for each partition P that contains |P | aggregatelocations Rk (1 ≤ k ≤ |P |), every estimator in the P (N = na |N (R1 ) = n1 , . . . , N (R|R| ) = n|R| )histogram is updated as follows: P (N = na , N (R1 ) = n1 , . . . , N (R|R| ) = n|R| ) Rk .N = No. of cells within Rk .Area , for G(i, j) ∈ Rk .Area P (N (R1 ) = n1 , . . . , N (R|R| ) = n|R| )H[i, j] = i i i |P | Vi ∈(VS ∩VA ) < v1 , v2 , . . . , vm > Rk .N−Rk .N H[i, j] + No. ofk=1 outside P.Area , for G(i, j) ∈ P.Area / = j j j , (1) Vj ∈VS < v1 , v2 , . . . , vm > cells where the notation V =< v1 , v2 , . . . , vm > represents the5 S YSTEM E VALUATION joint probability that there are vi objects in a subregionIn this section, we discuss an attacker model, the exper- Si (1 ≤ i ≤ m); the joint probability is computed asiment setting of our privacy-preserving location mon- 1≤i≤m P (N (Si ) = vi ). The lower and upper bounds ofitoring system in a wireless sensor network, and the vi (denoted as LB(vi ) and U B(vi ), respectively) are zeroperformance metrics. and the minimum nj of the aggregate locations inter-
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10 TABLE 1: Parameter settings 0.7 Resource-Aware 0.7 Resource-Aware 0.6 Quality-Aware 0.6 Quality-Aware Description Default Value Range Attack Model Error Attack Model Error 0.5 0.5 Histogram size (NR × NC ) 200 × 200 502 to 2502 Query region size ratio [0.001, 0.032] 0.001 to 0.256 0.4 0.4 Number of moving objects 5,000 2,000 to 10,000 0.3 0.3 k-anonymity level 20 10 to 30 0.2 0.2 Object mobility speed [0,5] [0,5] to [0,30] 0.1 0.1 0 0 10 15 20 25 30 2 4 6 8 10 Anonymity Levels Number of Objects (in thousands)secting Si , respectively. Thus, the possible value of vi is (a) Anonymity levels (b) Number of objectswithin a range of [0, minRj ∩Si =∅∧1≤i≤m∧1≤j≤|R| (nj )]. VSis the set of < v1 , v2 , . . . , vm > that is a solution to the Fig. 7: Attacker model error.following equations: VS : Si ∈R1 vi = n1 , Si ∈R2 vi =n2 , . . . , Si ∈R|R| vi = n|R| , where vi ≥ 0 for 1 ≤ i ≤ m.VA is the set of < v1 , v2 , . . . , vm > that satisﬁes the each sensor node per reporting period. This metric alsofollowing equation: VA : 1≤i≤m vi = na . indicates the network trafﬁc and the power consumption The attacker uses an exhaustive approach to ﬁnd of the sensor nodes. (3) Cloaked area size. This metricall possible solutions to VS , in order to compute the measures the quality of the aggregate locations reportedexpected value E(N ) of Equation 1 as the estimated by the sensor nodes. The smaller the cloaked area, thevalue of na . The complexity of computing E(N ) is better the accuracy of the aggregate location is. (4) Com-O( 1≤i≤m U B(vi )). Since the complexity of the attacker putational cost. We measure the computational cost ofmodel is an exponential function of m and m would our location anonymization algorithms in terms of thebe much larger than |R|, such exponential complexity average number of minimum bounding rectangle (MBR)makes it prohibitive for the attacker model to be used to computations that are needed to determine a resource- orprovide online location monitoring services; and there- quality-aware cloaked area. We compare our algorithmsfore, we use our spatial histogram to provide online ser- with a basic approach that computes the MBR for eachvices in the experiments. We will evaluate the resilience combination of the peers in the required search spaceof our system to the attacker model in Section 6.1. to ﬁnd the minimal cloaked area. The basic approach does not employ any optimization techniques proposed for our quality-aware algorithm. (5) Query error. This5.2 Simulation Settings metric measures the utility of our system, in terms ofIn all experiments, we simulate 30 × 30 sensor nodes the relative error between the query answer M , which isthat are uniformly distributed in a 600 × 600 system the estimated number of objects within the query regionspace. Each sensor node is responsible for monitoring based on a spatial histogram, and the actual answera 20 × 20 space. We generate a set of moving objects |M −M | M , respectively. The error is measured as . Whenthat freely roam around the system space. Unless men- M M = 0, we consider M as the error.tioned otherwise, the experiments consider 5,000 movingobjects that move at a random speed within a rangeof [0, 5] space unit(s) per time unit, and the required 6 E XPERIMENTAL R ESULTS AND A NALYSISanonymity level is k = 20. The spatial histogram contains In this section, we show and analyze the experimentalNR ×NC = 200×200 grid cells, and we issue 1,000 range results with respect to the privacy protection and thequeries whose query region size is speciﬁed by a ratio of quality of location monitoring services of our system.the query region area to the system area, that is, a queryregion size ratio. The default query region size ratiois uniformly selected within a range of [0.001, 0.032]. 6.1 Anonymization StrengthTable 1 gives a summary of the parameter settings. Figure 7 depicts the resilience of our system to the at- tacker model with respect to the anonymity level and the5.3 Performance Metrics number of objects. In the ﬁgure, the performance of the resource- and quality-aware algorithms is represented byWe evaluate our system in terms of ﬁve performance black and gray bars, respectively. Figure 7a depicts thatmetrics. (1) Attack model error. This metric measures the the stricter the anonymity level, the larger the attackerresilience of our system to the attacker model by the model error will be encountered by an adversary. Whenrelative error between the estimated number of objects N the anonymity level gets stricter, our algorithms generatein a sensor node’s sensing area and the actual one N . The larger cloaked areas, which reduce the accuracy of theerror is measured as |N−N | . When N = 0, we consider N aggregate locations reported to the server. Figure 7bN as the error. (2) Communication cost. We measure the shows that the attacker model error reduces, as thecommunication cost of our location anonymization algo- number of objects gets larger. This is because whenrithms in terms of the average number of bytes sent by there are more objects, our algorithms generate smaller
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11 0.8 k=10 if its query region size is not larger than 0.016 (it is k=15 0.7 k=20 k=25 about 16 sensor nodes’ sensing area). For the quality- 0.6 aware algorithm, Figure 8b shows that when k = 10, Query Answer Error k=30 0.5 a query region is said to be small if its query region 0.4 size is not larger than 0.002, while when k = 30, a query 0.3 region is only considered as small if its query region size 0.2 is not larger than 0.004. The results also show that the 0.1 quality-aware algorithm always performs better than the 0 0.001 0.002 0.004 0.008 0.016 0.032 0.064 0.128 0.256 resource-aware algorithm. Query Region Size Ratio (a) Resource-aware algorithm 6.3 Effect of the Number of Objects 0.6 k=10 Figure 9 depicts the performance of our system with k=15 0.5 k=20 respect to increasing the number of objects from 2,000 to k=25 10,000. Figure 9a shows that when the number of objects Query Answer Error k=30 0.4 increases, the communication cost of the resource-aware 0.3 algorithm is only slightly affected, but the quality-aware 0.2 algorithm signiﬁcantly reduces the communication cost. 0.1 The broadcast step of the resource-aware algorithm ef- fectively allows each sensor node to ﬁnd an adequate 0 0.001 0.002 0.004 0.008 0.016 0.032 0.064 0.128 0.256 number of objects to blur its sensing area. When there Query Region Size Ratio are more objects, the sensor node ﬁnds smaller cloaked (b) Quality-aware algorithm areas that satisfy the k-anonymity privacy requirement, as given in Figure 9b. Thus the required search space of Fig. 8: Query region size. a minimal cloaked area computed by the quality-aware algorithm becomes smaller; hence the communication cost of gathering the information of the peers in suchcloaked areas, which increase the accuracy of the aggre- a smaller required search space reduces. Likewise, sincegate locations reported to the server. It is difﬁcult to set a there are less peers in the smaller required search spacehard quantitative threshold for the attacker model error. as the number of objects increases, ﬁnding the minimalHowever, it is evident that the adversary cannot infer cloaked area incurs less minimum bounding rectanglethe number of objects in the sensor node’s sensing area (MBR) computation (Figure 9c). Since our algorithmswith any ﬁdelity. generate smaller cloaked areas when there are more users, the spatial histogram can gather more accurate6.2 Effect of Query Region Size aggregate locations to estimate the object distribution; therefore the query answer error reduces (Figure 9d). TheFigure 8 depicts the privacy protection and the quality result also shows that the quality-aware algorithm al-of our location monitoring system with respect to in- ways provides better quality services than the resource-creasing the query region size ratio from 0.001 to 0.256, aware algorithm.where the query region size ratio is the ratio of the queryregion area to the system area and the query region sizeratio 0.001 corresponds to the size of a sensor node’s 6.4 Effect of Privacy Requirementssensing area. The results give evidence that our system Figure 10 depicts the performance of our system withprovides low quality location monitoring services for the respect to varying the required anonymity level k fromrange query with a small query region, and better quality 10 to 30. When the k-anonymity privacy requirementservices for larger query regions. This is an important gets stricter, the sensor nodes have to enlist more peersfeature to protect personal location privacy, because for help to blur their sensing areas; therefore the commu-providing the accurate number of objects in a small area nication cost of our algorithms increases (Figure 10a). Tocould reveal individual location information; therefore satisfy the stricter anonymity levels, our algorithms gen-an adversary cannot use our system output to track the erate larger cloaked areas, as depicted in Figure 10b. Formonitored objects with any ﬁdelity. The deﬁnition of a the quality-aware algorithm, since there are more peerssmall query region is relative to the required anonymity in the required search space when the input (resource-level k. For example, we want to provide low quality aware) cloaked area gets larger, the computational costservices, such that the query error is at least 0.2, for of computing the minimal cloaked area by the quality-small query regions. For the resource-aware algorithm, aware algorithm and the basic approach gets worse (Fig-Figure 8a shows that when k = 10, a query region is said ure 10c). However, the quality-aware algorithm reducesto be small if its query region size is not larger than 0.002 the computational cost of the basic approach by at least(it is about two sensor nodes’ sensing area). However, four orders of magnitude. Larger cloaked areas givewhen k = 30, a query region is only considered as small more inaccurate aggregate location information to the
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12 10 2.6 108 0.25 Cloaked Area Size (in thousands) Number of Bytes (in thousands) Resource-Aware Resource-Aware Resource-Aware Resource-Aware 7 Quality-Aware 2.4 Quality-Aware 10 Quality-Aware Quality-Aware No. of MBR Computations 9 6 Basic 0.2 2.2 Query Answer Error 10 8 5 2 10 7 4 0.15 1.8 10 1.6 3 6 10 0.1 2 1.4 10 5 1 1.2 10 0.05 4 1 100 3 0.8 -1 0 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 Number of Objects (in thousands) Number of Objects (in thousands) Number of Objects (in thousands) Number of Objects (in thousands) (a) Communication cost (b) Cloaked area size (c) Computational cost (d) Estimation error Fig. 9: Number of objects. 9 13 3.5 10 0.3 Cloaked Area Size (in thousands) Number of Bytes (in thousands) Resource-Aware Resource-Aware Resource-Aware Resource-Aware 12 Quality-Aware Quality-Aware 108 Quality-Aware Quality-Aware No. of MBR Computations 3 7 Basic 0.25 11 10 Query Answer Error 10 2.5 106 0.2 9 105 4 8 2 10 0.15 3 7 10 1.5 2 0.1 6 10 5 1 101 0.05 0 4 10 3 0.5 10-1 0 10 15 20 25 20 10 15 20 25 30 10 15 20 25 30 10 15 20 25 30 Anonymity Levels Anonymity Levels Anonymity Levels Anonymity Levels (a) Communication cost (b) Cloaked area size (c) Computational cost (d) Estimation error Fig. 10: Anonymity levels.system, so the estimation error increases as the required internal data thefts or inadvertent disclosure. Recently,k-anonymity increases (Figure 10d). The quality-aware location anonymization techniques have been widelyalgorithm provides much better quality location moni- used to anonymize personal location information beforetoring services than the resource-aware algorithm, when any server gathers the location information, in orderthe required anonymity level gets stricter. to preserve personal location privacy in location-based services. These techniques are based on one of the three6.5 Effect of Mobility Speeds concepts. (1) False locations. Instead of reporting the monitored object’s exact location, the object reports nFigure 11 gives the performance of our system with different locations, where only one of them is the object’srespect to increasing the maximum object mobility speed actual location while the rest are false locations [18].from [0, 5] and [0, 30]. The results show that increas- (2) Spatial cloaking. The spatial cloaking technique blurs aing the object mobility speed only slightly affects the user’s location into a cloaked spatial area that satisfy thecommunication cost and the cloaked area size of our user’s speciﬁed privacy requirements [19], [20], [21], [22],algorithms, as depicted in Figures 11a and 11b, respec- [23], [24], [25], [26], [27], [28]. (3) Space transformation.tively. Since the resource-aware cloaked areas are slightly This technique transforms the location information ofaffected by the mobility speed, the object mobility speed queries and data into another space, where the spatialhas a very small effect on the required search space relationship among the query and data are encoded [29].computed by the quality-aware algorithm. Thus the Among these three privacy concepts, only the spatialcomputational cost of the quality-aware algorithm is cloaking technique can be applied to our problem. Thealso only slightly affected by the object mobility speed main reasons for this are that (a) the false location tech-(Figure 11c). Although Figure 11d shows that query niques cannot provide high quality monitoring servicesanswer error gets worse when the objects are moving due to a large amount of false location information;faster, the query accuracy of the quality-aware algorithm (b) the space transformation techniques cannot provideis consistently better than the resource-aware algorithm. privacy-preserving monitoring services as it reveals the monitored object’s exact location information to the7 R ELATED WORK query issuer; and (c) the spatial cloaking techniquesStraightforward approaches for preserving users’ loca- can provide aggregate location information to the servertion privacy include enforcing privacy policies to re- and balance a trade-off between privacy protection andstrict the use of collected location information [15], [16] the quality of services by tuning the speciﬁed privacyand anonymizing the stored data before any disclo- requirements, for example, k-anonymity and minimumsure [17]. However, these approaches fail to prevent area privacy requirements [17], [27]. Thus we adopt the
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