Privacy-Preserving Compressive Sensing for
Crowdsensing based Trajectory Recovery
Linghe Kong
∗‡
,LiangHe
†
, Xiao-Yang Liu
‡
,YuGu
§
, Min-You Wu
‡
,XueLiu
∗
∗
McGill University, Canada, Email: linghe.kong@mail.mcgill.ca, xueliu@cs.mcgill.ca
†
University of Michigan, USA, Email: lianghe.umich@gmail.com
‡
Shanghai Jiao Tong University, China, Email: {linghe.kong, yanglet, m wu}@sjtu.edu.cn
§
IBM Research - Austin, USA, Email: yugu@us.ibm.com
Abstract—Location based services ha ve experienced an explo-
sive growth and evolved from utilizing a single location to the
whole trajectory. Due to the hardware and energy constraints,
there are usually many missing data within a trajectory. In order
to accurately recover the complete trajectory, crowdsensing pro-
vides a promising method. This method resorts to the correlation
among multiple users’ trajectories and the advanced compressive
sensing technique, which significantly outperforms conventional
interpolation methods on accuracy. However, as trajectories
exposes users’ daily activities, the privacy issue is a major
concern in crowdsensing. While existing solutions independently
tackle the accurate trajectory recovery and privacy issues, yet
no single design is able to address these two challenges simul-
taneously. Therefore in this paper, we propose a novel Privacy
Preserving Compressive Sensing (PPCS) scheme, which encrypts
a trajectory with several other trajectories while maintaining
the homomorphic obfuscation property for compressive sensing.
Under PPCS, adversaries can only capture the encrypted data,
so the user privacy is preserved. Furthermore, the homomorphic
obfuscation property guarantees that the recovery accuracy of
PPCS is comparable to the state-of-the-art compressive sensing
design. Based on two publicly available traces with numerous
users and long durations, we conduct extensive simulations to
evaluate PPCS. The results demonstrate that PPCS achieves a
high accuracy of <53 m and a large distortion between the
encrypted and the original trajectories (a commonly adopted
metric of privacy strength) of >9,000 m even when up to 50%
original data are missing.
I. INTRODUCTION
Location based services (LBSs) [18, 37] have experienced
an explosive growth recently, which are evolving from utilizing
a single location [7] to harness the complete trajectory of a
mobile user [23, 26, 40]. For example, the Moves application,
which automatically tracks both activities and trajectories of
users, has been downloaded over 4 million times sinc e its
launch in Jan. 2013 and has been acquired by Facebook [1].
Although GPS is universally available on modern devices,
the trajectory of a mobile user may always be incomplete due
to none-line-of-sight to satellites [29]. In addition, since GPS
consumes a significant amount of energy, it is only activated
periodically to conserve energy [22]. Consequently, the trajec-
tory recovery [30] is one of the fundamental components of
LBSs to estimate the missing data in a incomplete trajectory.
For instance, tripperm ap [4] in Flickr can automatically repro-
duce a user’s travelling path based on her geotagged photos.
Considerable interpolation methods have been devoted to
trajectory recovery. With a single user’s incomplete trajectory
data, the methods such as nearest neighbors [31] and linear
interpolation [34] can attain only coarse-grained accuracy.
More recently, Rallapalli et al. [29] reveal that the trajectories
of multiple users within the same geographic area are strongly
correlated. For instance, students in the same campus have
similar time tables; vehicles in the same segment of freeway
moves with similar velocities. Leveraging such correlation s,
the crowdsensing technology [10, 11, 16, 17, 28, 35] provides
a promising recovery method, which collectively recovers all
users’ trajectories together using compressive sensing (CS).
This crowdsensing recovery method is proved to be superior
to interpolation methods with only single user data [29].
While the crowdsensing recovery method accomplishes the
better accuracy, the major drawback for applying it in practice
is its requirement to collect all users’ location data, which
poses great concerns for potential privacy leakage [32, 36].
Especially in crowdsensing, the users are willing to contribute
their personal data only when their privacies are preserved.
Currently, the most commonly adopted privacy-preserving ap-
proach is anonymization [24]. Nevertheless, latest studies [12,
38] reveal that the anonymization mechanism alone is inad e-
quate. To further improve the privacy, dummification [19] and
obfuscation [13, 15, 27] methods are introduced, which inject
fake trajectories and perturb original trajectories, respectively.
Although dummification and obfuscation methods reasonably
protect user privacies, they also pollute the original data, which
decreases the recovery accuracy with current crowdsensing
recovery method.
To tackle the challenges of accurate trajectory recovery
and privacy-preserving simultaneously, we design a novel
encryption method named K-vector perturbation (KVP) to
attain both objectives. The main idea of KVP is to use a private
key to perturb a user’s trajectory with K other trajectories
while maintaining the homomorphic obfuscation property for
compressive sensing. Based on KVP, we propose the privacy-
preserving compressive sensing (PPCS) scheme including
three major steps. First, every user encryp ts her incomplete
location data b y KVP and transmits the d ata in encrypted form
to the crowdsensing server. Second, the server does not need to
decrypt the data but directly recovers all users’ encrypted data
together with CS. Third, a user downloads her corresponding
recovered data and decrypts her own trajectory by inverse
KVP. Under PPCS, adversaries are possible to capture the
2015 IEEE 35th International Conference on Distributed Computing Systems
1063-6927/15 $31.00 © 2015 IEEE
DOI 10.1109/ICDCS.2015.12
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