Secure Spatial Query with Differentially Private Access Pattern
Feng Tian
1
, Zhenqiang Wu
1
, Hai Liu
1
, Laifeng Lu
2
1
School of Computer Science
2
School of Mathematics and Information Science
Shaanxi Normal University
Xi
an 710062, Shaanxi, China
Email: {tianfeng, zqiangwu, liuhai, lulaifeng}@snnu.edu.cn
Xiaolin Gui
3
School of Electronic and Information Engineering
3
Xi
an Jiaotong University
Xi
an 710049, Shaanxi, China
Email: xlgui@mail.xjtu.edu.cn
Abstract—The spatial transformation mechanism (e.g.,
space-filling curves) enables the spatial query in the encypted
spatial data stored on the third party service provider. Al-
though this mechanism will not reveal the original spatial
data nor the query content to the service provider, the service
provider can learn the relationship between the query tokens
and the accessed files, which is called the access pattern.
Several researches have demonstrated that the access pattern
can be used to recover the content of a query. In this paper,
we propose a secure spatial query scheme with differential
privacy access pattern. The proposed scheme employs the d-
privacy to measure the utilities of the candidate spatial indexes,
and applies subsampled exponential mechanism to select the
obfuscated spatial index. In this differentially private way, the
outsource spatial data is able to resist the query recovery
attacks. The experimental results demonstrate that our scheme
could generate high quality candidate spatial indexes for
the subsampled exponential mechanism, and achieve good
precision in the spatial range query.
Keywords-Spatial Query; Access Pattern; Differential Pri-
vacy; Privacy Preserving;
I. INTRODUCTION
A tremendous amount of valuable spatial data is accu-
mulated via the smartphones and exploited to offer various
location-based services (LBS), e.g., point of interests (POI)
discovery, proximity-based notification, and location-based
mobile advertising [1]. As the volume of the spatial data is
growing rapidly, the LBS provider, denoted as data owner,
is unable to support the storage of the tremendous volume
of data. Fortunately, the cloud has significant advantages
on cost-effective storage and computational resources. Thus,
outsourcing spatial data to the cloud is becoming a prevailing
paradigm.
In this paradigm, encryption is often applied to protect the
spatial data outsourced to the cloud service provider. More-
over, the secure spatial query mechanisms enable the spatial
data to be searched without exposing the query content.
Several research work has studied the secure spatial query to
support more query types, stronger security and better query
performance [1]–[3]. They employ spatial transformation
and cryptographic techniques to protect the service provider
from learning the content of the query or the retrieved
records. However, we should note that the service provider
is able to observe the accessed records corresponding to
a given query token. This kind of information leakage is
called the access pattern leakage. Recent researches [4],
[5] show that the attackers can recover the query content
with high accuracy according to their prior knowledge
and observations on queries issued by users, such as the
probability of POI occurence and the most frequent query
tokens.
Oblivious RAM (ORAM) [6] can preserve the access
pattern of the query by shuffling and re-encrypting the
accessed records. However, the communication overhead
makes it impractical to employ ORAM to protect the access
pattern since at least O(log n) records needs to be returned
when obliviously accessing a record from n recoreds. Xue
et al [7] present a two-cloud architecture and a series of
intersection protocols to provide sufficient privacy protection
against privacy leakage of statistical properties and access
pattern. By leveraging trusted hardware, Cui et al [8] pro-
posed a SGX-assisted scheme for performing search over
encrypted data. This scheme protected access pattern against
side channel attacks and showed good query efficiency.
Chen et al [9] proposed to protect searchable encryption
schemes against access pattern leakage with a form of
access pattern obfuscation, which is based on the d-privacy
[10]. d-privacy guarantees that the attackers is unable to
distinguish between queries using distinct query terms that
induce access patterns that are within specified distance of
one another. These schemes are efficient for keyword-based
or numeric-related searchable encryption. Nevertheless, in
spatial query scenario, these schemes cannot be applied
to protect the access pattern of the spatial query. It is
because we cannot enumerate all keywords in the spatial
query, which is different from the conventional searchable
encryption. Differential privacy [11] is a efficient framework
for preserving the access pattern while providing the query
services. In practice, exponential mechanism [12] is usually
applied to output obfuscated query result for access pattern
preservation. However, it is challenging to employ the ex-
ponential mechanism to secure spatial query, because the
exponential mechanism requires the quality function to be
calculated for every possible output. Since the output space
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2019 International Conference on Networking and Network Applications (NaNA)
978-1-7281-2629-6/19/$31.00 ©2019 IEEE
DOI 10.1109/NaNA.2019.00073