Mobile Information Systems

Volume 2016 (2016), Article ID 1763416, 9 pages

http://dx.doi.org/10.1155/2016/1763416

## A Perturbed Compressed Sensing Protocol for Crowd Sensing

Beijing Engineering Research Center of Massive Language Information Processing and Cloud Computing Application, School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Received 10 December 2015; Revised 28 April 2016; Accepted 10 May 2016

Academic Editor: Tony T. Luo

Copyright © 2016 Zijian Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Crowd sensing network is a data-centric network consisting of many participants uploading environmental data by smart mobile devices or predeployed sensors; however, concerns about communication complexity and data confidentiality arise in real application. Recently, Compressed Sensing (CS) is a booming theory which employs nonadaptive linear projections to reduce data quantity and then reconstructs the original signal. Unfortunately, privacy issues induced by untrusted network still remain to be unsettled practically. In this paper, we consider crowd sensing using CS in wireless sensor network (WSN) as the application scenario and propose a data collection protocol called perturbed compressed sensing protocol (PCSP) to preserve data confidentiality as well as its practicality. At first, we briefly introduce the CS theory and three factors correlated with reconstruction effect. Secondly, a secure CS-based framework using a secret disturbance is developed to protect raw data in WSN, in which each node collects, encrypts, measures, and transmits the sampled data in our protocol. Formally, we prove that our protocol is CPA-secure on the basis of a theorem. Finally, evaluation on real and simulative datasets shows that our protocol could not only achieve higher efficiency than related algorithms but also protect signal’s confidentiality.

#### 1. Introduction

Crowd sensing network is a powerful sensor network utilizing the force from crowd. Crowd sensing is a form of network wireless sensing, which can be achieved by exploiting WSN. With enormous sensors deployed, WSN is limited by its relatively weak computational capability and low energy reservation. The primary task of WSN is to sense, transmit, and process packets while maintaining the energy cost to the minimum.

In traditional WSN, where communication is conducted via intranet or private network, bandwidth is severely consumed and certain commands from sensor nodes cannot be timely relayed to information server because great amounts of data collected during collection phase need to be transmitted. On the other hand, since trust management is maintained in public network, data confidentiality may be exposed. Hence, how to reasonably design secure transmission schemes in WSN has become a precondition for applying WSN to many fields extensively.

Without the traditional signal acquisition process constraint, Compressed Sensing (CS), proposed by Candes et al. [1] and Donoho [2] in 2006, is a booming theory that captures and represents compressible signals at a sampling rate significantly lower than the Nyquist rate [3–6]. It first employs nonadaptive linear projections that preserve the structure of the signal, and then the signal reconstruction can be conducted using an optimization process from these projections. Compressive sensing has a wide range of applications such as compressive detection and estimation, DNA microarray, and distributed compressed video sending [7].

Moreover, traditional data compressing method of WSN comes with several disadvantages, including the following. Several important components and corresponding locations need to be preserved after orthogonal transformation in data compressing; otherwise, the original data could not be recovered [7]. In layered multihop WSN, owing to the hardware limitation, sensors’ energy storage is constrained to a low level. Intuitively, nodes closer to sink node will die sooner thanks to their faster battery consumption rate, which would result in the imbalance of energy consumption among sensors in different positions. Due to the advantages of CS, more and more CS techniques have been integrated into WSN, but most of them only consider the time relativity of a single node. In fact, space relativity can also be traced in nodes of WSN, leading to Distributed Compressed Sensing (DCS) which views the raw data as original signal and compress the signal before transmitting. DCS has advantages as follows. The random measurement from DCS is a random linear combination of every element in original signal. Thus, losing part of measurement will not affect the reconstruction of original signal. In DCS-based WSN model, data quantity of each node remains the same, so energy consumption is balanced and network lifetime is prolonged.

Although DCS can effectively solve the problems raised by traditional methods, data security can never be overlooked. Researches on CS security still need to be explored. Some [8–11] tried to modify the measurement matrix but failed to apply their schemes in WSN; others [12] performed encryption (like AES, etc.) after the data is compressed to protect data security, but secure network is required. Notice that most WSN is deployed in remote, unattended, or even hostile environment, meaning node’s reliability is difficult to guarantee. Therefore, it is crucial to design a secure model. In this paper, we propose a perturbed compressed sensing protocol (PCSP) to preserve data confidentiality with high practicality. Our contributions are listed as follows.(i)We propose a perturbed compressed sensing protocol (PCSP) in WSN for crowding sensing and our PCSP can reduce communication complexity explicitly.(ii)We prove that our PCSP can provide data confidentiality; to be more specific, our PCSP is proved to be chosen-plaintext attack secure.(iii)We systematically evaluate our PCSP by comparing its performance with existing approaches. Experiments show that our PCSP achieves higher accuracy of recovery.

*Organization*. The rest of this paper is organized as follows. In Section 2, we review the related work presented in the literature. Then, we briefly introduce the main idea of CS in Section 3. Section 4 illustrates our protocol in detail. While security is discussed in Section 5. We systematically evaluate performance of PCSP by making comparisons with existing approaches in Section 6; in addition, limitations of our protocol and future work are explained in Section 7. At last, we conclude this paper in Section 8.

#### 2. Related Work

Compressed Sensing (CS) is a new method for compressing signal which breaks through the traditional limit of sampling frequency. Through matrix computation at the encoding end, we can compress the original signal from high dimension to low dimension with a small sampling frequency and low computation complexity. At the decoding end, the original signal is reconstructed by solving a convex optimization problem.

Meanwhile, CS is capable of providing a good encryption feature on its interior structure level. Because the projection is a function value of measurement matrix which can be seen as a shared key between encoding end and decoding end.

Researches on CS put focus upon three factors associated with the reconstruction effect: sparse representation, measurement matrix, and reconstruction algorithm improvement. As a precondition for applying CS, common methods for sparse representation are discrete cosine transform basis, fast Fourier transform basis, disperse wavelet transform basis, Curvelet basis, Gabor basis, and redundant dictionary [15]. In particular, redundant dictionary or overcomplete dictionary can adaptively find out the optimal base according to the sparse property of different signal such that the minimum sparsity on this base and the best signal compression degree are both reached. For measurement matrix, Null Space Property (NSP) [16] and Restricted Isometry Property (RIP) [1, 17–19] should be satisfied; these matrixes include Gauss random matrix, Bernoulli measurement matrix, sparse stochastic matrix, toeplitz matrix, and circulant matrix. The work in [1, 2, 15, 20] proved that measurement matrix making up of independent and identical distributed Gauss random variable is irrelevant with any overcomplete redundant dictionaries, and accurate recovery of original signal can be guaranteed even after the signal is compressed. Hence, Gauss random matrix is one of the best options for measurement matrix, but doing so brings high complexity and pseudorandom matrix is an alternative choice in researches. In recent years, researchers have been working on robust pursuit algorithm, such as greedy pursuit (including MP [21], OMP [22], StOMP [23], and ROMP [24]), convex relaxed approach (including BP [25], interior point method [26], gradient projection method [27], and iterative threshold method [28]), and the combination of the former two (including Fourier sampling [29] and HHS [30]).

The classic OMP [22] is a greedy pursuit, the basic idea is transvection computation, and the most related (to compressed value ) column vector is selected in each iteration, until the reconstruction sparse representation of original signal is found. Then we can retrieve original signal through spares inverse operation and decryption. Its advantage is convenient implementation, whereas the disadvantage is that multiple measurements are required.

As long as CS is proposed, how to use CS to provide data security is also a research hotspot. The work in [30–33] pointed out that the linear projection on measurement matrix is essentially a protection of data secrecy to some extent. The work in [30] analyzed the security of CS under several possible attacks. The work in [31] compared CS with other encryption methods through quantization. The work in [32, 33] designed the measurement matrix as symmetric secret keys such that eavesdroppers cannot obtain original signal. The work in [12] adopted AES and SHA to provide data confidentiality and data integrity after data compression.

Regarding the security problem raised by applying CS to WSN, this paper proposes an encryption method based on existing DCS model. Analysis and experiments show that our approach can provide data confidentiality with high accuracy.

#### 3. Preliminary

First, let us take a review at the basic principles of CS. CS theory suggests that -dimension original signal can be linearly projected into matrix by measurement matrix . If using some orthogonal basis or atomic set , such as Gabor basis and redundant dictionary [15], which is used in our frame, can be interpreted as a vector with only nonzero elements which means

We call -sparse and the solution to equation above sparse representation or sparse decomposition. To further explain (1), we have and (2) can be inferred by substituting , so we haveThen can be projected on measurement matric to obtain vector:where is the sensing matrix. Meanwhile, the measurement matrix requires satisfying NSP and RIP. In [18, 34], Gauss random matrix is proved to be appropriate, so it is used in our protocol to measure signal. Then the -dimension projection is transmitted to receiver for recovering original signal. As introduced in Section 2, in CS field, OMP algorithm is a classical recovery algorithm, which can obtain the sparsity coefficient of data. Therefore, our recovery algorithm is based on OMP algorithm. To further study it, OMP algorithm is described in Algorithm 1.