2332-7790 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TBDATA.2017.2711040, IEEE Transactions on Big Data 1 Computation Outsourcing Meets Lossy Channel: Secure Sparse Robustness Decoding Service in Multi-Clouds Yushu Zhang, Jiantao Zhou, Member, IEEE, Yong Xiang, Senior Member, IEEE, Leo Yu Zhang, Fei Chen, Shaoning Pang, Senior Member, IEEE, and Xiaofeng Liao, Senior Member, IEEE Abstract—This paper addresses the problem of lossy outsourc- ing, i.e., clients outsource computation needs to the cloud side through lossy channels, which is very common in practice. We focus on the case that the clients transmit 2D sparse signals to the semi-trusted clouds over packet-loss networks, and the clouds provide sparse robustness decoding service (SRDS) for the users. In order to achieve high level of efficiency and security, we propose to jointly exploit parallel compressive sensing for robust signal encoding and employ multiple cloud servers for SRDS. Specifically, prior to encoding, a signal is encrypted by only altering the indices and amplitudes of its non-zero entries. The encrypted signal is sensed using a Gaussian measurement matrix and the generated compressive measurements are then sent to multi-clouds for SRDS, along with the occurrence of packet loss. Each column in compressive measurements can be regarded as a packet and each description consists of a certain number of packets. Each description together with a small portion of support set is distributed to a cloud. When receiving the request from a user, each cloud performs SRDS using the acquired description, where the reconstructed signal is still in encrypted form so that the signal privacy is well preserved. After receiving the reconstructed signal, the user accomplishes the decryption operation. Experimental results show that the en- cryption algorithm improves compressibility and reconstruction performance compared with the case of no encryption, and the proposed privacy-assured outsourcing of SRDS is highly robust and efficient. Index Terms—Parallel compressive sensing, sparse robustness decoding service, packet-loss, cloud computing. I. I NTRODUCTION This work was supported by the National Natural Science Foundation of China (Grant Nos. 61502399, 61402547, 61502314, 61672358, 61572089). Y. Zhang is with the Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronics and Information Engineering, Southwest University, Chongqing 400715, China, and also with the School of Information Technology, Deakin University, Victoria 3125, Australia (e-mail: yushuboshi@163.com). J. Zhou is with the Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau (e-mail: jtzhou@umac.mo). Y. Xiang is with the School of Information Technology, Deakin University, Victoria 3125, Australia (e-mail: yxiang@deakin.edu.au). L. Zhang is with the Department of Electronic Engineering, City University of Hong Kong, Hong Kong (e-mail: leocityu@gmail.com). F. Chen is with the College of Computer Science and Engineering, Shen- zhen University, Shenzhen 518060, China (e-mail: chenfeiorange@163.com) S. Pang is with the Department of Computing, Unitec Institute of Technolo- gy, Private Bag 92025, Auckland, New Zealand (e-mail: ppang@unitec.ac.nz). X. Liao is with the Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronics and Informa- tion Engineering, Southwest University, Chongqing 400715, China (e-mail: xfliao@swu.edu.cn). W ith the arrival of big data era, there has been dramatic increase of demand on fast data computation and stor- age. Clouds can be a promising platform for this thanks to their powerful computation and storage capabilities. However, the untrust nature of cloud environments makes privacy-assured outsourcing essential [1]–[5]. Computation outsourcing has been studied for many years and the computation tasks har- nessed by the resource-constrained clients can be off-loaded to powerful computation devices like cloud servers. The input and output privacy of outsourcing computation to the clouds needs to be pretected as these tasks are often sensitive and the clouds might not be honest to the clients. So far, many kinds of computation problems have been considered. Linear programming outsourcing mechanism was proposed in [6], [7] by developing efficient privacy-preserving transformation techniques. Large-scale systems of linear equa- tions computation outsourcing was designed in [8], [9] through an iterative method. Sparse matrix [10] and matrix addition [11] techniques were also employed for efficient outsourc- ing of large-scale systems of linear equations to reduce the computational complexity. Chen et al. [12] further improved two outsourcing protocols for linear equations and linear programming by utilizing some special linear transforms and reformulating the problem in the standard and natural form, respectively. Lei et al. applied random permutation operation to some large matrix calculation outsourcing projects such as matrix inversion [13], matrix multiplication [14] and matrix determinant [15]. In addition, some other computation out- sourcings have been proposed in terms of convex optimization [16], linear regression [17], etc. However, the existing methods on computation outsourcing do not consider the case of lossy channel between client and cloud, which is often encountered in practical applications. For example, due to channel fading effect, long burst errors can occur in the wireless channel between client and cloud or an intermediate blocking will lead to a temporarily declining physical link. On the other hand, for resource-constrained transmission, it is unrealistic to carry out re-transmission once partial data are lost. Meanwhile, the user can accept the lossy data sent by the clouds, e.g., the recovery of a certain degree of lossy image does not affect the visual effect of the recovered image. In the face of such lossy channel, a good solution is to perform robust transmission. In this paper, we consider the situation where a client needs to transmit 2D sparse signals to some semi-trusted cloud servers over lossy channels through packet-loss networks. The clouds provide storage and decoding service, called sparse ro- bustness decoding service (SRDS), for the user. For efficiency