SCIENCE CHINA Information Sciences, Volume 61, Issue 3: 032112(2018) https://doi.org/10.1007/s11432-017-9208-3

## Privacy-preserving large-scale systems of linear equations in outsourcing storage and computation

• AcceptedAug 16, 2017
• PublishedFeb 2, 2018
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### Abstract

Along with the prevalence of cloud computing, it can be realised to efficiently outsource costly storage or computations to cloud servers. Recently, secure outsourcing mechanism has received more and more attention. We focus on secure outsourcing storage and computation for large-scale systems of linear equations (LEs) in this paper. Firstly, we construct a new efficient matrix encryption scheme. Then we exploit this encryption scheme to develop a new algorithm which can implement outsourcing storage and computation for large-scale linear equations in the semi-honest setting. Compared with the previous work, the proposed algorithm requires lower storage overhead and is with competitive efficiency.

### Acknowledgment

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61371083, 61373154, 61632012, 61672239), Prioritized Development Projects through the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130073130004), and Shanghai High-Tech Field Project (Grant No. 16511101400).

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• Figure 1

Framework for our scheme.

• Figure 2

(Color online) Computation cost in the user side.

• Figure 3

(Color online) Storage cost in the user side.

• Table 1   Comparison with the existing schemes
 Scheme [11] Scheme [12] Scheme [13] Our scheme Storage cost O($n^2$) O($n^2$ ) O($n^2$ ) O(1) Computation of ProbGen ($2n^2+n)M+2.25k^2n^2M$ $(4n^2+4n)M$ $((2\lambda+1)n^2+\lambda~n)M$ $(2n^2+n)M+1.5knM$ Computation of solve $2.25k^2LnM$ $(22Ln-4L)M$ $\lambda~nM$ $1.5knM+nM$ Communication round $L$ $L$ 1 1
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