Cloud computing has become ubiquitous, offers an economical solution for convenient on-demand access to computing resources, which enable the resource-constrained clients to execute extensive computation. However, outsourcing of data and computation to the cloud server is a great cause of concern, such as confidentiality of input/output and verifiability of the result. This paper addresses the problem of designing outsourcing algorithm for linear regression analysis (LR), which is an important data analysis technique and widely applied across multiple domains. The outsourcing framework illustrated by the following scenario: a client is having a large dataset and needs to perform regression analysis, but unable to process due to lack of computing resources. Therefore, the client outsources the computation to the cloud server. In the proposed LR outsourcing algorithm, the client outsources LR problem to the cloud server without revealing to them either the input dataset and the output. The algorithm is a non-interactive solution to the client, it sends only input and receives output along with the proof of verification from the cloud server. The client in the proposed algorithm able to verify the correctness of result with an optimal probability. The analytical analysis shows that the algorithm is successfully meeting the challenges of correctness, security, verifiability, and efficiency. The experimental evaluation validates the proposed algorithm. The result analysis shows that the algorithm is highly efficient and endorses the practical usability of the algorithm.
ShirazM., GaniA., KhokharR.H. and BuyyaR., A review on distributed application processing frameworks in smart mobile devices for mobile cloud computing, IEEE Commun Surv Tutorials15(3) (2013), 1294–1313.
2.
XiaoZ. and XiaoY., Security and privacy in cloud computing, IEEE Commun Surv Tutorials15(2) (2013), 843–859.
3.
MarstonS., Bandyopadhyay and Ghalsasia, Cloud Computing - The Business Perspective, 44th Hawaii Int Conf Syst Sci, 2011, pp. 1–11.
4.
GreenbergA., HamiltonJ., MaltzD.A. and PatelP., The cost of a cloud: Research problems in data center networks, ACM SIGCOMM Comput Commun Rev39(1) (2009), 68–73.
5.
MurugesanS., Harnessing green IT: Principles and practices, IT Professional10(1) (2008), 24–33.
6.
AtallahM.J. and FrikkenK.B., Securely Outsourcing Linear Algebra Computations, Proc 5th ACM Symp Information, Comput Commun Secur - ASIACCS, 2010, pp. 48–59.
7.
BednarzA., BeanN. and RoughanM., Hiccups on the road to privacy-preserving linear programming, Proc 8th ACM Work Priv Electron Soc - WPES, 2009, pp. 117–120.
8.
LinK. and ChenM.S., Privacy-preserving outsourcing support vector machines with random transformation, Proc 16th ACM SIGKDD Int Conf Knowl Discov Data Min, 2010, pp. 363–372.
9.
ChenF., XiangT. and YangY., Privacy-preserving and verifiable protocols for scientific computation outsourcing to the cloud, J Parallel Distrib Comput74(3) (2014), 2141–2151.
10.
MohasselP., Efficient and secure delegation of linear algebra, IACR Cryptol ePrint Arch (2011), 1–33.
11.
ChenX., HuangX., LiJ., MaJ., LouW. and WongD.S., New algorithms for secure outsourcing of large-scale systems of linear equations, IEEE Trans on Infor Forens and Secur10(1) (2015), 69–78.
12.
BealeC.M., LennonJ.J., YearsleyJ.M., BrewerM.J. and ElstonD.A., Regression analysis of spatial data, Ecol Lett13(2) (2010), 246–264.
13.
HarrellF., Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis. Springer, 2015.
14.
De WolfE.D., MaddenL.V. and LippsP.E., Risk assessment models for wheat Fusarium head blight epidemics based on within-season weather data, Phytopathology93(4) (2003), 428–435.
15.
ChuC., KimS.K., LinY.A., YuY., BradskiG., NgA.Y. and OlukotunK., Map-reduce for machine learning on multicore, Adv Neural Inf Process Syst19 (2007), 281.
16.
GuestrinC., BodikP., ThibauxR., PaskinM. and MaddenS., Distributed regression: An efficient framework for modeling sensor network data, Third International Symposium on in Information Processing in Sensor Networks, 2004, pp. 1–10.
17.
ShankarV., ManneringF. and BarfieldW., Effect of roadway geometrics and environmental factors on rural freeway accident frequencies, Accid Anal Prev27(3) (1995), 371–389.
18.
SeshadriA., LukM., ShiE., PerrigA. and VanL., Doorn and P. Khosla, Pioneer: Verifying integrity and guaranteeing execution of code on legacy platforms, In Proceedings of ACM Symposium on Operating Systems Principles (SOSP), 2005, 173.
19.
BelenkiyM., ChaseM., ErwayC.C., JannottiJ., KüpçüA. and LysyanskayaA., Incentivizing outsourced computation, In Proceedings of the 3rd International Workshop on Economics of Networked Systems, 2008, pp. 85–90.
20.
MonroseF., WyckoffP. and RubinA., Distributed execution with remote audit, Ndss99 (1999), 3–5.
21.
YeeB., Using secure coprocessors, PhD Dissertation, CMU, 1994.
22.
SmithS.W. and WeingartS., Building a high-performance, programmable secure coprocessor, Comput Networks31(8) (1999), 831–860.
23.
BajikarS., Trusted platform module (tpm) based security on notebook pcs-white paper, Mob Platforms Gr Intel Corp (2002), 1–20.
24.
GoldwasserS., KalaiY.T. and RothblumG.N., Delegating computation: Interactive proofs for muggles, Stoc62(4) (2008), 113–122.
25.
GoldwasserS., MicaliS. and RackoffC., The knowledge complexity of interactive proof systems, SIAM J Comput18(1) (1989), 186–208.
26.
FortnowL. and LundC., Interactive proof systems and alternating time— space complexity, Theor Comput Sci113(1) (1993), 55–73.
WangC., RenK., WangJ. and WangQ., Harnessing the cloud for securely outsourcing large-scale systems of linear equations, IEEE Trans Parallel Distrib Syst24(6) (2013), 1172–1181.
29.
LaudP. and PankovaA., Transformation-based outsourcing of linear equation systems over real numbers, IACR Cryptology ePrint Archive (2015), 322.
30.
HongY., VaidyaJ. and LuH., Secure and efficient distributed linear programming, J Comput Secur20(5) (2012), 583–634.
31.
ChenF., XiangT., LeiX. and ChenJ., Highly efficient linear regression outsourcing to a Cloud, IEEE Trans Cloud Comput2(4) (2014), 499–508.
32.
WangC., RenK., WangJ. and UrsK.M., Harnessing the Cloud for Securely Solving Large-Scale Systems of Linear Equations, 31st Int Conf Distrib Comput Syst, 2011, pp. 549–558.
33.
LeiX., LiaoX., HuangT., LiH. and HuC., Outsourcing large matrix inversion computation to a public cloud, IEEE Trans Cloud Comput1(1) (2013), 78–87.
34.
ChenX., LiJ. and MaJ., New algorithms for secure outsourcing of modular exponentiations, IEEE Trans Parallel Distrib25(9) (2014), 2386–2396.
35.
LeiX., LiaoX., MemberS., HuangT. and LiH., Cloud Computing Service: The case of large matrix determinant computation, IEEE Trans. on Services Comput8(5) (2015), 688–700.
36.
HuX. and TangC., Secure outsourced computation of the characteristic polynomial and eigenvalues of matrix, J Cloud Comput4(1) (2015), 4–9.
37.
ZhouL. and LiC., Outsourcing eigen-decomposition and singular value decomposition of large matrix to a public cloud, in IEEE Access4 (2016), 869–879. doi: 10.1109/ACCESS.2016.2535103
ChungK.M., KalaiY. and VadhanS., Improved delegation of computation using fully homomorphic encryption, Lect Notes Comput Sci (including Subser Lect Notes Artif Intell Lect Notes Bioinformatics)6223 (2010), 483–501.
44.
LeiX., LiaoX., HuangT. and HeriniainaF., Achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud, Inf Sci (Ny)280 (2014), 205–217.
45.
WangC., RenK. and WangJ., Secure and Practical Outsourcing of Linear Programming in Cloud Computing, Proc IEEE INFOCOM, 2011, pp. 820–828.
46.
BlantonM., ZhangY. and FrikkenK.B., Secure and verifiable outsourcing of large-scale biometric computations, ACM Trans Inf Syst Secur16(3) (2016), 1–33.
47.
Troncoso-PastorizaJ.R., ComesanaP. and GonzálezF., Secure Direct and Iterative Protocols for Solving Systems of Linear Equations, In Proc of 1st International Workshop on Signal Processing in the EncryptEd Domain (SPEED), 2009, pp. 122–141.
48.
GoldreichW.A., MicaliO., GoldreichS.O., MicaliS. and WigdersonA., How To Play Any Mental Game, or A Completeness Theorem for Protocols with Honest Majority, Proceedings of 19th Annual ACM Symposium on Theory of Computing, 1987, pp. 218–229.
49.
DuW., ChenS. and HanY.S., Privacy-Preserving Multivariate Statistical Analysis: Linear Regression and Classification, Proc 4th SIAM Int Conf Data Min, 2004, pp. 222–233.
50.
KnuthD.E., The Art of Computer Programming: Sorting And Searching, 3, Pearson Education, 1998.
51.
AndersonM.J. and RobinsonJ., Permutation tests for linear models, Aust N Z J Stat43(1) (2001), 75–88.
52.
DreierJ. and KerschbaumF., Practical secure and efficient multiparty linear programming based on problem transformation, IACR Cryptology ePrint Archive, 2011, p. 108.
53.
LindellY. and PinkasB., Secure multiparty computation for privacy-preserving data mining, J Priv Confidentiality, Berkeley Electronic Press1(1) (2009), 59–98.
54.
López-AltA., TromerE. and VaikuntanathanV., On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption, Proc 44th Symp Theory Comput–STOC, 2012, pp. 1219–1234.
