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

  • Dongmei Li
  • Xiaolei Dong
  • Zhenfu Cao
  • Haijiang Wang
Research Paper
  • 40 Downloads

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.

Keywords

cloud computing privacy-preserving linear equations encryption security 

Notes

Acknowledgements

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).

References

  1. 1.
    Cloud Security Alliance. Security guidance for critical areas of focus in cloud computing. 2009. http://www.cloudsecurityalliance.orgGoogle Scholar
  2. 2.
    Wang C, Ren K, Wang J. Secure optimization computation outsourcing in cloud computing: a case study of linear programming. IEEE Comput Soc, 2016, 65: 216–229MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Loftus J, Smart N P. Secure outsourced computation. In: Proceedings of International Conference on Cryptology in Africa, Dakar, 2011. 1–20Google Scholar
  4. 4.
    Zhou J, Cao Z F, Dong X L, et al. EVOC: more efficient verifiable outsourced computation from any one-way trapdoor function. In: Proceedings of IEEE International Conference on Communications, London, 2015. 7444–7449Google Scholar
  5. 5.
    Pearson S, Benameur A. Privacy, security and trust issues arising from cloud computing. In: Proceeding of IEEE Second International Conference on Cloud Computing Technology and Science, Indianapolis, 2010. 693–702Google Scholar
  6. 6.
    Zissis D, Lekkas D. Addressing cloud computing security issues. Future Gener Comput Syst, 2012, 28: 583–592CrossRefGoogle Scholar
  7. 7.
    Sen J. Security and privacy issues in cloud computing. Comput Sci, 2013, 7: 238–252Google Scholar
  8. 8.
    Cao Z F. New trends of information security — how to change people’s life style? Sci China Inf Sci, 2016, 59: 050106CrossRefGoogle Scholar
  9. 9.
    Benzi M. Preconditioning techniques for large linear systems: a survey. J Comput Phys, 2002, 182: 418–477MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Edelman A. Large dense numerical linear algebra in 1993: the parallel computing influence. Int J High Perform Comput Appl, 1993, 7: 113–128Google Scholar
  11. 11.
    Wang C, Ren K, Wang J, et al. Harnessing the cloud for securely outsourcing large-scale systems of linear equations. IEEE Trans Parall Distrib Syst, 2013, 24: 1172–1181CrossRefGoogle Scholar
  12. 12.
    Salinas S, Luo C Q, Chen X H, et al. Efficient secure outsourcing of large-scale linear systems of equations. In: Proceedings of IEEE Conference on Computer Communications, Hong Kong, 2015. 281–292Google Scholar
  13. 13.
    Chen X F, Huang X Y, Li J, et al. New algorithms for secure outsourcing of large-scale systems of linear equations. IEEE Trans Inf Foren Secur, 2015, 10: 69–78CrossRefGoogle Scholar
  14. 14.
    Gennaro R, Gentry C, Parno B. Non-interactive verifiable computing: outsourcing computation to untrusted workers. Lect Notes Comput Sci, 2010, 6223: 465–482MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Yao A C. Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science. Washington: IEEE, 1982. 160–164Google Scholar
  16. 16.
    Gentry C. Fully homomorphic encryption using ideal lattices. In: Proceedings of ACM Symposium on Theory of Computing, Bethesda, 2009. 169–178Google Scholar
  17. 17.
    Atallah M J, Frikken K B. Securely outsourcing linear algebra computations. In: Proceedings of ACM Symposium on Information, Computer and Communications Security, Beijing, 2010. 48–59Google Scholar
  18. 18.
    Nassar M, Erradi A, Malluhi Q M. Practical and secure outsourcing of matrix computations to the cloud. In: Proceedings of the 33rd International Conference on Distributed Computing Systems, Pennsylvania, 2013. 70–75Google Scholar
  19. 19.
    Li D M, Dong X L, Cao Z F. Secure and privacy-preserving pattern matching in outsourced computing. Secur Commun Netw, 2016, 9: 3444–3451CrossRefGoogle Scholar
  20. 20.
    Lei X Y, Liao X F, Huang T W, et al. Outsourcing large matrix inversion computation to a public cloud. IEEE Trans Cloud Comput, 2013, 1: 78–87Google Scholar
  21. 21.
    Paillier P. Public-key cryptosystems based on composite degree residuosity classes. In: Proceedings of International Conference on Theory and Application of Cryptographic Techniques, Prague, 1999. 223–238Google Scholar
  22. 22.
    Bellare M. Random oracles are practical: a paradigm for designing efficient protocols. In: Proceedings of ACM Conference on Computer and Communications Security, Virginia, 1993. 62–73Google Scholar
  23. 23.
    Goldwasser S, Micali S, Rivest R L. A digital signature scheme secure against adaptive chosen-message attacks. Soc Ind Appl Math, 1988, 17: 281–308MathSciNetMATHGoogle Scholar
  24. 24.
    Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Commun ACM, 1978, 21: 120–126MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Williams H. A modification of the RSA public-key encryption procedure. IEEE Trans Inf Theory, 1980, 26: 726–729MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Blum L. A simple unpredictable pseudo-random number generator. SIAM J Comput, 1986, 15: 364–383MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Hohenberger S, Lysyanskaya A. How to securely outsource cryptographic computations. Theory Cryptogr, 2005, 3378: 264–282MathSciNetMATHGoogle Scholar
  28. 28.
    Liu X M, Deng R H, Ding W X, et al. Privacy-preserving outsourced calculation on floating point numbers. IEEE Trans Inf Foren Secur, 2017, 11: 2513–2527CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Dongmei Li
    • 1
  • Xiaolei Dong
    • 2
  • Zhenfu Cao
    • 2
  • Haijiang Wang
    • 1
  1. 1.Department of Computer Science and EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Trustworthy ComputingEast China Normal UniversityShanghaiChina

Personalised recommendations