Skip to main content

MD-\(\mathcal {VC}_{Matrix}\): An Efficient Scheme for Publicly Verifiable Computation of Outsourced Matrix Multiplication

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9955))

Abstract

Cloud service provider that is equipped with tremendous resources enables the terminals with constrained resources to perform outsourced query or computation on large scale data. Security challenges are always the research hotspots in the outsourced computation community. In this paper, we investigate the problem of publicly verifiable outsourced matrix multiplication. However, in the state-of-the-art scheme, a large number of computationally expensive operations are adopted to achieve the goal of public verification. Thus, the state-of-the-art scheme works inefficiently actually due to the fact that most of the time is spent on the verification-related computing. To lower the verification-related time cost, we propose an efficient scheme for public verification of outsourced matrix multiplication. The two-dimensional matrix is transformed into a one-dimensional vector, which retains the computing ability and is used as the substitute for subsequent verification-related work. The security analysis demonstrates the security of the proposed outsourcing scheme, and the performance analysis shows the running efficiency of the scheme.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Fiore, D., Gennaro, R.: Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: 19th ACM Conference on Computer and Communications Security, pp. 501–512. ACM, New York (2012)

    Google Scholar 

  2. Li, H., Zhang, S., Luan, T.H., Ren, H., Dai, Y., Zhou, L.: Enabling efficient publicly verifiable outsourcing computation for matrix multiplication. In: International Telecommunication Networks and Applications Conference (ITNAC), pp. 44–50. IEEE Press, New York (2015)

    Google Scholar 

  3. Jia, K., Li, H., Liu, D., Yu, S.: Enabling efficient and secure outsourcing of large matrix multiplications. In: IEEE Global Communications Conference (GLOBECOM), pp. 1–6. IEEE Press, New York (2015)

    Google Scholar 

  4. Gennaro, R., Gentry, C., Parno, B.: Non-interactive verifiable computing: outsourcing computation to untrusted workers. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 465–482. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14623-7_25

    Chapter  Google Scholar 

  5. Hu, X., Pei, D., Tang, C., Wong, D.: Verifiable and secure outsourcing of matrix calculation and its application. Scientia inica (Informationis) 43(7), 842–852 (2013)

    Google Scholar 

  6. Chen, X., Huang, X., Li, J., Ma, J., Lou, W., Wong, D.: New algorithms for secure outsourcing of large-scale systems of linear equations. IEEE Trans. Inf. Forensics Secur. 10(1), 69–78 (2015)

    Article  Google Scholar 

  7. Caro, D., Iovino, V.: jPBC: java pairing based cryptography. In: IEEE Symposium on Computers and Communications, pp. 850–855. IEEE Press, New York (2011)

    Google Scholar 

  8. Atallah, M., Frikken, K.: Securely outsourcing linear algebra computations. In: 5th ACM Symposium on Information, Computer and Communications Security, pp. 48–59. ACM Press, New York (2010)

    Google Scholar 

  9. Benjamin, D., Atallah, M.J.: Private and cheating-free outsourcing of algebraic computations. In: Sixth Annual Conference on Privacy, Security and Trust (PST 2008), pp. 240–245. IEEE Press, New York (2008)

    Google Scholar 

  10. Mohassel, P.: Efficient and secure delegation of linear algebra. Technical report, Cryptology ePrint Archive, Report 2011/605 (2011)

    Google Scholar 

  11. Lei, X., Liao, X., Huang, T., Li, H., Hu, C.: Outsourcing large matrix inversion computation to a public cloud. IEEE Trans. Cloud Comput. 1(1), 1 (2013). http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6613485&tag=1

  12. Lei, X., Liao, X., Huang, T., Heriniaina, F.: Achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud. Inf. Sci. 280, 205–217 (2014)

    Article  Google Scholar 

  13. Lei, X., Liao, X., Huang, T., Li, H.: Cloud computing service: the case of large matrix determinant computation. IEEE Trans. Serv. Comput. 8(5), 688–700 (2015)

    Article  Google Scholar 

  14. Wang, C., Ren, K., Wang, J., Wang, Q.: Harnessing the cloud for securely outsourcing large-scale systems of linear equations. IEEE Trans. Parallel Distrib. Syst. 24(6), 1172–1181 (2013)

    Article  Google Scholar 

  15. Chen, F., Xiang, T., Yang, Y.: Privacy-preserving and verifiable protocols for scientific computation outsourcing to the cloud. J. Parallel Distrib. Comput. 74(3), 2141–2151 (2014)

    Article  MATH  Google Scholar 

  16. Nie, H., Ma, H., Wang, J., Chen, X.: Verifiable algorithm for secure outsourcing of systems of linear equations in the case of no solution. In: Ninth International Conference on Broadband and Wireless Computing, Communication and Applications, pp. 572–577. IEEE Press, New York (2014)

    Google Scholar 

  17. Salinas, S., Luo, C., Chen, X., Li, P.: Efficient secure outsourcing of large-scale linear systems of equations. In: IEEE INFOCOM 2015, pp. 1035–1043. IEEE Press, New York (2015)

    Google Scholar 

  18. Murugesan, M., Jiang, W., Clifton, C., Si, L., Vaidya, J.: Efficient privacy-preserving similar document detection. VLDB J. 19(4), 457–475 (2010)

    Article  Google Scholar 

  19. Sheng, G., Wen, T., Guo, Q., Yin, Y.: Secure scalar product computation of vectors in cloud computing. J. Northeast. Univ. 34(6), 786–791 (2013)

    MATH  Google Scholar 

  20. Backes, M., Fiore, D., Reischuk, R.M.: Verifiable delegation of computation on outsourced data. In: 2013 ACM SIGSAC Conference on Computer & Communications Security, pp. 863–874. ACM, New York (2013)

    Google Scholar 

  21. Wang, C., Ren, K., Wang, J.: Secure practical outsourcing of linear programming in cloud computing. In: IEEE INFOCOM 2011, pp. 820–828. IEEE Press, New York (2011)

    Google Scholar 

  22. Xiang, C., Tang, C., Cai, Y., Xu, Q.: Privacy-preserving face recognition with outsourced computation. Soft Comput. 20(9), 3735–3744 (2016)

    Article  Google Scholar 

  23. Liu, A., Zhengy, K., Liz, L., Liu, G., Zhao, L., Zhou, X.: Efficient secure similarity computation on encrypted trajectory data. In: IEEE 31st International Conference on Data Engineering, pp. 66–77. IEEE Press, New York (2015)

    Google Scholar 

  24. Jung, T., Mao, X., Li, X.Y., Tang, S.J., Gong, W., Zhang, L.: Privacy-preserving data aggregation without secure channel: multivariate polynomial evaluation. In: IEEE INFOCOM 2013, pp. 2634–2642. IEEE Press, New York (2013)

    Google Scholar 

Download references

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under Grant No. 11271226,61272182, the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No. 20134410110003, High Level Talents Project of Guangdong, Guangdong Provincial Natural Science Foundation under Grant No. S2012010009950, the Project of Department of Education of Guangdong Province under Grant No. 2013KJ-CX0146, the Natural Science Foundation of Bureau of Education of Guangzhou under Grant No. 2012A004, the basic research major projects of Department of Education of Guangdong Province under Grant No. 2004KZDXM044, and the Guangzhou Zhujiang Science and Technology Future Fellow Fund under Grant No. 2012J2200094.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gang Sheng .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Sheng, G., Tang, C., Gao, W., Yin, Y. (2016). MD-\(\mathcal {VC}_{Matrix}\): An Efficient Scheme for Publicly Verifiable Computation of Outsourced Matrix Multiplication. In: Chen, J., Piuri, V., Su, C., Yung, M. (eds) Network and System Security. NSS 2016. Lecture Notes in Computer Science(), vol 9955. Springer, Cham. https://doi.org/10.1007/978-3-319-46298-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46298-1_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46297-4

  • Online ISBN: 978-3-319-46298-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics