Skip to main content
Springer Nature Link
Log in

Secure and efficient publicly verifiable outsourcing of matrix multiplication in online mode

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

With the emergence of cloud computing paradigm in many scientific applications, outsourcing of computation has attracted a great amount of attention from the research community. Outsourcing of heavy computations such as multiplication of two large matrices has raised some security concerns. Data and the result of computation should be protected not only from attackers, but also from the cloud servers. Moreover, data owner should be able to verify the correctness of computation with complexity less than the original computation. The previous schemes either have expensive offline phase or do not support public verifiability. In this paper, first we find a security vulnerability in the Zhang-Lei’s scheme for outsourcing of matrix multiplication where the cloud server can forge the result and pass the verification phase. Then, we present a secure and efficient publicly verifiable outsourcing of matrix multiplication scheme which achieves privacy protection of outsourced data and result, unforgeability of result, public verifiability and high efficiency. Our analyses show that compared with the related work, the proposed scheme is superior in terms of functionality, computation, communication and storage overhead, especially in verification computation overhead.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Atallah, M., et al.: Secure outsourcing of scientific computations. Adv. Comput. 54, 215–272 (2002)

    Article  Google Scholar 

  2. Atallah, M., Frikken, K.: Securely outsourcing linear algebra computations. In: Proceedings of the 5th ACM Symposium on Information, Computer and Communications Security, pp. 48–59 (2010)

  3. Benjamin, D., Atallah, M.: Private and cheating-free outsourcing of algebraic computations. In: PST’08. Sixth Annual Conference on Privacy, Security and Trust, 2008, pp. 240–245 (2008)

  4. Chen, Z., et al.: Secure and verifiable outsourcing of large-scale matrix inversion without precondition in cloud computing. In: 2018 IEEE International Conference on Communications (ICC), pp. 1–6. IEEE (2018)

  5. Chen, X., et al.: Efficient algorithms for secure outsourcing of bilinear pairings. Theor. Comput. Sci. 562, 112–121 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Daly, A., Marnane, W.: Efficient architectures for implementing Montgomery modular multiplication and RSA modular exponentiation on reconfigurable logic. In: Proceedings of the 2002 ACM/SIGDA Tenth International Symposium on Field-Programmable Gate Arrays, pp. 40–49. ACM (2002)

  7. De Caro, A., Iovino, V.: jPBC: Java pairing based cryptography. In: 2011 IEEE Symposium on Computers and Communications (ISCC), pp. 850–855. IEEE (2011)

  8. Elkhiyaoui, K. et al.: Efficient techniques for publicly verifiable delegation of computation. In: Proceedings of the 11th ACM on Asia Conference on Computer and Communications Security, pp. 119–128 (2016)

  9. Erfan, F., Mala. H.: Online privacy preserving outsourcing of large matrix multiplication. In: 7th International Conference on Computer and Knowledge Engineering (ICCKE), pp. 235–240, IEEE (2017)

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

  11. Gennaro, R., et al.: Non-interactive verifiable computing: Outsourcing computation to untrusted workers. In: Advances in Cryptology-CRYPTO, pp. 465–482. Springer, Berlin (2010)

  12. Gentry, C., et al.: Fully homomorphic encryption using ideal lattices. STOC 9, 169–178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hen, X., et al.: New algorithms for secure outsourcing of modular exponentiations. IEEE Trans. Parallel Distrib. Syst. 25(9), 2386–2396 (2013)

    Google Scholar 

  14. Hu, C. et al.: A secure and verifiable outsourcing scheme for matrix inverse computation. In: IEEE INFOCOM 2017-IEEE Conference on Computer Communications pp. 1–9. IEEE (2017)

  15. Jia, K., et al.: Enabling efficient and secure outsourcing of large matrix multiplications. In: Conference on IEEE Global Communication (GLOBECOM), pp. 1–6. San Diego, California (2015)

  16. Jiang, X., et al.: Secure outsourced matrix computation and application to neural networks. In Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 1209–1222. ACM (2018)

  17. Kong, S., et al.: Cloud outsourcing computing security protocol of matrix multiplication computation based on similarity transformation. Int. J. Wirel. Mob. Comput. 14(1), 90–96 (2018)

    Article  Google Scholar 

  18. Lei, X., et al.: Outsourcing large matrix inversion computation to a public cloud. IEEE Trans. Cloud Comput. 1(1), 1–1 (2013)

    Google Scholar 

  19. Lei, X. et al.: Achieving security, robust cheating resistance, and high-efficiency for outsourcing large matrix multiplication computation to a malicious cloud. In: information Science, vol. 280, pp. 205–217 (2014)

  20. 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 (2014)

    Article  Google Scholar 

  21. Li, H., et al.: Enabling efficient publicly verifiable outsourcing computation for matrix multiplication. In: International Telecommunication Networks and Applications Conference (ITNAC), pp. 44–50. IEEE (2015)

  22. Liu, M., et al.: Verifiable outsourcing computation for modular exponentiation from shareable functions. Clust. Comput. (2019). https://doi.org/10.1007/s10586-019-02930-4

    Article  Google Scholar 

  23. Ma, X., et al.: Outsourcing computation of modular exponentiations in cloud computing. Clust. Comput. 16(4), 787–796 (2013)

    Article  Google Scholar 

  24. Mohassel, P.: Efficient and Secure Delegation of Linear Algebra. IACR Cryptology ePrint Archive, Report 605 (2011)

  25. Speed benchmarks for some of cryptographic algorithms. https://www.cryptopp.com/benchmarks.html

  26. Xiao, X., et al.: Efficient and secure outsourcing of DFT, IDFT, and circular convolution. IEEE Access 7, 60126–60133 (2019)

    Article  Google Scholar 

  27. Yao, A.C.: Protocols for secure computations. In: SFCS’08. 23rd Annual Symposium on Foundations of Computer Science, 1982, pp. 160–164. IEEE (1982)

  28. Ye, J., et al.: Secure outsourcing of modular exponentiations in cloud and cluster computing. Clust. Comput. 19(2), 811–820 (2016)

    Article  Google Scholar 

  29. Zhang, L.F., Safavi-Naini, R.: ’Private outsourcing of polynomial evaluation and matrix multiplication using multilinear maps. International Conference on Cryptology and Network Security, pp. 329–348. Springer, Cham (2013)

    Chapter  Google Scholar 

  30. Zhang, S., et al.: Efficient secure outsourcing computation of matrix multiplication in cloud computing. In: Global Communications Conference (GLOBECOM), pp. 1–6. IEEE (2016)

  31. Zihao, Sh, et al.: Practical secure computation outsourcing: a survey. ACM Comput. Surv. 51(2), 31–71 (2019)

    Google Scholar 

  32. Zhang, Y., Blanton, M.: Efficient secure and verifiable outsourcing of matrix multiplications. In: International Conference on Information Security, pp. 158–178 (2014)

  33. Zhang, S., et al.: Verifiable outsourcing computation for matrix multiplication with improved efficiency and applicability. IEEE Internet Things J. 5(6), 5076–5088 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Technology Engineering, Faculty of Computer Engineering, University of Isfahan, Hezar Jerib St., Isfahan, 81746-73441, Iran

    Fatemeh Erfan & Hamid Mala

Authors
  1. Fatemeh Erfan
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Hamid Mala
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Hamid Mala.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Erfan, F., Mala, H. Secure and efficient publicly verifiable outsourcing of matrix multiplication in online mode. Cluster Comput 23, 2835–2845 (2020). https://doi.org/10.1007/s10586-020-03049-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-020-03049-7

Keywords