Efficient and Secure Outsourced Linear Regression

  • Haomiao YangEmail author
  • Weichao HeEmail author
  • Qixian ZhouEmail author
  • Hongwei Li
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11336)


The linear regression, as a classical machine learning algorithm, is often used to be a predictor. In the era of big data, the data owner can outsource their linear regression task and data to the cloud server, which has powerful calculation and storage resources. However, outsourcing data may break the privacy of the data. It is a well-known method to encrypt them prior to uploading to the cloud by using the homomorphic encryption (HE). Nevertheless, it is a difficult problem to apply the linear regression protocol in the encrypted domain. With this observation, we propose an efficient and secure linear regression protocol over outsourced encrypted data by using the vector HE, named ESLR, and in our protocol, we further present a privacy-preserving gradient descent method. Security analysis shows that our protocol can guarantee the confidentiality of data. And compared to the linear regression over plaintexts, our proposal can achieve almost the same accuracy and efficiency over ciphertexts.


Machine learning Homomorphic encryption Linear regression Gradient descent 



Our work is supported by of the National Key Research and Development Program of China (2017YFB0802003), the National Natural Science Foundation of China (U1633114) and the Sichuan Science and Technology Program (2018GZ0202).


  1. 1.
    Asuncion, A., Newman, D.: UCI machine learning repository (2007)Google Scholar
  2. 2.
    Ben-David, A., Nisan, N., Pinkas, B.: FairplayMP: a system for securemulti-party computation. In: Proceedings of the 15th ACM Conference on Computer and Communications Security, pp. 257–266. ACM (2008)Google Scholar
  3. 3.
    Dankar, F.K., El Emam, K.: The application of differential privacy to healthdata. In: Proceedings of the 2012 Joint EDBT/ICDT Workshops, pp. 158–166. ACM (2012)Google Scholar
  4. 4.
    Centers for Disease Control and Prevention, et al.: HIPAA privacy rule and public health. guidance from CDC and the us department of health and human services. MMWR Morb. Mortal. Wkly. Rep. 52(Suppl. 1), 1–17 (2003)Google Scholar
  5. 5.
    Du, W., Atallah, M.J.: Secure multi-party computation problems and their applications: a review and open problems. In: Proceedings of the 2001 Workshop on New Security Paradigms, pp. 13–22. ACM (2001)Google Scholar
  6. 6.
    Dwork, C.: Differential privacy: a survey of results. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008). Scholar
  7. 7.
    Dwork, C., Roth, A., et al.: The algorithmic foundations of differential privacy. Found. Trends® Theor. Comput. Sci. 9(3–4), 211–407 (2014)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Fletcher, R., Powell, M.J.: A rapidly convergent descent method for minimization. Comput. J. 6(2), 163–168 (1963)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Goldreich, O.: Secure multi-party computation. Manuscript. Preliminary version, pp. 86–97 (1998)Google Scholar
  10. 10.
    Halevi, S., Shoup, V.: Helib (2014). Retrieved from HELib:
  11. 11.
    Huang, Z.: Extensions to the k-means algorithm for clustering large data sets with categorical values. Data Min. Knowl. Discov. 2(3), 283–304 (1998)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lee, L.M., Gostin, L.O.: Ethical collection, storage, and use of public health data: a proposal for a national privacy protection. Jama 302(1), 82–84 (2009)CrossRefGoogle Scholar
  13. 13.
    McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: 48th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2007, pp. 94–103. IEEE (2007)Google Scholar
  14. 14.
    Regev, O.: On lattices, learning with errors, random linear codes, andcryptography. J. ACM 56(6), 1–40 (2009)CrossRefGoogle Scholar
  15. 15.
    van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010). Scholar
  16. 16.
    Wold, S., Ruhe, A., Wold, H., Dunn III, W.: The collinearity problem in linear regression. The partial least squares (PLS) approach to generalized inverses. SIAM J. Sci. Stat. Comput. 5(3), 735–743 (1984)CrossRefGoogle Scholar
  17. 17.
    Zhou, H., Wornell, G.: Efficient homomorphic encryption on integer vectors and its applications. In: Information Theory and Applications Workshop (ITA), 2014, pp. 1–9. IEEE (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Computer Science and Engineering and Center for Cyber SecurityUniversity of Electronic Science and Technology of ChinaChengduChina

Personalised recommendations