Privacy Preserving Hu’s Moments in Encrypted Domain

  • G. Preethi
  • Aswani Kumar Cherukuri
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 736)


Privacy preserving image processing is an active area of research that focuses on ensuring security of sensitive images stored in an untrusted environment like cloud. Hu introduced the concept of moment invariants that are widely employed in pattern recognition. The moment invariants are used to represent the global shape features of an image that are insensitive to basic geometric transformations like rotation, scaling and translation. In view of this fact, this paper addresses the problem of moment invariants computation in an encrypted domain. A secure Hu’s moments computation is proposed based on a fully homomorphic encryption scheme. This method may be employed for feature extraction without revealing sensitive image information in an untrusted environment.


Privacy Homomorphic encryption Feature extraction Geometric moment Central moment Normalized central moment Hu’s moments 


  1. 1.
    ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inf. Theor. 31, 469–472 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Proceedings of EUROCRYPT-99, pp. 223–238. Springer, Heidelberg (1999)Google Scholar
  3. 3.
    Gentry, C.: A fully homomorphic encryption scheme. Ph.D thesis. Stanford University, September 2009.
  4. 4.
    Van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Proceedings of Eurocrypt-10. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)Google Scholar
  5. 5.
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: FOCS 2011 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 97–106 (2011)Google Scholar
  6. 6.
    Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Advances in Cryptology CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)Google Scholar
  7. 7.
    Fan, J., Vercauteren, F.: Somewhat Practical Fully Homomorphic Encryption, Cryptology ePrint Archive, Report 2012/144 (2012).
  8. 8.
    Aslett, L.J.M., Esperan, P.M., Holmes, C.C.: A Review of Homomorphic Encryption and Software Tools for Encrypted Statistical Machine Learning, Technical Report. University of Oxford (2015)Google Scholar
  9. 9.
    Baby, T., Cherukuri, A.K.: On query execution over encrypted data. Secur. Commun. Netw. 8(2), 321–331 (2015)CrossRefGoogle Scholar
  10. 10.
    Hsu, C.Y., Lu, C.S., Pei, S.C.: Image feature extraction in encrypted domain with privacy-preserving SIFT. IEEE Trans. Image Process. 21, 4593–4607 (2012). MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Bai, Y., Zhuo, L., Cheng, B. and Peng, Y. F.: Surf feature extraction in encrypted domain. In: IEEE International Conference on Multimedia and Expo (2014).
  12. 12.
    Hu, M.: Visual pattern recognition by moment invariants. IRE Trans. Inf. Theor. IT–08, 179–187 (1962)zbMATHGoogle Scholar
  13. 13.
    Huang, Z., Leng, J.: Analysis of Hu’s moment invariants on image scaling and rotation. In: 2nd International Conference on Computer Engineering and Technology, pp. 476–480 (2010).
  14. 14.
    Urooj, S., Singh, S.P.: Geometric invariant feature extraction of medical images using Hu’s invariants. In: 3rd International Conference on Computing for Sustainable Global Development (INDIACom), New Delhi, pp. 1560–1562 (2016)Google Scholar
  15. 15.
    Isnanto, R.R., Zahra, A.A., Julietta, P.: Pattern recognition on herbs leaves using region-based invariants feature extraction. In: 3rd International Conference on Information Technology, Computer, and Electrical Engineering (ICITACEE), Semarang, pp. 455–459 (2016).
  16. 16.
    Zhang, Y.: Pathological brain detection based on wavelet entropy and Hu moment invariants. Bio-Med. Mater. Eng. 26, 1283–1290 (2015)CrossRefGoogle Scholar
  17. 17.
    Xu, D., Li, H.: Geometric moment invariants. Pattern Recognit. 41(1), 240–249 (2008)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information Technology and EngineeringVIT UniversityVelloreIndia

Personalised recommendations