Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Data Privacy Management

International Workshop on Autonomous and Spontaneous Security

DPM 2013, SETOP 2013: Data Privacy Management and Autonomous Spontaneous Security pp 34–50Cite as

Practical Packing Method in Somewhat Homomorphic Encryption

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8247))

Abstract

Somewhat homomorphic encryption is public key encryption supporting a limited number of both additions and multiplications on encrypted data, which is useful for performing fundamental computations with protecting the data confidentiality. In this paper, we focus on the scheme proposed by Lauter, Naehrig and Vaikuntanathan (ACM CCSW 2011), and present two types of packed ciphertexts based on their packing technique. Combinations of two types of our packing method give practical size and performance for wider computations such as statistical analysis and distances. To demonstrate its efficiency, we implemented the scheme with our packing method for secure Hamming distance, which is often used in privacy-preserving biometrics. For secure Hamming distance between two binary vekoshiba@mail.saitama-u.ac.jpctors of 2048-bit, it takes 5.31 ms on an Intel Xeon X3480 at 3.07 GHz. This gives the best performance in the state-of-the-art work using homomorphic encryption.

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

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. Belguechi, R., Alimi, V., Cherrier, E., Lacharme, P., Rosenberger, C.: An overview on privacy preserving biometrics. http://cdn.intechopen.com/pdfs/17038/InTech-An_overview_on_privacy_preserving_biometrics.pdf

  2. Blanton, M., Gasti, P.: Secure and efficient protocols for iris and fingerprint identification. In: Atluri, V., Diaz, C. (eds.) ESORICS 2011. LNCS, vol. 6879, pp. 190–209. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 325–341. Springer, Heidelberg (2005)

    Google Scholar 

  4. Boneh, D., Gentry, C., Halevi, S., Wang, F., Wu, D.J.: Private database queries using somewhat homomorphic encryption. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 102–118. Springer, Heidelberg (2013)

    Google Scholar 

  5. Brakerski, Z., Gentry, C., Halevi, S.: Packed ciphertexts in LWE-based homomorphic encryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 1–13. Springer, Heidelberg (2013)

    Google Scholar 

  6. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Innovations in Theoretical Computer Science-ITCS 2012, pp. 309–325. ACM (2012)

    Google Scholar 

  7. Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Foundations of Computer Science-FOCS 2011, pp. 97–106. IEEE (2011)

    Google Scholar 

  9. Chen, Y., Nguyen, P.Q.: BKZ 2.0: better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Cloud Security Alliance (CSA), Security guidance for critical areas of focus in cloud computing. https://cloudsecurityalliance.org/csaguide.pdf, December 2009

  11. Coron, J.-S., Mandal, A., Naccache, D., Tibouchi, M.: Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487–504. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Cramer, R., Gennaro, R., Schoenmakers, B.: A secure and optimally efficient multi-authority election scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)

    Google Scholar 

  13. Damgård, I., Geisler, M., Krøigård, M.: Homomorphic encryption and secure comparison. J. Appl. Crypt. 1(1), 22–31 (2008)

    MATH  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Symposium on Theory of Computing-STOC 2009, pp. 169–178. ACM (2009)

    Google Scholar 

  16. Gentry, C., Halevi, S.: Implementing gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850–867. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Goldwasser, S., Micali, S.: Probabilistic encryption and how to play mental poker keeping secrete all partial information. In: Symposium on Theory of Computing-STOC 1982, pp. 365–377. ACM (1982)

    Google Scholar 

  19. Hattori, M., Matsuda, N., Ito, T., Takashima, K., Yoneda, T.: Provably-secure cancelable biometrics using 2-DNF evaluation. J. Inf. Process. 20(2), 496–507 (2012)

    Google Scholar 

  20. Jain, A.K., Nandakumar, K., Nagar, A.: Biometric template security (review article). EURASIP J. Adv. Sig. Process 2008, 1–17 (2008)

    Article  Google Scholar 

  21. Jarrous, A., Pinkas, B.: Secure hamming distance based computation and its applications. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 107–124. Springer, Heidelberg (2009)

    Google Scholar 

  22. Lauter, K., Naehrig, M., Vaikuntanathan, V.: Can homomorphic encryption be practical?.  In: ACM Workshop on Cloud Computing Security Workshop-CCSW 2011, pp. 113–124. ACM (2011)

    Google Scholar 

  23. Lindner, R., Peikert, C.: Better key sizes (and Attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319–339. Springer, Heidelberg (2011)

    Google Scholar 

  24. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  25. Osadchy, M., Pinkas, B., Jarrous, A., Moskovich, B.: SCiFI - a system for secure face recognition. In: IEEE Security and Privacy, pp. 239–254. IEEE Computer Society (2010)

    Google Scholar 

  26. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)

    Google Scholar 

  27. Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  28. Schoenmakers, B., Tuyls, P.: Efficient binary conversion for paillier encrypted values. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 522–537. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  29. Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes. Cryptogr. 71, 57–81 (2014)

    Article  MATH  Google Scholar 

  30. U.S. Department of Homeland Security, Privacy impact assessment for the biometric storage system. http://www.dhs.gov/xlibrary/assets/privacy/privacy_pia_cis_bss.pdf, 28 March, 2007

  31. Yasuda, M., Shimoyama, T., Kogure, J., Yokoyama, K., Koshiba, T.: Packed homomorphic encryption based on ideal lattices and its application to biometrics. In: Cuzzocrea, A., Kittl, C., Simos, D.E., Weippl, E., Xu, L. (eds.) CD-ARES Workshops 2013. LNCS, vol. 8128, pp. 55–74. Springer, Heidelberg (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fujitsu Laboratories Ltd., Kamikodanaka 4-chome, Nakahara-ku, Kawasaki, 211-8588, Japan

    Masaya Yasuda, Takeshi Shimoyama & Jun Kogure

  2. Department of Mathematics, Rikkyo University, Nishi-Ikebukuro, Tokyo, 171-8501, Japan

    Kazuhiro Yokoyama

  3. Division of Mathematics, Electronics and Informatics, Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama, 338-8570, Japan

    Takeshi Koshiba

Authors
  1. Masaya Yasuda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takeshi Shimoyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jun Kogure
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kazuhiro Yokoyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Takeshi Koshiba
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masaya Yasuda .

Editor information

Editors and Affiliations

  1. TELECOM SudParis, Evry, France

    Joaquin Garcia-Alfaro

  2. National Technical University of Athens, Athens, Greece

    Georgios Lioudakis

  3. TELECOM Bretagne, Cesson Sévigné, France

    Nora Cuppens-Boulahia

  4. University College Cork, Cork, Ireland

    Simon Foley

  5. IDA Ovens, EMC Information Systems International, Cork, Ireland

    William M. Fitzgerald

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yasuda, M., Shimoyama, T., Kogure, J., Yokoyama, K., Koshiba, T. (2014). Practical Packing Method in Somewhat Homomorphic Encryption. In: Garcia-Alfaro, J., Lioudakis, G., Cuppens-Boulahia, N., Foley, S., Fitzgerald, W. (eds) Data Privacy Management and Autonomous Spontaneous Security. DPM SETOP 2013 2013. Lecture Notes in Computer Science(), vol 8247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54568-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54568-9_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54567-2

  • Online ISBN: 978-3-642-54568-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation