Skip to main content
SpringerLink
Log in

On-the-fly Homomorphic Batching/Unbatching

  • Conference paper
  • First Online:
Financial Cryptography and Data Security (FC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9604))

Included in the following conference series:

Abstract

We introduce a homomorphic batching technique that can be used to pack multiple ciphertext messages into one ciphertext for parallel processing. One is able to use the method to batch or unbatch messages homomorphically to further improve the flexibility of encrypted domain evaluations. In particular, we show various approaches to implement Number Theoretic Transform (NTT) homomorphically in Fast Fourier Transform (FFT) speed. Also, we present the limitations that we encounter in application of these methods. We implement homomorphic batching in various settings and present concrete performance figures. Finally, we present an implementation of a homomorphic NTT method in which we process each element in an independent ciphertext. The advantage of this method is we are able to batch independent homomorphic NTT evaluations and achieve better amortized time.

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

Access this chapter

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

Institutional subscriptions

References

  1. Bos, J.W., Lauter, K., Naehrig, M.: Private predictive analysis on encrypted medical data. Technical report MSR-TR-2013-81 (2013). http://research.microsoft.com/apps/pubs/default.aspx?id=200652

  2. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical gapSVP. IACR Cryptology ePrint Archive 2012/78 (2012)

    Google Scholar 

  3. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd Innovations inTheoretical Computer Science Conference, pp. 309–325. ACM (2012)

    Google Scholar 

  4. 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 

  5. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. SIAM J. Comput. 43(2), 831–871 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheon Jung, H., Miran, K., Kristin, L.: Secure DNA-sequence analysis on encrypted DNA nucleotides (2014). http://media.eurekalert.org/aaasnewsroom/MCM/-FIL_000000001439/EncryptedSW.pdf

  7. Dai, W., Doröz, Y., Sunar, B.: Accelerating NTRU based homomorphic encryption using GPUs. In: 2014 IEEE High Performance Extreme Computing Conference (HPEC), pp. 1–6 (2014)

    Google Scholar 

  8. Dai, W., Sunar, B.: cuHE: a homomorphic encryption accelerator library. In: Pasalic, E., et al. (eds.) BalkanCryptSec 2015. LNCS, vol. 9540, pp. 169–186. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29172-7_11

    Chapter  Google Scholar 

  9. 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 

  10. Doröz, Y., Hu, Y., Sunar, B.: Homomorphic AES evaluation using the modified LTV scheme. Des. Codes Cryptogr. 80, 1–26 (2015)

    MathSciNet  Google Scholar 

  11. Doröz, Y., Shahverdi, A., Eisenbarth, T., Sunar, B.: Toward practical homomorphic evaluation of block ciphers using prince. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014 Workshops. LNCS, vol. 8438, pp. 208–220. Springer, Heidelberg (2014)

    Google Scholar 

  12. Gentry, C.: A Fully Homomorphic Encryption Scheme. Ph.D. thesis, Stanford University (2009)

    Google Scholar 

  13. Gentry, C.: Fully homomorphic encryption using ideal lattices In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 169–178. ACM (2009)

    Google Scholar 

  14. Gentry, C., Halevi, S.: Fully homomorphic encryption without squashing using depth-3 arithmetic circuits. IACR Cryptology ePrint Archive 2011/279 (2011)

    Google Scholar 

  15. 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 

  16. Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. IACR Cryptology ePrint Archive 2012 (2012)

    Google Scholar 

  17. Dai, W., Sunar, B.: cuHE: a homomorphic encryption accelerator library. In: Pasalic, E., et al. (eds.) BalkanCryptSec 2015. LNCS, vol. 9540, pp. 169–186. Springer, Heidelberg (2016). doi:10.1007/978-3-319-29172-7_11

    Chapter  Google Scholar 

  18. Graepel, T., Lauter, K., Naehrig, M.: ML confidential: machine learning on encrypted data. In: Lee, M.-K., Kwon, D., Kwon, T. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 1–21. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Halevi, S., Shoup, V.: HElib, homomorphic encryption library. Internet Source (2012)

    Google Scholar 

  20. Lagendijk, R., Erkin, Z., Barni, M.: Encrypted signal processing for privacy protection: conveying the utility of homomorphic encryption and multiparty computation. IEEE Signal Process. Mag. 30(1), 82–105 (2013)

    Article  Google Scholar 

  21. Lauter, K., López-Alt, A., Naehrig, M.: Private computation on encrypted genomic data. In: Aranha, D.F., Menezes, A. (eds.) LATINCRYPT 2014. LNCS, vol. 8895, pp. 3–27. Springer, Heidelberg (2015)

    Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-flymultiparty computation on the cloud via multikey fully homomorphic encryption. In: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing STOC 2012, pp. 1219–1234. ACM (2012)

    Google Scholar 

  24. Naehrig, M., Lauter, K., Vaikuntanathan, V.: Can homomorphic encryption bepractical? In: Proceedings of the 3rd ACM Workshop on Cloud ComputingSecurity Workshop, CCSW 2011, pp. 113–124. ACM (2011)

    Google Scholar 

  25. Shoup, V.: NTL: A library for doing number theory (2001). http://www.shoup.net/ntl/

  26. Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Cryptogr. 71(1), 57–81 (2014)

    Article  MATH  Google Scholar 

  27. Stehlé, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 27–47. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Worcester Polytechnic Institute, Worcester, USA

    Yarkın Doröz, Gizem S. Çetin & Berk Sunar

Authors
  1. Yarkın Doröz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gizem S. Çetin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Berk Sunar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yarkın Doröz .

Editor information

Editors and Affiliations

  1. Concordia University, Montreal, Québec, Canada

    Jeremy Clark

  2. University College London, London, United Kingdom

    Sarah Meiklejohn

  3. Université du Luxembourg, Luxembourg, Luxembourg

    Peter Y.A. Ryan

  4. Rice University, Houston, Texas, USA

    Dan Wallach

  5. Leibniz Universität Hannover, Hannover, Germany

    Michael Brenner

  6. New Jersey Institute of Technology, Newark, New Jersey, USA

    Kurt Rohloff

Rights and permissions

Reprints and permissions

Copyright information

© 2016 International Financial Cryptography Association

About this paper

Cite this paper

Doröz, Y., Çetin, G.S., Sunar, B. (2016). On-the-fly Homomorphic Batching/Unbatching. In: Clark, J., Meiklejohn, S., Ryan, P., Wallach, D., Brenner, M., Rohloff, K. (eds) Financial Cryptography and Data Security. FC 2016. Lecture Notes in Computer Science(), vol 9604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53357-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53357-4_19

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53356-7

  • Online ISBN: 978-3-662-53357-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation