Skip to main content
SpringerLink
Log in

Ring-LWE: Applications to Cryptography and Their Efficient Realization

  • Conference paper
  • First Online:
Security, Privacy, and Applied Cryptography Engineering (SPACE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10076))

Abstract

The persistent progress of quantum computing with algorithms of Shor and Proos and Zalka has put our present RSA and ECC based public key cryptosystems at peril. There is a flurry of activity in cryptographic research community to replace classical cryptography schemes with their post-quantum counterparts. The learning with errors problem introduced by Oded Regev offers a way to design secure cryptography schemes in the post-quantum world. Later for efficiency LWE was adapted for ring polynomials known as Ring-LWE. In this paper we discuss some of these ring-LWE based schemes that have been designed. We have also drawn comparisons of different implementations of those schemes to illustrate their evolution from theoretical proposals to practically feasible schemes.

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. Bai, S., Galbraith, S.D.: An improved compression technique for signatures based on learning with errors. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 28–47. Springer, Heidelberg (2014). doi:10.1007/978-3-319-04852-9_2

    Chapter  Google Scholar 

  2. BBC News. NSA developing code-cracking quantum computer (2014). http://www.bbc.com/news/technology-25588605

  3. Boorghany, A., Sarmadi, S.B., Jalili, R.: On constrained implementation of lattice-based cryptographic primitives and schemes on smart cards. Cryptology ePrint Archive, Report 2014/514 (2014)

    Google Scholar 

  4. Bos, J., Costello, C., Ducas, L., Mironov, I., Naehrig, M., Nikolaenko, V., Raghunathan, A., Stebila, D.: Frodo: take off the ring! practical, quantum-secure key exchange from LWE. Cryptology ePrint Archive, Report 2016/659 (2016)

    Google Scholar 

  5. Bos, J.W., Lauter, K., Loftus, J., Naehrig, M.: Improved security for a ring-based fully homomorphic encryption scheme. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 45–64. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45239-0_4

    Chapter  Google Scholar 

  6. Boutin, C.: Nist kicks off effort to defend encrypted data from quantum computer threat (2016). http://www.nist.gov/itl/csd/nist-kicks-off-effort-to-defend-encrypted-data-from-quantum-computer-threat.cfm

  7. de Clercq, R., Roy, S.S., Vercauteren, F., Verbauwhede, I.: Efficient software implementation of ring-LWE encryption. In: Proceedings of the 2015 Design, Automation & Test in Europe Conference & Exhibition (DATE 2015), pp. 339–344 (2015)

    Google Scholar 

  8. Devroye, L.: Non-uniform Random Variate Generation. Springer, Heidelberg (1986)

    Book  MATH  Google Scholar 

  9. Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal gaussians. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 40–56. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40041-4_3

    Chapter  Google Scholar 

  10. Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive, Report 2012/144 (2012). http://eprint.iacr.org/

  11. Gentry, C., Szydlo, M.: Cryptanalysis of the revised NTRU signature scheme. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 299–320. Springer, Heidelberg (2002). doi:10.1007/3-540-46035-7_20

    Chapter  Google Scholar 

  12. Göttert, N., Feller, T., Schneider, M., Buchmann, J., Huss, S.: On the design of hardware building blocks for modern lattice-based encryption schemes. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 512–529. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33027-8_30

    Chapter  Google Scholar 

  13. Güneysu, T., Lyubashevsky, V., Pöppelmann, T.: Practical lattice-based cryptography: a signature scheme for embedded systems. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 530–547. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33027-8_31

    Chapter  Google Scholar 

  14. Güneysu, T., Oder, T., Pöppelmann, T., Schwabe, P.: Software speed records for lattice-based signatures. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 67–82. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38616-9_5

    Chapter  Google Scholar 

  15. Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: digital signatures using the NTRU lattice. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 122–140. Springer, Heidelberg (2003). doi:10.1007/3-540-36563-X_9

    Chapter  Google Scholar 

  16. Hoffstein, J., Pipher, J., Schanck, J.M., Silverman, J.H., Whyte, W.: Practical signatures from the partial fourier recovery problem. In: Boureanu, I., Owesarski, P., Vaudenay, S. (eds.) ACNS 2014. LNCS, vol. 8479, pp. 476–493. Springer, Heidelberg (2014). doi:10.1007/978-3-319-07536-5_28

    Google Scholar 

  17. Lepoint, T., Naehrig, M.: A comparison of the homomorphic encryption schemes FV and YASHE. In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT 2014. LNCS, vol. 8469, pp. 318–335. Springer, Heidelberg (2014). doi:10.1007/978-3-319-06734-6_20

    Chapter  Google Scholar 

  18. Liu, M., Nguyen, P.Q.: Solving BDD by enumeration: an update. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 293–309. Springer, Heidelberg (2013). doi:10.1007/978-3-642-36095-4_19

    Chapter  Google Scholar 

  19. Liu, Z., Seo, H., Sinha Roy, S., Großschädl, J., Kim, H., Verbauwhede, I.: Efficient ring-LWE encryption on 8-bit AVR processors. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 663–682. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48324-4_33

    Chapter  Google Scholar 

  20. Lyubashevsky, V.: Lattice signatures without trapdoors. Cryptology ePrint Archive, Report 2011/537 (2011). http://eprint.iacr.org/2011/537

  21. 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). doi:10.1007/978-3-642-13190-5_1

    Chapter  Google Scholar 

  22. Melchor, C.A., Boyen, X., Deneuville, J.-C., Gaborit, P.: Sealing the leak on classical NTRU signatures. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 1–21. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11659-4_1

    Google Scholar 

  23. Nguyen, P.Q., Regev, O.: Learning a parallelepiped: cryptanalysis of GGH and NTRU signatures. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 271–288. Springer, Heidelberg (2006). doi:10.1007/11761679_17

    Chapter  Google Scholar 

  24. Pöppelmann, T., Ducas, L., Güneysu, T.: Enhanced lattice-based signatures on reconfigurable hardware. Cryptology ePrint Archive, Report 2014/254(2014). http://eprint.iacr.org/

  25. Pöppelmann, T., Güneysu, T.: Towards practical lattice-based public-key encryption on reconfigurable hardware. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 68–85. Springer, Heidelberg (2014). doi:10.1007/978-3-662-43414-7_4

    Chapter  Google Scholar 

  26. Pöppelmann, T., Güneysu, T.: Area optimization of lightweight lattice-based encryption on reconfigurable hardware. In: Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS 2014) Preprint (2014)

    Google Scholar 

  27. Pöppelmann, T., Oder, T., Güneysu, T.: High-performance ideal lattice-based cryptography on 8-bit ATxmega microcontrollers. In: Lauter, K., Rodríguez-Henríquez, F. (eds.) LATINCRYPT 2015. LNCS, vol. 9230, pp. 346–365. Springer, Heidelberg (2015). doi:10.1007/978-3-319-22174-8_19

    Chapter  Google Scholar 

  28. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 84–93, New York, NY, USA. ACM (2005)

    Google Scholar 

  29. Roy, S.S., Vercauteren, F., Mentens, N., Chen, D.D., Verbauwhede, I.: Compact ring-LWE cryptoprocessor. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 371–391. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44709-3_21

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Research Council KU Leuven: C16/15/058. G.0876.14N, and by the European Commission through the Horizon 2020 research and innovation programme under contract No H2020-ICT-2014-644371 WITDOM, H2020-ICT-2014-644209 HEAT and the ERC grant.

Author information

Authors and Affiliations

  1. ESAT/COSIC and IMinds, KU Leuven, Kasteelpark Arenberg 10, 3001, Leuven-heverlee, Belgium

    Sujoy Sinha Roy, Angshuman Karmakar & Ingrid Verbauwhede

Authors
  1. Sujoy Sinha Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angshuman Karmakar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ingrid Verbauwhede
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ingrid Verbauwhede .

Editor information

Editors and Affiliations

  1. Universities of Paris 8 and Paris 13, LAGA, Paris, France

    Claude Carlet

  2. University of Waterloo, Waterloo, Ontario, Canada

    M. Anwar Hasan

  3. CRRao AIMSCS, Hyderabad, India

    Vishal Saraswat

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Roy, S.S., Karmakar, A., Verbauwhede, I. (2016). Ring-LWE: Applications to Cryptography and Their Efficient Realization. In: Carlet, C., Hasan, M., Saraswat, V. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2016. Lecture Notes in Computer Science(), vol 10076. Springer, Cham. https://doi.org/10.1007/978-3-319-49445-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-49445-6_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-49444-9

  • Online ISBN: 978-3-319-49445-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation