Skip to main content

Software Speed Records for Lattice-Based Signatures

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7932)

Abstract

Novel public-key cryptosystems beyond RSA and ECC are urgently required to ensure long-term security in the era of quantum computing. The most critical issue on the construction of such cryptosystems is to achieve security and practicability at the same time. Recently, lattice-based constructions were proposed that combine both properties, such as the lattice-based digital signature scheme presented at CHES 2012. In this work, we present a first highly-optimized SIMD-based software implementation of that signature scheme targeting Intel’s Sandy Bridge and Ivy Bridge microarchitectures. This software computes a signature in only 634988 cycles on average on an Intel Core i5-3210M (Ivy Bridge) processor. Signature verification takes only 45036 cycles. This performance is achieved with full protection against timing attacks.

Keywords

  • Post-quantum cryptography
  • lattice-based cryptography
  • cryptographic signatures
  • software implementation
  • AVX
  • SIMD

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-38616-9_5
  • Chapter length: 16 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-38616-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arora, S., Ge, R.: New Algorithms for Learning in Presence of Errors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 403–415. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  2. Bernstein, D.J.: The Salsa20 Family of Stream Ciphers. In: Robshaw, M., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 84–97. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  3. Bernstein, D.J., Duif, N., Lange, T., Schwabe, P., Yang, B.-Y.: High-speed high-security signatures. J. Cryptographic Engineering 2(2), 77–89 (2012)

    CrossRef  Google Scholar 

  4. Bernstein, D.J., Lange, T.: eBACS: ECRYPT benchmarking of cryptographic systems, http://bench.cr.yp.to (accessed January 25, 2013)

  5. Boyen, X.: Lattice Mixing and Vanishing Trapdoors: A Framework for Fully Secure Short Signatures and More. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  6. Buchmann, J., Dahmen, E., Hülsing, A.: XMSS - A Practical Forward Secure Signature Scheme Based on Minimal Security Assumptions. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 117–129. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  7. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai Trees, or How to Delegate a Lattice Basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  8. Chen, A.I.-T., Chen, M.-S., Chen, T.-R., Cheng, C.-M., Ding, J., Kuo, E.L.-H., Lee, F.Y.-S., Yang, B.-Y.: SSE Implementation of Multivariate PKCs on Modern x86 CPUs. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 33–48. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  9. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)

    Google Scholar 

  10. Fog, A.: The microarchitecture of Intel, AMD and VIA CPUs: An optimization guide for assembly programmers and compiler makers (2010), http://www.agner.org/optimize/microarchitecture.pdf (version February 29, 2012)

  11. Gligoroski, D., Ødegård, R.S., Jensen, R.E., Perret, L., Faugère, J.-C., Knapskog, S.J., Markovski, S.: MQQ-SIG – an ultra-fast and provably CMA resistant digital signature scheme. In: Chen, L., Yung, M., Zhu, L. (eds.) INTRUST 2011. LNCS, vol. 7222, pp. 184–203. Springer, Heidelberg (2012)

    CrossRef  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)

    CrossRef  Google Scholar 

  13. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Miller, G.L. (ed.) Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, May 22-24, pp. 212–219. ACM (1996)

    Google Scholar 

  14. 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)

    CrossRef  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)

    CrossRef  Google Scholar 

  16. Landais, G., Sendrier, N.: Implementing CFS. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 474–488. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  17. Lyubashevsky, V.: Lattice Signatures without Trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  18. 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)

    CrossRef  Google Scholar 

  19. Nguyên, 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)

    CrossRef  Google Scholar 

  20. Petzoldt, A., Thomae, E., Bulygin, S., Wolf, C.: Small Public Keys and Fast Verification for \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic Public Key Systems. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 475–490. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  21. John, M.: Pollard. The Fast Fourier Transform in a finite field. Mathematics of Computation 25(114), 365–374 (1971)

    MathSciNet  CrossRef  Google Scholar 

  22. Shoup, V.: NTL: A library for doing number theory, http://www.shoup.net/ntl/ (accessed March 18, 2013)

  23. Weiden, P., Hülsing, A., Cabarcas, D., Buchmann, J.: Instantiating treeless signature schemes. IACR Crptology ePrint archive report 2013/065 (2013), http://eprint.iacr.org/2013/065

  24. Winkler, F.: Polynomial Algorithms in Computer Algebra (Texts and Monographs in Symbolic Computation). Springer, 1st edn. (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Güneysu, T., Oder, T., Pöppelmann, T., Schwabe, P. (2013). Software Speed Records for Lattice-Based Signatures. In: Gaborit, P. (eds) Post-Quantum Cryptography. PQCrypto 2013. Lecture Notes in Computer Science, vol 7932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38616-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38616-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38615-2

  • Online ISBN: 978-3-642-38616-9

  • eBook Packages: Computer ScienceComputer Science (R0)