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Improving the Parallel Schnorr-Euchner LLL Algorithm

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Algorithms and Architectures for Parallel Processing (ICA3PP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7016))

Abstract

This paper introduces a number of modifications that allow for significant improvements of parallel LLL reduction. Experiments show that these modifications result in an increase of the speed-up by a factor of more than 1.35 for SVP challenge type lattice bases in comparing the new algorithm with the state-of-the-art parallel LLL algorithm.

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References

  1. Backes, W., Wetzel, S.: Heuristics on Lattice Basis Reduction in Practice. ACM Journal on Experimental Algorithms, 7 (2002)

    Google Scholar 

  2. Backes, W., Wetzel, S.: Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm. In: Sips, H., Epema, D., Lin, H.-X. (eds.) Euro-Par 2009. LNCS, vol. 5704, pp. 960–973. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Coster, M., Joux, A., LaMacchia, B., Odlyzko, A., Schnorr, C., Stern, J.: Improved Low-Density Subset Sum Algorithm. Journal of Computational Complexity 2, 111–128 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gentry, C.: Toward Basing Fully Homomorphic Encryption on Worst-Case Hardness. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 116–137. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Goldstein, A., Mayer, A.: On the Equidistribution of Hecke Points. Forum Mathematicum 15, 165–189 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Heckler, C., Thiele, L.: A Parallel Lattice Basis Reduction for Mesh-Connected Processor Arrays and Parallel Complexity. In: Proceedings of Symposium on Parallel and Distributed Processing (SPDP 1993), pp. 400–407. IEEE, Los Alamitos (1993)

    Chapter  Google Scholar 

  7. Joux, A.: A Fast Parallel Lattice Basis Reduction Algorithm. In: Proceedings of the Second Gauss Symposium, pp. 1–15. deGruyter, Berlag (1993)

    Google Scholar 

  8. Lenstra, A., Lenstra, H., Lovász, L.: Factoring Polynomials with Rational Coefficients. Math. Ann. 261, 515–534 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nguyen, P., Stehlé, D.: Floating-Point LLL Revisited. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 215–233. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Nguyen, P., Stehlé, D.: An LLL Algorithm with Quadratic Complexity. SIAM J. Comput. 39(3), 874–903 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Peikert, C.: Public-key Cryptosystems from the Worst-Case Shortest Vector Problem (Extended Abstract). In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC 2009), pp. 333–342. ACM, New York (2009)

    Chapter  Google Scholar 

  12. Regev, O.: Lattice-based Cryptography. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 131–141. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Schnorr, C., Euchner, M.: Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems. In: Budach, L. (ed.) FCT 1991. LNCS, vol. 529, pp. 68–85. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  14. SVP Challenge TU Darmstadt (July 2011), http://www.latticechallenge.org/svp-challenge/

  15. NTL - Homepage (July 2011), http://www.shoup.net/ntl/

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Author information

Authors and Affiliations

  1. Stevens Institute of Technology Castle Point on Hudson, Hoboken, NJ, 07030, USA

    Werner Backes & Susanne Wetzel

Authors
  1. Werner Backes
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  2. Susanne Wetzel
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Editor information

Editors and Affiliations

  1. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125,, Burwood, VIC, Australia

    Yang Xiang

  2. ICAR-CNR and University of Calabria, Via P. Bucci 41 C, 87036, Rende (CS), Italy

    Alfredo Cuzzocrea

  3. School of Information Technology, Deakin University, Geelong Waurn Ponds Campus, Pigdons Road, 3217, Geelong, VIC, Australia

    Michael Hobbs

  4. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Wanlei Zhou

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Backes, W., Wetzel, S. (2011). Improving the Parallel Schnorr-Euchner LLL Algorithm. In: Xiang, Y., Cuzzocrea, A., Hobbs, M., Zhou, W. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2011. Lecture Notes in Computer Science, vol 7016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24650-0_4

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  • DOI: https://doi.org/10.1007/978-3-642-24650-0_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24649-4

  • Online ISBN: 978-3-642-24650-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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