Advertisement

A Comprehensive Empirical Comparison of Parallel ListSieve and GaussSieve

  • Artur Mariano
  • Özgür Dagdelen
  • Christian Bischof
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8805)

Abstract

The security of lattice-based cryptosystems is determined by the performance of practical implementations of, among others, algorithms for the Shortest Vector Problem (SVP).

In this paper, we conduct a comprehensive, empirical comparison of two SVP-solvers: ListSieve and GaussSieve. We also propose a practical parallel implementation of ListSieve, which achieves super-linear speedups on multi-core CPUs, with efficiency levels as high as 183%. By comparing our implementation with a parallel implementation of GaussSieve, we show that ListSieve can, in fact, outperform GaussSieve for a large number of threads, thus answering a question that was still open to this day.

Keywords

sieving superlinear speedup shortest vector parallel 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC 1996, pp. 99–108. ACM (1996)Google Scholar
  2. 2.
    Ajtai, M.: The Shortest Vector Problem in L2 is NP-hard for Randomized Reductions (Extended Abstract). In: STOC 1998, pp. 10–19. ACM, NY (1998)Google Scholar
  3. 3.
    Fitzpatrick, R., et al.: Tuning GaussSieve for Speed. In: LATINCRYPT 2014, Florianópolis, Brazil (September 2014)Google Scholar
  4. 4.
    Dagdelen, Ö., Schneider, M.: Parallel enumeration of shortest lattice vectors. In: D’Ambra, P., Guarracino, M., Talia, D. (eds.) Euro-Par 2010, Part II. LNCS, vol. 6272, pp. 211–222. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Detrey, J., Hanrot, G., Pujol, X., Stehlé, D.: Accelerating Lattice Reduction with FPGAs. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 124–143. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Gama, N., Nguyen, P.Q., Regev, O.: Lattice enumeration using extreme pruning. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 257–278. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Klein, P.: Finding the closest lattice vector when it’s unusually close. In: SODA 2000, pp. 937–941 (2000)Google Scholar
  8. 8.
    Kuo, P.-C., Schneider, M., Dagdelen, Ö., Reichelt, J., Buchmann, J., Cheng, C.-M., Yang, B.-Y.: Extreme Enumeration on GPU and in Clouds. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 176–191. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    Lenstra, A., et al.: Factoring polynomials with rational coefficients. Mathematische Annalen 261(4), 515–534 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Mariano, A., et al.: Lock-free GaussSieve for Linear Speedups in Parallel High Performance SVP Calculation. In: SBAC-PAD 2014, Paris, France (2014)Google Scholar
  11. 11.
    Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. In: SODA 2010, PA, USA, pp. 1468–1480 (2010)Google Scholar
  12. 12.
    Milde, B., Schneider, M.: A parallel implementation of GaussSieve for the shortest vector problem in lattices. In: Malyshkin, V. (ed.) PaCT 2011. LNCS, vol. 6873, pp. 452–458. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Schneider, M.: Analysis of Gauss-Sieve for Solving the Shortest Vector Problem in Lattices. In: Katoh, N., Kumar, A. (eds.) WALCOM 2011. LNCS, vol. 6552, pp. 89–97. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Schnorr, C., Euchner, M.: Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Math. Programming 66(1-3), 181–199 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Artur Mariano
    • 1
  • Özgür Dagdelen
    • 2
  • Christian Bischof
    • 1
  1. 1.Institute for Scientific ComputingTechnische Universität DarmstadtGermany
  2. 2.Cryptography and Computer AlgebraTechnische Universität DarmstadtGermany

Personalised recommendations