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.
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Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC 1996, pp. 99–108. ACM (1996)
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)
Fitzpatrick, R., et al.: Tuning GaussSieve for Speed. In: LATINCRYPT 2014, Florianópolis, Brazil (September 2014)
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)
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)
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)
Klein, P.: Finding the closest lattice vector when it’s unusually close. In: SODA 2000, pp. 937–941 (2000)
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)
Lenstra, A., et al.: Factoring polynomials with rational coefficients. Mathematische Annalen 261(4), 515–534 (1982)
Mariano, A., et al.: Lock-free GaussSieve for Linear Speedups in Parallel High Performance SVP Calculation. In: SBAC-PAD 2014, Paris, France (2014)
Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. In: SODA 2010, PA, USA, pp. 1468–1480 (2010)
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)
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)
Schnorr, C., Euchner, M.: Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Math. Programming 66(1-3), 181–199 (1994)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
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Mariano, A., Dagdelen, Ö., Bischof, C. (2014). A Comprehensive Empirical Comparison of Parallel ListSieve and GaussSieve. In: Lopes, L., et al. Euro-Par 2014: Parallel Processing Workshops. Euro-Par 2014. Lecture Notes in Computer Science, vol 8805. Springer, Cham. https://doi.org/10.1007/978-3-319-14325-5_5
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DOI: https://doi.org/10.1007/978-3-319-14325-5_5
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