nach oben

Erschienen in:

2015 | OriginalPaper | Buchkapitel

Nearest Planes in Practice

verfasst von : Christian Bischof, Johannes Buchmann, Özgür Dagdelen, Robert Fitzpatrick, Florian Göpfert, Artur Mariano

Erschienen in: Cryptography and Information Security in the Balkans

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The learning with errors (LWE) problem is one of the most attractive problems that lattice-based cryptosystems base their security on. Thus, assessing the hardness in theory and practice is of prime importance. Series of work investigated the hardness of LWE from a theoretical point of view. However, it is quite common that in practice one can solve lattice problems much faster than theoretical estimates predict.

The most promising approach to solve LWE is the decoding method, which converts an LWE instance to an instance of the closest vector problem (CVP). The latter instance can then be solved by a CVP solver. In this work, we investigate how the nearest planes algorithm proposed by Lindner and Peikert (CT-RSA 2011) performs in practice. This algorithm improves an algorithm by Babai, and is a state-of-the-art CVP solver.

We present the first parallel version of the nearest planes algorithm. Our implementation achieves speedup factors of more than 11x on a machine with four CPU-chips totaling 16 cores. In fact, to the best of our knowledge, there is not even a single parallel implementation publicly available of any LWE solver so far. We also compare our results with heuristics on the running time of a single nearest planes run claimed by Lindner and Peikert and subsequently used by others for runtime estimations.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel On the Anonymization of Cocks IBE Scheme

Nächstes Kapitel Timed-Release Secret Sharing Schemes with Information Theoretic Security

http://www.top500.org/.

Albrecht, M.R., Fitzpatrick, R., Göpfert, F.: On the efficacy of solving LWE by reduction to unique-SVP. In: Lee, H.-S., Han, D.-G. (eds.) ICISC 2013. LNCS, vol. 8565, pp. 293–310. Springer, Heidelberg (2014)

Albrecht, M.R., Cid, C., Faugère, J.C., Fitzpatrick, R., Perret, L.: On the complexity of the BKW algorithm on LWE. Des. Codes Crypt. 74(2), 325–354 (2013)CrossRef

Albrecht, M.R., Faugère, J.-C., Fitzpatrick, R., Perret, L.: Lazy modulus switching for the BKW algorithm on LWE. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 429–445. Springer, Heidelberg (2014) CrossRef

Babai, L.: On Lovász’ lattice reduction and the nearest lattice point problem. Combinatorica 6(1), 1–13 (1986)MathSciNetCrossRef

Bai, S., Galbraith, S.D.: Lattice decoding attacks on binary LWE. Cryptology ePrint Archive, Report 2013/839 (2013). http://eprint.iacr.org/

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) CrossRef

Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506–519 (2003)MathSciNetCrossRef

Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309–325 (2012)

Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from Ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011) CrossRef

10.

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) CrossRef

11.

Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal gaussians. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 40–56. Springer, Heidelberg (2013) CrossRef

12.

Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford, CA, USA (2009)

13.

Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Kaliski Jr, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997) CrossRef

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

15.

Han, D., Kim, M.-H., Yeom, Y.: Cryptanalysis of the Paeng-Jung-Ha Cryptosystem from PKC 2003. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 107–117. Springer, Heidelberg (2007) CrossRef

16.

Hermans, J., Schneider, M., Buchmann, J., Vercauteren, F., Preneel, B.: Parallel shortest lattice vector enumeration on graphics cards. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 52–68. Springer, Heidelberg (2010) CrossRef

17.

Kannan, R.: Minkowski’s convex body theorem and integer programming. Math. Oper. Res. 12(3), 415–440 (1987)MathSciNetCrossRefMATH

18.

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) CrossRef

19.

Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319–339. Springer, Heidelberg (2011) CrossRef

20.

Hojsík, M., Půlpánová, V.: A fully homomorphic cryptosystem with approximate perfect secrecy. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 375–388. Springer, Heidelberg (2013) CrossRef

21.

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

22.

Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012) CrossRef

23.

Nguyên, P.Q.: Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto 1997. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 288. Springer, Heidelberg (1999)

24.

Plantard, T., Susilo, W.: Broadcast attacks against lattice-based cryptosystems. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 456–472. Springer, Heidelberg (2009) CrossRef

25.

Pöppelmann, T., Güneysu, T.: Towards practical lattice-based public-key encryption on reconfigurable hardware. In: Selected Areas in Cryptography, pp. 68–85 (2013)

26.

Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93 (2005)

Titel: Nearest Planes in Practice
verfasst von: Christian Bischof
Johannes Buchmann
Özgür Dagdelen
Robert Fitzpatrick
Florian Göpfert
Artur Mariano
Verlag: Springer International Publishing
Buch: Cryptography and Information Security in the Balkans
Print ISBN: 978-3-319-21355-2

Electronic ISBN: 978-3-319-21356-9

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-21356-9_14

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner