NFLlib: NTT-based fast lattice library

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 9610, Issue , 2016, Pages 341-356

  Aguilar Melchor, Carlos ^a   Barrier, Joris ^a   Guelton, Serge ^b   Guinet, Adrien ^b   Killijian, Marc Olivier ^a   Lepoint, Tancrède ^c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b Quarkslab   (France)

^c Quarkslab ^*  (France)

Author keywords

C++ library; Chinese remainder theorem; Ideal lattice cryptography; Implementation; Number theoretic transform; SEE specializations

Indexed keywords

C++ (PROGRAMMING LANGUAGE); CRYPTOGRAPHY; LIBRARIES; MATHEMATICAL TRANSFORMATIONS; NUMBER THEORY; OPEN SOURCE SOFTWARE; POLYNOMIALS;

C++ LIBRARIES; CHINESE REMAINDER THEOREM; IMPLEMENTATION; NUMBER THEORETIC TRANSFORM; SEE SPECIALIZATIONS;

LATTICE THEORY;

EID: 84959020487     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-319-29485-8_20     Document Type: Conference Paper

References (31)

1. Albrecht, M.R., Cocis, C., Laguillaumie, F., Langlois, A.: Implementing candidate graded encoding schemes from ideal lattices. Cryptology ePrint Archive, Report 2014/928 (2014). http://eprint.iacr.org/2014/928
2. 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)
3. Albrecht, M.R., Player, R., Scott, S.: On the concrete hardness of learning with errors. Cryptology ePrint Archive, Report 2015/046 (2015). http://eprint.iacr.org/2015/046
4. Bos, J.W., Lauter, K., Loftus, J., Naehrig, M.: Improved security for a ring-based fully homomorphic encryption scheme. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 45-64. Springer, Heidelberg (2013)
5. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS 2012, pp. 309325. ACM, January 2012
6. Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 575-584. ACM Press, June 2013
7. Dai, W., Doröz, Y., Sunar, B.: Accelerating NTRU based homomorphic encryption using GPUs. In: IEEE High Performance Extreme Computing Conference, HPEC 2014, Waltham, MA, USA, 9-11 September 2014, pp. 1-6. IEEE (2014)
8. Doröz, Y., Shahverdi, A., Eisenbarth, T., Sunar, B.: Toward practical homomorphic evaluation of block ciphers using prince. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014 Workshops. LNCS, vol. 8438, pp. 208-220. Springer, Heidelberg (2014)
9. 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)
10. Ducas, L., Lyubashevsky, V., Prest, T.: Efficient identity-based encryption over NTRU lattices. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 22-41. Springer, Heidelberg (2014)
11. Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 617-640. Springer, Heidelberg (2015)
12. El Bansarkhani, R., Buchmann, J.: High performance lattice-based CCA-secure encryption. Cryptology ePrint Archive, Report 2015/042 (2015). http://eprint.iacr.org/2015/042
13. Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850-867. Springer, Heidelberg (2012)
14. 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)
15. Güneysu, T., Oder, T., Pöppelmann, T., Schwabe, P.: Software speed records for lattice-based signatures. In: Gaborit, P. (ed.) PQCrypto 2013. LNCS, vol. 7932, pp. 67-82. Springer, Heidelberg (2013)
16. Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 554-571. Springer, Heidelberg (2014)
17. Halevi, S., Shoup, V.: Bootstrapping for HElib. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 641-670. Springer, Heidelberg (2015)
18. Hart, W., et al.: Fast library for number theory (Version 2.5) (2015). http://www.flintlib.org
19. Harvey, D.: Faster arithmetic for number-theoretic transforms. J. Symb. Comput. 60, 113-119 (2014)
20. Itkis, G.: Forward security, adaptive cryptography: time evolution (2004). http://www.cs.bu.edu/fac/itkis/pap/forward-secure-survey.pdf
21. Khedr, A., Gulak, G., Vaikuntanathan, V.: SHIELD: scalable homomorphic implementation of encrypted data-classifiers. Cryptology ePrint Archive, Report 2014/838 (2014). http://eprint.iacr.org/2014/838
22. Lepoint, T., Naehrig, M.: A comparison of the homomorphic encryption schemes FV and YASHE. In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT. LNCS, vol. 8469, pp. 318-335. Springer, Heidelberg (2014)
23. 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)
24. Lyubashevsky, V., Micciancio, D.: Generalized compact knapsacks are collision resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 144-155. Springer, Heidelberg (2006)
25. Moller, N., Granlund, T.: Improved division by invariant integers. IEEE Trans. Comput. 60(2), 165-175 (2011)
26. Oder, T., Pöppelmann, T., Güneysu, T.: Beyond ECDSA and RSA: lattice-based digital signatures on constrained devices. In: The 51st Annual Design Automation Conference 2014, DAC 2014, San Francisco, CA, USA, 1-5 June 2014, pp. 1-6 (2014)
27. Peikert, C., Rosen, A.: Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 145-166. Springer, Heidelberg (2006)
28. Pollard, J.M.: The fast Fourier transform in a finite field. Math. Comput. 25(114), 365-374 (1971)
29. Pöppelmann, T., Güneysu, T.: Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware. In: Hevia, A., Neven, G. (eds.) LatinCrypt 2012. LNCS, vol. 7533, pp. 139-158. Springer, Heidelberg (2012)
30. Shoup, V.: Number theory library (Version 8.1) (2015). http://www.shoup.net/ntl
31. Steffen, A., et al.: strongSwan (Version 5.2.2) (2015). https://www.strongswan.org/