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A Comparison of the Homomorphic Encryption Schemes FV and YASHE

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Progress in Cryptology – AFRICACRYPT 2014 (AFRICACRYPT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8469))

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Abstract

We conduct a theoretical and practical comparison of two Ring-LWE-based, scale-invariant, leveled homomorphic encryption schemes – Fan and Vercauteren’s adaptation of BGV and the YASHE scheme proposed by Bos, Lauter, Loftus and Naehrig. In particular, we explain how to choose parameters to ensure correctness and security against lattice attacks. Our parameter selection improves the approach of van de Pol and Smart to choose parameters for schemes based on the Ring-LWE problem by using the BKZ-2.0 simulation algorithm.

We implemented both encryption schemes in C++, using the arithmetic library FLINT, and compared them in practice to assess their respective strengths and weaknesses. In particular, we performed a homomorphic evaluation of the lightweight block cipher SIMON. Combining block ciphers with homomorphic encryption allows to solve the gargantuan ciphertext expansion in cloud applications.

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References

  1. Bansarkhani, R.E., Buchmann, J.: Improvement and efficient implementation of a lattice-based signature scheme. Cryptology ePrint Archive, Report 2013/297 (2013), http://eprint.iacr.org/

  2. Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. Cryptology ePrint Archive, Report 2013/404 (2013), http://eprint.iacr.org/

  3. Bos, J.W., Lauter, K., Loftus, J., Naehrig, M.: Improved security for a ring-based fully homomorphic encryption scheme. In: Stam (ed.) [37], pp. 45–64

    Google Scholar 

  4. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical gapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS, pp. 309–325. ACM (2012)

    Google Scholar 

  6. Canetti, R., Garay, J.A. (eds.): CRYPTO 2013, Part I. LNCS, vol. 8042. Springer, Heidelberg (2013)

    Google Scholar 

  7. Chen, Y., Nguyen, P.Q.: BKZ 2.0: Better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1–20. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Chen, Y., Nguyen, P.Q.: BKZ 2.0: Better lattice security estimates (2013), http://www.di.ens.fr/~ychen/research/Full_BKZ.pdf

  9. Cheon, J.H., Coron, J.-S., Kim, J., Lee, M.S., Lepoint, T., Tibouchi, M., Yun, A.: Batch fully homomorphic encryption over the integers. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 315–335. Springer, Heidelberg (2013)

    Google Scholar 

  10. Coron, J.-S., Lepoint, T., Tibouchi, M.: Scale-invariant fully homomorphic encryption over the integers. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 311–328. Springer, Heidelberg (2014)

    Google Scholar 

  11. Coron, J.S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, Johansson (eds.) [34], pp. 446–464

    Google Scholar 

  12. van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)

    Google Scholar 

  13. Ducas, L., Durmus, A., Lepoint, T., Lyubashevsky, V.: Lattice signatures and bimodal gaussians. In: Canetti, Garay (eds.) [6], pp. 40–56

    Google Scholar 

  14. Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. IACR Cryptology ePrint Archive 2012, 144 (2012)

    Google Scholar 

  15. Gama, N., Nguyen, P.Q.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) STOC, pp. 169–178. ACM (2009)

    Google Scholar 

  17. Gentry, C., Halevi, S.: mplementing Gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)

    Google Scholar 

  18. Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, Johansson (eds.) [34] , pp. 465–482

    Google Scholar 

  19. 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)

    Google Scholar 

  20. Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, Garay (eds.) [6], pp. 75–92

    Google Scholar 

  21. Graepel, T., Lauter, K., Naehrig, M.: ML confidential: Machine learning on encrypted data. In: Kwon, T., Lee, M.-K., Kwon, D. (eds.) ICISC 2012. LNCS, vol. 7839, pp. 1–21. Springer, Heidelberg (2013)

    Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Hart, W.: et al.: Fast Library for Number Theory, Version 2.4 (2013), http://www.flintlib.org

  24. Lauter, K.E.: Practical applications of homomorphic encryption. In: Yu, T., Capkun, S., Kamara, S. (eds.) CCSW, pp. 57–58. ACM (2012)

    Google Scholar 

  25. Lenstra, A.K., Jr Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515–534 (1982)

    Google Scholar 

  26. Lepoint, T.: A proof-of-concept implementation of the homomorphic evaluation of SIMON using FV and YASHE leveled homomorphic cryptosystems (2014), https://github.com/tlepoint/homomorphic-simon

  27. Lepoint, T., Naehrig, M.: A comparison of the homomorphic encryption schemes FV and YASHE (full version). Cryptology ePrint Archive, Report 2014/062 (2014), http://eprint.iacr.org/

  28. 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)

    Chapter  Google Scholar 

  29. Liu, M., Nguyen, P.Q.: Solving BDD by enumeration: An update. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 293–309. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  30. López-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: STOC, pp. 1219–1234 (2012)

    Google Scholar 

  31. Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  32. Micciancio, D., Regev, O.: Lattice-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 147–191. Springer, Heidelberg (2009)

    Google Scholar 

  33. Naehrig, M., Lauter, K., Vaikuntanathan, V.: Can homomorphic encryption be practical? In: Cachin, C., Ristenpart, T. (eds.) CCSW, pp. 113–124. ACM (2011)

    Google Scholar 

  34. Pointcheval, D., Johansson, T. (eds.): EUROCRYPT 2012. LNCS, vol. 7237. Springer, Heidelberg (2012)

    Google Scholar 

  35. van de Pol, J., Smart, N.P.: Estimating key sizes for high dimensional lattice-based systems. In: Stam (ed.) [37], pp. 290–303

    Google Scholar 

  36. Schnorr, C.P., Euchner, M.: Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Math. Program. 66, 181–199 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  37. Stam, M. (ed.): IMACC 2013. LNCS, vol. 8308. Springer, Heidelberg (2013)

    Google Scholar 

  38. Stehlé, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 27–47. Springer, Heidelberg (2011)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CryptoExperts, École Normale Supérieure and University of Luxembourg, Luxembourg

    Tancrède Lepoint

  2. Microsoft Research, USA

    Michael Naehrig

Authors
  1. Tancrède Lepoint
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  2. Michael Naehrig
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Editor information

Editors and Affiliations

  1. Computer Science Department, Ecole Normale Supérieure, 45, rue d’Ulm, 75005, Paris, France

    David Pointcheval  & Damien Vergnaud  & 

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Lepoint, T., Naehrig, M. (2014). A Comparison of the Homomorphic Encryption Schemes FV and YASHE . In: Pointcheval, D., Vergnaud, D. (eds) Progress in Cryptology – AFRICACRYPT 2014. AFRICACRYPT 2014. Lecture Notes in Computer Science, vol 8469. Springer, Cham. https://doi.org/10.1007/978-3-319-06734-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-06734-6_20

  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-06734-6

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