FHEW with Efficient Multibit Bootstrapping

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9230)

Abstract

In this paper, we describe a generalization of the fully homomorphic encryption scheme FHEW described by Ducas and Micciancio [8]. It is characterized by an efficient bootstrapping procedure performed after each gate, as opposed to the HElib of Halevi and Shoup that handles batches of encryptions periodically. While the Ducas-Micciancio scheme was limited to NAND gates, we propose a generalization that can handle arbitrary gates for only one call to the bootstrapping procedure. We also show how bootstrapping can be parallelized and address its performances in a multicore environment.

Keywords

Fully homomorphic encryption LWE Bootstrapping Parallelization 

References

  1. 1.
    Alperin-Sheriff, J., Peikert, C.: Practical bootstrapping in quasilinear time. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 1–20. Springer, Heidelberg (2013) Google Scholar
  2. 2.
    Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 297–314. Springer, Heidelberg (2014) Google Scholar
  3. 3.
    Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009) Google Scholar
  4. 4.
    Blum, A., Furst, M.L., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994) Google Scholar
  5. 5.
    Brakerski, Z., Gentry, C., Halevi, S.: Packed ciphertexts in LWE-based homomorphic encryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 1–13. Springer, Heidelberg (2013) Google Scholar
  6. 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.) Symposium on Theory of Computing Conference, STOC 2013, Palo Alto, CA, USA, June 1–4, pp. 575–584. ACM (2013)Google Scholar
  7. 7.
    Ducas, L., Durmus, A.: Ring-LWE in polynomial rings. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 34–51. Springer, Heidelberg (2012) Google Scholar
  8. 8.
    Ducas, L., Micciancio, D.: FHEW: Bootstrapping homomorphic encryption in less than a second. Cryptology ePrint Archive, Report 2014/816 (2014). http://eprint.iacr.org/
  9. 9.
    Ducas, L., Micciancio, D.: Implementation of FHEW (2014). https://github.com/lducas/FHEW
  10. 10.
    Frigo, M., Johnson, S.: The design and implementation of FFTW3. In: Proceedings of the IEEE, 93(2):216–231. Special issue on “Program Generation, Optimization, and Platform Adaptation” (2005)Google Scholar
  11. 11.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 169–178. ACM, New York (2009)Google Scholar
  12. 12.
    Gentry, C., Halevi, S.: Implementing gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011) Google Scholar
  13. 13.
    Gentry, C., Halevi, S., Peikert, C., Smart, N.P.: Ring switching in BGV-style homomorphic encryption. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 19–37. Springer, Heidelberg (2012) Google Scholar
  14. 14.
    Gentry, C., Halevi, S., Smart, N.P.: Better bootstrapping in fully homomorphic encryption. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 1–16. Springer, Heidelberg (2012) Google Scholar
  15. 15.
    Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012) Google Scholar
  16. 16.
    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
  17. 17.
    Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013) Google Scholar
  18. 18.
    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) Google Scholar
  19. 19.
    Halevi, S., Shoup, V.: Algorithms in HElib. IACR Cryptology ePrint Archive 2014:106 (2014)Google Scholar
  20. 20.
    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) Google Scholar
  21. 21.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H., Fagin, R. (eds.) Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22–24, pp. 84–93. ACM (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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