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Practical Covertly Secure MPC for Dishonest Majority – Or: Breaking the SPDZ Limits

  • Ivan Damgård
  • Marcel Keller
  • Enrique Larraia
  • Valerio Pastro
  • Peter Scholl
  • Nigel P. Smart
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8134)

Abstract

SPDZ (pronounced “Speedz”) is the nickname of the MPC protocol of Damgård et al. from Crypto 2012. In this paper we both resolve a number of open problems with SPDZ; and present several theoretical and practical improvements to the protocol. In detail, we start by designing and implementing a covertly secure key generation protocol for obtaining a BGV public key and a shared associated secret key. We then construct both a covertly and actively secure preprocessing phase, both of which compare favourably with previous work in terms of efficiency and provable security.

We also build a new online phase, which solves a major problem of the SPDZ protocol: namely prior to this work preprocessed data could be used for only one function evaluation and then had to be recomputed from scratch for the next evaluation, while our online phase can support reactive functionalities. This improvement comes mainly from the fact that our construction does not require players to reveal the MAC keys to check correctness of MAC’d values.

Keywords

Full Version Homomorphic Encryption Random Oracle Model Active Security Online Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aliasgari, M., Blanton, M., Zhang, Y., Steele, A.: Secure computation on floating point numbers. In: Network and Distributed System Security Symposium, NDSS 2013. Internet Society (2013)Google Scholar
  2. 2.
    Aumann, Y., Lindell, Y.: Security against covert adversaries: Efficient protocols for realistic adversaries. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 137–156. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Aumann, Y., Lindell, Y.: Security against covert adversaries: Efficient protocols for realistic adversaries. J. Cryptology 23(2), 281–343 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992)Google Scholar
  5. 5.
    Bogdanov, D., Laur, S., Willemson, J.: Sharemind: A framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. In: ITCS, pp. 309–325. ACM (2012)Google Scholar
  7. 7.
    Catrina, O., Saxena, A.: Secure computation with fixed-point numbers. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 35–50. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally secure constant-rounds multi-party computation for equality, comparison, bits and exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Damgård, I., Geisler, M., Krøigaard, M., Nielsen, J.B.: Asynchronous multiparty computation: Theory and implementation. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 160–179. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Damgård, I., Keller, M.: Secure multiparty AES. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 367–374. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Damgård, I., Keller, M., Larraia, E., Miles, C., Smart, N.P.: Implementing AES via an actively/covertly secure dishonest-majority MPC protocol. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 241–263. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: Breaking the SPDZ limits (2012)Google Scholar
  13. 13.
    Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Kreuter, B., Shelat, A., Shen, C.-H.: Towards billion-gate secure computation with malicious adversaries. In: USENIX Security Symposium 2012, pp. 285–300 (2012)Google Scholar
  17. 17.
    Lindell, Y., Pinkas, B., Smart, N.P.: Implementing two-party computation efficiently with security against malicious adversaries. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 2–20. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  18. 18.
    Malkhi, D., Nisan, N., Pinkas, B., Sella, Y.: Fairplay - Secure two-party computation system. In: USENIX Security Symposium 2004, pp. 287–302 (2004)Google Scholar
  19. 19.
    Montgomery, P.L.: Modular multiplication without trial division. Math. Comp. 44, 519–521 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Pinkas, B., Schneider, T., Smart, N.P., Williams, S.C.: Secure two-party computation is practical. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 250–267. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    SIMAP Project. SIMAP: Secure information management and processing, http://alexandra.dk/uk/Projects/Pages/SIMAP.aspx

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Marcel Keller
    • 2
  • Enrique Larraia
    • 2
  • Valerio Pastro
    • 1
  • Peter Scholl
    • 2
  • Nigel P. Smart
    • 2
  1. 1.Department of Computer ScienceAarhus UniversityDenmark
  2. 2.Department of Computer ScienceUniversity of BristolUK

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