Advertisement

More Efficient Constant-Round Multi-party Computation from BMR and SHE

  • Yehuda Lindell
  • Nigel P. Smart
  • Eduardo Soria-Vazquez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9985)

Abstract

We present a multi-party computation protocol in the case of dishonest majority which has very low round complexity. Our protocol sits philosophically between Gentry’s Fully Homomorphic Encryption based protocol and the SPDZ-BMR protocol of Lindell et al. (CRYPTO 2015). Our protocol avoids various inefficiencies of the previous two protocols. Compared to Gentry’s protocol we only require Somewhat Homomorphic Encryption (SHE). Whilst in comparison to the SPDZ-BMR protocol we require only a quadratic complexity in the number of players (as opposed to cubic), we have fewer rounds, and we require less proofs of correctness of ciphertexts. Additionally, we present a variant of our protocol which trades the depth of the garbling circuit (computed using SHE) for some more multiplications in the offline and online phases.

Keywords

Homomorphic Encryption Online Phase Offline Phase Output Wire Input Wire 
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.

Notes

Acknowledgements

The first author was supported in part by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC consolidators grant agreement n. 615172 (HIPS), and by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minster’s Office. The second author was supported in part by ERC Advanced Grant ERC-2010-AdG-267188-CRIPTO, DARPA and the US Navy under contract #N66001-15-C-4070, and by EPSRC via grants EP/I03126X and EP/N021940/1. The third author was supported in part by the Marie Sklodowska-Curie ITN ECRYPT-NET (Project Reference 643161). All authors were also supported by an award from EPSRC (grant EP/M012824), from the Ministry of Science, Technology and Space, Israel, and the UK Research Initiative in Cyber Security.

References

  1. 1.
    Asharov, G., Lindell, Y., Schneider, T., Zohner, M.: More efficient oblivious transfer and extensions for faster secure computation. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS 2013, 4–8 November 2013, pp. 535–548. ACM (2013)Google Scholar
  2. 2.
    Baum, C., Damgård, I., Toft, T., Zakarias, R.: Better preprocessing for secure multiparty computation. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 327–345. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-39555-5_18 CrossRefGoogle Scholar
  3. 3.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Ortiz, H. (ed.), 22nd STOC, pp. 503–513. ACM (1990)Google Scholar
  4. 4.
    Bellare, M., Hoang, V.T., Keelveedhi, S., Rogaway, P.: Efficient garbling from a fixed-key blockcipher. In: 2013 IEEE Symposium on Security and Privacy, SP 2013, 19–22 May 2013, Berkeley, CA, USA, pp. 478–492. IEEE Computer Society (2013)Google Scholar
  5. 5.
    Canetti, R., Cohen, A., Lindell. Y.: A simpler variant of universally composable security for standard multiparty computation. In: Gennaro and Robshaw [15], pp. 3–22 (2015)Google Scholar
  6. 6.
    Canetti, R., Garay, J.A. (eds.): CRYPTO 2013. LNCS, vol. 8043. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40084-1_2 zbMATHGoogle Scholar
  7. 7.
    Choi, S.G., Hwang, K.-W., Katz, J., Malkin, T., Rubenstein, D.: Secure multi-party computation of Boolean circuits with applications to privacy in on-line marketplaces. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 416–432. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-27954-6_26 CrossRefGoogle Scholar
  8. 8.
    Choi, S.G., Katz, J., Malozemoff, A.J., Zikas, V.: Efficient three-party computation from cut-and-choose. In: Garay and Gennaro [13], pp. 513–530 (2014)Google Scholar
  9. 9.
    Costache, A., Smart, N.P.: Which ring based somewhat homomorphic encryption scheme is best? In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 325–340. Springer, Heidelberg (2016). doi: 10.1007/978-3-319-29485-8_19 CrossRefGoogle Scholar
  10. 10.
    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. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-40203-6_1 CrossRefGoogle Scholar
  11. 11.
    Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini and Canetti [32], pp. 643–662 (2012)Google Scholar
  12. 12.
    Damgård, I., Polychroniadou, A., Rao, V.: Adaptively secure multi-party computation from LWE (via equivocal FHE). In: Cheng, C.-M., et al. (eds.) PKC 2016. LNCS, vol. 9615, pp. 208–233. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49387-8_9 CrossRefGoogle Scholar
  13. 13.
    Garay, J.A., Gennaro, R. (eds.): CRYPTO 2014. LNCS, vol. 8617. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44381-1_29 zbMATHGoogle Scholar
  14. 14.
    Garg, S., Mukherjee, P., Pandey, O., Polychroniadou, A.: The exact round complexity of secure computation. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 448–476. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49896-5_16 CrossRefGoogle Scholar
  15. 15.
    Gennaro, R., Robshaw, M. (eds.): CRYPTO 2015. LNCS, vol. 9216. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48000-7_1 zbMATHGoogle Scholar
  16. 16.
    Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009). http://crypto.stanford.edu/craig
  17. 17.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or A completeness theorem for protocols with honest majority. In: Aho, A.V. (ed.) Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pp. 218–229. ACM, New York (1987)Google Scholar
  18. 18.
    Goldwasser, S., Lindell, Y.: Secure multi-party computation without agreement. J. Cryptology 18(3), 247–287 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Huang, Y., Katz, J., Evans, D.: Efficient secure two-party computation using symmetric cut-and-choose. In: Canetti and Garay [6], pp. 18–35 (2013)Google Scholar
  20. 20.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-85174-5_32 CrossRefGoogle Scholar
  21. 21.
    Katz, J., Ostrovsky, R.: Round-optimal secure two-party computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-28628-8_21 CrossRefGoogle Scholar
  22. 22.
    Larraia, E., Orsini, E., Smart. N.P.: Dishonest majority multi-party computation for binary circuits. In: Garay and Gennaro [13], pp. 495–512 (2014)Google Scholar
  23. 23.
    Lindell, Y.: Fast cut-and-choose based protocols for malicious and covert adversaries. In: Canetti and Garay [6], pp. 1–17 (2013)Google Scholar
  24. 24.
    Lindell, Y., Oxman, E., Pinkas, B.: The IPS compiler: optimizations, variants and concrete efficiency. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 259–276. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-22792-9_15 CrossRefGoogle Scholar
  25. 25.
    Lindell, Y., Pinkas, B.: An efficient protocol for secure two-party computation in the presence of malicious adversaries. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 52–78. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-72540-4_4 CrossRefGoogle Scholar
  26. 26.
    Lindell, Y., Pinkas, B.: Secure two-party computation via cut-and-choose oblivious transfer. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 329–346. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19571-6_20 CrossRefGoogle Scholar
  27. 27.
    Lindell, Y., Pinkas, B., Smart, N.P., Yanai, A.: Efficient constant round multi-party computation combining BMR and SPDZ. In: Gennaro and Robshaw [15], pp. 319–338 (2015)Google Scholar
  28. 28.
    Lindell, Y., Riva, B.: Cut-and-choose Yao-based secure computation in the online/offline and batch settings. In: Garay and Gennaro [13], pp. 476–494 (2014)Google Scholar
  29. 29.
    Lindell, Y., Riva, B.: Blazing fast 2PC in the offline/online setting with security for malicious adversaries. In: Ray, I., Li, N., Kruegel, C. (eds.) Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security, 12–6 October 2015, Denver, CO, USA, pp. 579–590. ACM (2015)Google Scholar
  30. 30.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini and Canetti [32], pp. 681–700 (2012)Google Scholar
  31. 31.
    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
  32. 32.
    Safavi-Naini, R., Canetti, R. (eds.): CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32009-5_38 CrossRefzbMATHGoogle Scholar
  33. 33.
    Schneider, T., Zohner, M.: GMW vs. Yao? efficient secure two-party computation with low depth circuits. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 275–292. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-39884-1_23 CrossRefGoogle Scholar
  34. 34.
    shelat, A., Shen, C.: Two-output secure computation with malicious adversaries. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 386–405. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-20465-4_22 CrossRefGoogle Scholar
  35. 35.
    Yao, A.C.-C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science, 3–5 November 1982, Chicago, Illinois, USA, pp. 160–164. IEEE Computer Society (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Yehuda Lindell
    • 1
  • Nigel P. Smart
    • 2
  • Eduardo Soria-Vazquez
    • 2
  1. 1.Bar-Ilan UniversityRamat GanIsrael
  2. 2.University of BristolBristolUK

Personalised recommendations