Linear Overhead Optimally-Resilient Robust MPC Using Preprocessing

  • Ashish Choudhury
  • Emmanuela Orsini
  • Arpita Patra
  • Nigel P. SmartEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9841)


We present a new technique for robust secret reconstruction with \(\mathcal {O}(n)\) communication complexity. By applying this technique, we achieve \(\mathcal {O}(n)\) communication complexity per multiplication for a wide class of robust practical Multi-Party Computation (MPC) protocols. In particular our technique applies to robust threshold computationally secure protocols in the case of \(t<n/2\) in the pre-processing model. Previously in the pre-processing model, \(\mathcal {O}(n)\) communication complexity per multiplication was only known in the case of computationally secure non-robust protocols in the dishonest majority setting (i.e. with \(t<n\)) and in the case of perfectly-secure robust protocols with \(t<n/3\). A similar protocol was sketched by Damgård and Nielsen, but no details were given to enable an estimate of the communication complexity. Surprisingly our robust reconstruction protocol applies for both the synchronous and asynchronous settings.



This work has been supported in part by ERC Advanced Grant ERC-2010-AdG-267188-CRIPTO, by EPSRC via grants EP/I03126X and EP/M016803, by DARPA and the US Navy under contract #N66001-15-C-4070, and by the Infosys Foundation.


  1. 1.
    Asharov, G., Jain, A., López-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483–501. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Backes, M., Bendun, F., Choudhury, A., Kate, A.: Asynchronous MPC with a strict honest majority using non-equivocation. In: Halldórsson, M.M., Dolev, S. (eds.) PODC, pp. 10–19. ACM (2014)Google Scholar
  3. 3.
    Baron, J., J., Defrawy, J., Lampkins, J., Ostrovsky, R.: How to withstand mobile virus attacks, revisited. In: Halldórsson, M.M., Dolev, S. (eds.) PODC, pp. 293–302. ACM (2014)Google 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.
    Beerliová-Trubíniová, Z., Hirt, M.: Efficient multi-party computation with dispute control. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 305–328. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Beerliová-Trubíniová, Z., Hirt, M.: Perfectly-secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213–230. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: Kosaraju, S.R., Johnson, D.S., Aggarwal, A. (eds) STOC, pp. 52–61. ACM (1993)Google Scholar
  8. 8.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: Simon, J. (ed.) STOC, pp. 1–10. ACM (1988)Google Scholar
  9. 9.
    Ben-Sasson, E., Fehr, S., Ostrovsky, R.: Near-linear unconditionally-secure multiparty computation with a dishonest minority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 663–680. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. TOCT 6(3), 13:1–13:36 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Canetti, R.: Studies in secure multiparty computation and applications. Ph.D. thesis, Weizmann Institute, Israel (1995)Google Scholar
  13. 13.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptol. 13(1), 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: STOC, pp. 11–19. ACM (1988)Google Scholar
  15. 15.
    Choudhury, A., Hirt, M., Patra, A.: Asynchronous multiparty computation with linear communication complexity. In: Afek, Y. (ed.) DISC 2013. LNCS, vol. 8205, pp. 388–402. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Choudhury, A., Loftus, J., Orsini, E., Patra, A., Smart, N.P.: Between a rock and a hard place: interpolating between MPC and FHE. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 221–240. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. 17.
    Choudhury, A., Patra, A.: Optimally resilient asynchronous MPC with linear communication complexity. In: Das, S.K., Krishnaswamy, D., Karkar, S., Korman, A., Kumar, M., Portmann, M., Sastry, S. (eds.) ICDCN, pp. 5:1–5:10. ACM (2015)Google Scholar
  18. 18.
    Clement, A., Junqueira, F., Kate, A., Rodrigues, R.: On the (limited) power of non-equivocation. In: Kowalski, D., Panconesi, A. (eds.) PODC, pp. 301–308. ACM (2012)Google Scholar
  19. 19.
    Damgård, I., Geisler, M., Krøigaard, M., Nielsen, J.B.: Asynchronous multiparty computation: theory and implementation. In: Jarecki, S., Tsudik, G. (eds.) PKC, pp. 160–179 (2009)Google Scholar
  20. 20.
    Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly secure multiparty computation and the computational overhead of cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445–465. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Damgård, I.B., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572–590. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Damgård, I., Pastro, V., Smart, N., 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
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Fitzi, M., Hirt, M.: Optimally efficient multi-valued Byzantine agreement. In: Ruppert, E., Malkhi, D. (eds.) PODC, pp. 163–168. ACM Press (2006)Google Scholar
  25. 25.
    Genkin, D., Ishai, Y., Polychroniadou, A.: Efficient multi-party computation: from passive to active security via secure SIMD circuits. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 721–741. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  26. 26.
    Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fact-track multiparty computations with applications to threshold cryptography. In: Coan, B.A., Afek, Y. (eds.) PODC, pp. 101–111. ACM (1998)Google Scholar
  27. 27.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC, pp. 218–229. ACM (1987)Google Scholar
  28. 28.
    Hirt, M., Nielsen, J.B.: Robust multiparty computation with linear communication complexity. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 463–482. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  29. 29.
    Hirt, M., Nielsen, J.B., Przydatek, B.: Cryptographic asynchronous multi-party computation with optimal resilience (extended abstract). In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 322–340. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  30. 30.
    Hirt, M., Nielsen, J.B., Przydatek, B.: Asynchronous multi-party computation with quadratic communication. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 473–485. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  31. 31.
    Katz, J., Koo, C.-Y.: On expected constant-round protocols for Byzantine agreement. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 445–462. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  32. 32.
    Keller, M., Scholl, P., Smart, N.P.: An architecture for practical actively secure MPC with dishonest majority. In: Sadeghi, A.-R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 549–560. ACM (2013)Google Scholar
  33. 33.
    Yao, A.C.: Protocols for secure computations (extended abstract). In: FOCS, pp. 160–164. IEEE Computer Society (1982)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ashish Choudhury
    • 1
  • Emmanuela Orsini
    • 2
  • Arpita Patra
    • 3
  • Nigel P. Smart
    • 2
    Email author
  1. 1.International Institute of Information TechnologyBangaloreIndia
  2. 2.Department of Computer ScienceUniversity of BristolBristolUK
  3. 3.Department of Computer Science and AutomationIndian Institute of ScienceBangaloreIndia

Personalised recommendations