Round and Communication Efficient Unconditionally-Secure MPC with \(t<n/3\) in Partially Synchronous Network

  • Ashish ChoudhuryEmail author
  • Arpita Patra
  • Divya Ravi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)


In this work, we study unconditionally-secure multi-party computation (MPC) tolerating \(t < n/3\) corruptions, where n is the total number of parties involved. In this setting, it is well known that if the underlying network is completely asynchronous, then one can achieve only statistical security; moreover it is impossible to ensure input provision and consider inputs of all the honest parties. The best known statistically-secure asynchronous MPC (AMPC) with \(t<n/3\) requires a communication of \(\varOmega (n^5)\) field elements per multiplication. We consider a partially synchronous setting, where the parties are assumed to be globally synchronized initially for few rounds and then the network becomes completely asynchronous. In such a setting, we present a MPC protocol, which requires \(\mathcal {O}(n^2)\) communication per multiplication while ensuring input provision. Our MPC protocol relies on a new four round, communication efficient statistical verifiable secret-sharing (VSS) protocol with broadcast communication complexity independent of the number of secret-shared values.


  1. 1.
    Asharov, G., Lindell, Y.: A full proof of the BGW protocol for perfectly-secure multiparty computation. J. Cryptol. 30(1), 58–151 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    Beerliová-Trubíniová, Z., Hirt, M.: Simple and efficient perfectly-secure asynchronous MPC. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 376–392. Springer, Heidelberg (2007). CrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    Beerliová-Trubíniová, Z., Hirt, M., Nielsen, J.B.: On the theoretical gap between synchronous and asynchronous MPC protocols. In: Proceedings of the PODC, pp. 211–218. ACM (2010)Google Scholar
  7. 7.
    Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: Proceedings of the 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: Proceedings of the STOC, pp. 1–10. ACM (1988)Google Scholar
  9. 9.
    Ben-Or, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience (Extended Abstract). In: Proceedings of the PODC, pp. 183–192. ACM (1994)Google Scholar
  10. 10.
    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
  11. 11.
    Canetti, R.: Studies in Secure Multiparty Computation and Applications. Ph.D. thesis, Weizmann Institute, Israel (1995)Google Scholar
  12. 12.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (Extended Abstract). In: STOC, pp. 11–19. ACM (1988)Google Scholar
  13. 13.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: FOCS, pp. 383–395. IEEE Computer Society (1985)Google Scholar
  14. 14.
    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
  15. 15.
    Choudhury, A., Patra, A.: An efficient framework for unconditionally secure multiparty computation. IEEE Trans. Inf. Theor. 63(1), 428–468 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Cramer, R., Damgård, I., Dziembowski, S., Hirt, M., Rabin, T.: Efficient multiparty computations secure against an adaptive adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311–326. Springer, Heidelberg (1999). CrossRefGoogle Scholar
  17. 17.
    Cramer, R., Damgård, I., Maurer, U.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000). CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Damgård, I., Ishai, Y., Krøigaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241–261. Springer, Heidelberg (2008). CrossRefGoogle Scholar
  20. 20.
    Damgård, I., 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
  21. 21.
    Fitzi, M., Garay, J., Gollakota, S., Rangan, C.P., Srinathan, K.: Round-optimal and efficient verifiable secret sharing. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 329–342. Springer, Heidelberg (2006). CrossRefGoogle Scholar
  22. 22.
    Fitzi, M., Hirt, M.: Optimally efficient multi-valued byzantine agreement. In: PODC, pp. 163–168. ACM Press (2006)Google Scholar
  23. 23.
    Fitzi, M., Nielsen, J.B.: On the number of synchronous rounds sufficient for authenticated Byzantine agreement. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 449–463. Springer, Heidelberg (2009). CrossRefGoogle Scholar
  24. 24.
    Franklin, M.K., Yung, M.: Communication complexity of secure computation (Extended Abstract). In: STOC, pp. 699–710. ACM (1992)Google Scholar
  25. 25.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The round complexity of verifiable secret sharing and secure multicast. In: STOC, pp. 580–589. ACM (2001)Google Scholar
  26. 26.
    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
  27. 27.
    Hirt, M., Maurer, U., Przydatek, B.: Efficient secure multi-party computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000). CrossRefGoogle Scholar
  28. 28.
    Katz, J., Koo, C.Y., Kumaresan, R.: Improving the round complexity of VSS in point-to-point networks. Inf. Comput. 207(8), 889–899 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Kushilevitz, E., Lindell, Y., Rabin, T.: Information-theoretically secure protocols and security under composition. SIAM J. Comput. 39(5), 2090–2112 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)zbMATHGoogle Scholar
  31. 31.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and reed-solomon codes. Commun. ACM 24(9), 583–584 (1981)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Patra, A., Choudhary, A., Pandu Rangan, C.: Efficient statistical asynchronous verifiable secret sharing and multiparty computation with optimal resilience. IACR Cryptology ePrint Archive, 2009:492 (2009)Google Scholar
  33. 33.
    Patra, A., Choudhury, A., Pandu Rangan, C.: Asynchronous Byzantine agreement with optimal resilience. Distrib. Comput. 27(2), 111–146 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Patra, A., Choudhury, A., Pandu Rangan, C.: Efficient asynchronous verifiable secret sharing and multiparty computation. J. Cryptology 28(1), 49–109 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Patra, A.: Error-free multi-valued broadcast and Byzantine agreement with optimal communication complexity. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 34–49. Springer, Heidelberg (2011). CrossRefGoogle Scholar
  36. 36.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (Extended Abstract). In: STOC, pp. 73–85. ACM (1989)Google Scholar
  37. 37.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Yao, A.C.: Protocols for secure computations. In: FOCS, pp. 160–164. IEEE Computer Society (1982)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.International Institute of Information TechnologyBangaloreIndia
  2. 2.Indian Institute of ScienceBangaloreIndia

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