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Communication Efficient Statistical Asynchronous Multiparty Computation with Optimal Resilience

  • Arpita Patra
  • Ashish Choudhary
  • C. Pandu Rangan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6151)

Abstract

We propose an efficient statistically secure asynchronous multiparty computation (AMPC) protocol with optimal fault tolerance; i.e., with n = 3t + 1, where n is the total number of parties and t is the number of parties that can be under the influence of a Byzantine (active) adversary \({\cal A}_t\) having unbounded computing power. Our protocol privately communicates \({\cal O}(n^5 \kappa)\) bits per multiplication gate and involves a negligible error probability of 2 − Ω(κ), where κ is the error parameter. As far as our knowledge is concerned, the only known statistically secure AMPC protocol with n = 3t + 1 is due to [7], which privately communicates Ω(n 11 κ 4) bits and A-casts Ω(n 11 κ 2 log(n)) bits per multiplication gate. Here A-cast is an asynchronous broadcast primitive, which allows a party to send some information to all other parties identically. Thus our AMPC protocol shows significant improvement in communication complexity over the AMPC protocol of [7].

Keywords

Secret Sharing Communication Complexity Multiplication Gate Honest Party Bivariate Polynomial 
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.
    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
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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
  5. 5.
    Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: STOC, pp. 52–61 (1993)Google Scholar
  6. 6.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC, pp. 1–10 (1988)Google Scholar
  7. 7.
    Ben-Or, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience. In: PODC, pp. 183–192 (1994)Google Scholar
  8. 8.
    Bracha, G.: An asynchronous \(\lfloor (n - 1) / 3 \rfloor\)-resilient consensus protocol. In: PODC, pp. 154–162 (1984)Google Scholar
  9. 9.
    Canetti, R.: Studies in Secure Multiparty Computation and Applications. PhD thesis, Weizmann Institute, Israel (1995)Google Scholar
  10. 10.
    Canetti, R., Rabin, T.: Fast asynchronous Byzantine Agreement with optimal resilience. In: STOC, pp. 42–51 (1993)Google Scholar
  11. 11.
    Chaum, D., Crpeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: STOC, pp. 11–19 (1988)Google Scholar
  12. 12.
    Cramer, R., Damgård, I.: Multiparty Computation, an Introduction. In: Contemporary Cryptography. Birkhuser, Basel (2005)Google Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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
  15. 15.
    Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fact-track multiparty computations with applications to threshold cryptography. In: PODC, pp. 101–111 (1998)Google Scholar
  16. 16.
    Patra, A., Choudhary, A., Pandu Rangan, C.: Efficient statistical asynchronous verifiable secret sharing and multiparty computation with optimal resilience. In: Cryptology ePrint Archive, Report 2009/492. A preliminary version of this paper got accepted in ICITS 2009 (2009)Google Scholar
  17. 17.
    Patra, A., Choudhary, A., Pandu Rangan, C.: Simple and efficient asynchronous Byzantine Agreement with optimal resilience. In: Cryptology ePrint Archive, Report 2008/424. Also appeared in Proc. of PODC (2009)Google Scholar
  18. 18.
    Rabin, T.: Robust sharing of secrets when the dealer is honest or cheating. J. ACM 41(6), 1089–1109 (1994)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC, pp. 73–85 (1989)Google Scholar
  20. 20.
    Yao, A.C.: Protocols for secure computations. In: FOCS, pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Arpita Patra
    • 1
  • Ashish Choudhary
    • 1
  • C. Pandu Rangan
    • 1
  1. 1.Dept of Computer Science and EngineeringIIT MadrasChennaiIndia

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