Advertisement

Universally Composable Simultaneous Broadcast

  • Alejandro Hevia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4116)

Abstract

Simultaneous Broadcast protocols allow different parties to broadcast values in parallel while guaranteeing mutual independence of the broadcast values. The problem of simultaneous broadcast was suggested by Chor et al. (FOCS 1985) who proposed a linear-round solution, and later improved by Chor and Rabin (PODC 1987) and Gennaro (IEEE Trans. on Parallel and Distributed Systems 2000). The most efficient solution, in terms of round complexity, is the one due to Gennaro, which is in the common random string model. This construction has constant round complexity but is not very practical, as it requires generic zero-knowledge proofs, non-interactive zero-knowledge proofs of knowledge, and commitment schemes. All the mentioned solutions were proven secure under security definitions with weak or no composition guarantees – only sequential composition for the initial construction by Chor et al.

In this work, we explore the problem of Simultaneous Broadcast under Universally Composable (UC) security (Canetti 2001). We give a definition of Simultaneous Broadcast in this framework, which is shown to imply all past definitions. We also show this notion can be achieved by a computationally efficient, constant-round construction (building on the verifiable secret sharing scheme of Cramer et al. at Eurocrypt 1999), which is secure under an honest majority. Our results rely on (and benefit from) capturing synchronous communication as a functionality within the UC model, as suggested by Canetti (IACR eprint 2005). Indeed, we show that this approach of modeling synchronous communication can lead to better understanding of where synchronicity is needed, and also simpler constructions and proofs.

Keywords

Secret Sharing Synchronous Communication Broadcast Protocol Honest Party Byzantine Agreement 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abe, M., Fehr, S.: Adaptively secure feldman VSS and applications to universally-composable threshold cryptography. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 317–334. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Barak, B., Lindell, Y., Rabin, T.: Protocol initialization for the framework of universal composability. Cryptology ePrint Archive, Report 2004/006 (2004), http://eprint.iacr.org/
  3. 3.
    Ben-Or, M., Canetti, R., Goldreich, O.: Asynchronous secure computation. In: ACM STOC 1993, pp. 52–61. ACM Press, New York (1993)CrossRefGoogle Scholar
  4. 4.
    Ben-Or, M., El-Yaniv, R.: Resilient-optimal interactive consistency in constant time. Distributed Computing 16(4), 249–262 (2003)CrossRefGoogle Scholar
  5. 5.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for noncryptographic fault-tolerant distributed computations. In: ACM STOC 1988, pp. 1–10. ACM Press, New York (1988)Google Scholar
  6. 6.
    Ben-Or, M., Kelmer, B., Rabin, T.: Asynchronous secure computations with optimal resilience (extended abstract). In: ACM PODC 1994, pp. 183–192 (1994)Google Scholar
  7. 7.
    Cachin, C., Kursawe, K., Petzold, F., Shoup, V.: Secure and efficient asynchronous broadcast protocols. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 524–541. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. Report 2000/067, Cryptology ePrint Archive (January 2005); Full version of that in IEEE Symposium on Foundations of Computer Science, FOCS 2001 (2001)Google Scholar
  9. 9.
    Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: ACM STOC 1996. ACM Press, New York (1996)Google Scholar
  10. 10.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: ACM STOC 2002 (2002)Google Scholar
  11. 11.
    Canetti, R., Rabin, T.: Fast asynchronous Byzantine agreement with optimal resilience (extended abstract). In: ACM STOC 1993, pp. 42–51. ACM Press, New York (1993)CrossRefGoogle Scholar
  12. 12.
    Chor, B., Goldwasser, S., Micali, S., Awerbuch, B.: Verifiable secret sharing and achieving simultaneity in the presence of faults. In: IEEE Symposium on Foundations of Computer Science (FOCS 1985), pp. 383–395. IEEE CS, Los Alamitos (1985)CrossRefGoogle Scholar
  13. 13.
    Chor, B., Rabin, M.O.: Achieving independence in logarithmic number of rounds. In: ACM Symposium on Principles of Distributed Computing (PODC 1987), pp. 260–268. ACM Press, New York (1987)CrossRefGoogle Scholar
  14. 14.
    Cramer, R., Damgård, I.B., 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
  15. 15.
    Damgård, I.B., Nielsen, J.B.: Universally composable efficient multiparty computation from threshold homomorphic encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  16. 16.
    Damgård, I.B., Nielsen, J.B.: Improved non-committing encryption schemes based on a general complexity assumption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 432–450. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM Journal on Computing 30(2), 391–437 (2001)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Feldman, P., Micali, S.: An optimal probabilistic protocol for synchronous byzantine agreement. SIAM Journal on Computing 26(4), 873–933 (1997)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Gennaro, R.: A protocol to achieve independence in constant rounds. IEEE Transactions on Parallel and Distributed Systems 11(7), 636–647 (2000)CrossRefGoogle Scholar
  20. 20.
    Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. Journal of the ACM 38(3), 691–729 (1991)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Hevia, A.: Universally composable simultaneous broadcast. Full version of this paper (2006), Available from: http://www.dcc.uchile.cl/~ahevia/pubs/
  22. 22.
    Hevia, A., Micciancio, D.: Simultaneous broadcast revisited. In: ACM PODC 2005, pp. 324–333. ACM Press, New York (2005)CrossRefGoogle Scholar
  23. 23.
    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
  24. 24.
    Hofheinz, D., Muller-quade, J.: A synchronous model for multi-party computation and the incompleteness of oblivious transfer (2004), Available from: http://eprint.iacr.org/2004/016
  25. 25.
    Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)MATHCrossRefGoogle Scholar
  26. 26.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: On the composition of authenticated byzantine agreement. In: ACM STOC 2002, pp. 514–523. ACM Press, New York (2002)Google Scholar
  27. 27.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: Sequential composition of protocols without simultaneous termination. In: ACM PODC 2002, pp. 203–212 (2002)Google Scholar
  28. 28.
    Lysyanskaya, A.: Threshold cryptography secure against the adaptive adversary, concurrently. Report 2000/019, Cryptology ePrint Archive (2000)Google Scholar
  29. 29.
    Micali, S., Rabin, T.: Collective coin tossing without assumptions nor broadcasting. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 253–266. Springer, Heidelberg (1991)Google Scholar
  30. 30.
    Nielsen, J.B.: On Protocol Security in the Cryptographic Model. Ph.D. thesis, Aarhus University (2003)Google Scholar
  31. 31.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreements in the presence of faults. Journal of the ACM 27(2), 228–234 (1980)MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Pfitzmann, B., Waidner, M.: A model for asynchronous reactive systems and its application to secure message transmission. In: IEEE Symposium on Security and Privacy (S&P 2001), pp. 184–201. IEEE CS, Los Alamitos (2001)CrossRefGoogle Scholar
  33. 33.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: ACM STOC 1989, pp. 73–85. ACM Press, New York (1989)Google Scholar
  34. 34.
    De Santis, A., Persiano, G.: Zero-knowledge proofs of knowledge without interaction (extended abstract). In: IEEE Symposium on Foundations of Computer Science (FOCS 1992), pp. 427–436. IEEE CS, Los Alamitos (1992)Google Scholar
  35. 35.
    Shamir, A.: How to share a secret. Communications of the ACM 22(11) (1979)Google Scholar
  36. 36.
    von Ahn, L., Bortz, A., Hopper, N.J.: k-Anonymous message transmission. In: ACM Conference on Computer and Communication Security – CCS 2003, pp. 122–130. ACM Press, New York (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alejandro Hevia
    • 1
  1. 1.Department of Computer ScienceUniversidad de ChileSantiagoChile

Personalised recommendations