Advertisement

Information-Theoretic Broadcast with Dishonest Majority for Long Messages

  • Wutichai ChongchitmateEmail author
  • Rafail Ostrovsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11239)

Abstract

Byzantine broadcast is a fundamental primitive for secure computation. In a setting with n parties in the presence of an adversary controlling at most t parties, while a lot of progress in optimizing communication complexity has been made for \(t < n/2\), little progress has been made for the general case \(t<n\), especially for information-theoretic security. In particular, all information-theoretic secure broadcast protocols for \(\ell \)-bit messages and \(t<n\) and optimal round complexity \({\mathcal {O}}(n)\) have, so far, required a communication complexity of \({\mathcal {O}}(\ell n^2)\). A broadcast extension protocol allows a long message to be broadcast more efficiently using a small number of single-bit broadcasts. Through broadcast extension, so far, the best achievable round complexity for \(t<n\) setting with the optimal communication complexity of \({\mathcal {O}}(\ell n)\) is \({\mathcal {O}}(n^4)\) rounds.

In this work, we construct a new broadcast extension protocol for \(t<n\) with information-theoretic security. Our protocol improves the round complexity to \({\mathcal {O}}(n^3)\) while maintaining the optimal communication complexity for long messages. Our result shortens the gap between the information-theoretic setting and the computational setting, and between the optimal communication protocol and the optimal round protocol in the information-theoretic setting for \(t<n\).

References

  1. 1.
    Beaver, D.: Correlated pseudorandomness and the complexity of private computations. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 479–488. ACM (1996)Google Scholar
  2. 2.
    Chaum, D., Roijakkers, S.: Unconditionally-secure digital signatures. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 206–214. Springer, Heidelberg (1991).  https://doi.org/10.1007/3-540-38424-3_15CrossRefGoogle Scholar
  3. 3.
    Dolev, D., Reischuk, R.: Bounds on information exchange for byzantine agreement. J. ACM (JACM) 32(1), 191–204 (1985)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dolev, D., Strong, H.R.: Authenticated algorithms for byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fitzi, M., Hirt, M.: Optimally efficient multi-valued byzantine agreement. In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Principles of Distributed Computing, pp. 163–168. ACM (2006)Google Scholar
  6. 6.
    Ganesh, C., Patra, A.: Optimal extension protocols for byzantine broadcast and agreement. IACR Cryptol. ePrint Arch. 2017, 63 (2017)Google Scholar
  7. 7.
    Hirt, M., Raykov, P.: Multi-valued byzantine broadcast: The \(t < n\) case. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 448–465. Springer, Berlin (2014).  https://doi.org/10.1007/978-3-662-45608-8_24CrossRefGoogle Scholar
  8. 8.
    Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending oblivious transfers efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-540-45146-4_9CrossRefGoogle Scholar
  9. 9.
    Liang, G., Vaidya, N.: Error-free multi-valued consensus with byzantine failures. In: Proceedings of the 30th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 11–20. ACM (2011)Google Scholar
  10. 10.
    Lindell, Y., Zarosim, H.: On the feasibility of extending oblivious transfer. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 519–538. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-36594-2_29CrossRefzbMATHGoogle Scholar
  11. 11.
    Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32009-5_40CrossRefGoogle Scholar
  12. 12.
    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).  https://doi.org/10.1007/978-3-642-25873-2_4CrossRefGoogle Scholar
  13. 13.
    Pease, M., Shostak, R., Lamport, L.: Reaching agreement in the presence of faults. J. ACM (JACM) 27(2), 228–234 (1980)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Pfitzmann, B., Waidner, M.: Unconditional byzantine agreement for any number of faulty processors. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 337–350. Springer, Heidelberg (1992).  https://doi.org/10.1007/3-540-55210-3_195CrossRefGoogle Scholar
  15. 15.
    Pfitzmann, B., Waidner, M.: Information-Theoretic Pseudosignatures and Byzantine Agreement for \(t > n/3\). IBM, Armonk (1996)Google Scholar
  16. 16.
    Turpin, R., Coan, B.A.: Extending binary byzantine agreement to multivalued byzantine agreement. Inf. Process. Lett. 18(2), 73–76 (1984)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of ScienceChulalongkorn UniversityBangkokThailand
  2. 2.Department of Computer Science and Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations