Pseudo-signatures, Broadcast, and Multi-party Computation from Correlated Randomness

  • Matthias Fitzi
  • Stefan Wolf
  • Jürg Wullschleger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3152)


Unconditionally secure multi-party computations in general, and broadcast in particular, are impossible if any third of the players can be actively corrupted and if no additional information-theoretic primitive is given. In this paper, we relativize this pessimistic result by showing that such a primitive can be as simple as noisy communication channels between the players or weakly correlated pieces of information. We consider the scenario where three players have access to random variables X, Y, and Z, respectively, and give the exact condition on the joint distribution P XYZ under which unconditional broadcast is possible. More precisely, we show that this condition characterizes the possibility of realizing so-called pseudo-signatures between the players. As a consequence of our results, we can give conditions for the possibility of achieving unconditional broadcast between n players and any minority of cheaters and, hence, general multi-party computation under the same condition.


Unconditional security pseudo-signatures broadcast multi-party computation information theory 


  1. 1.
    Beaver, D.: Multiparty protocols tolerating half faulty processors. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 560–572. Springer, Heidelberg (1990)Google Scholar
  2. 2.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 1–10. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  3. 3.
    Blahut, R.E.: Principles and practice of information theory. Addison-Wesley, Reading (1988)Google Scholar
  4. 4.
    Bos, J.N.E., den Boer, B.: Detection of disrupters in the DC protocol. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 320–327. Springer, Heidelberg (1990)Google Scholar
  5. 5.
    Chaum, D.: The Dining Cryptographers Problem: Unconditional sender and recipient untraceability. Journal of Cryptology 1(1), 65–75 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM Press, New York (1988)CrossRefGoogle Scholar
  7. 7.
    Chaum, D., Roijakkers, S.: Unconditionally secure digital signatures. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 206–214. Springer, Heidelberg (1991)Google Scholar
  8. 8.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: ACM Symposium on Theory of Computing (STOC 1986), pp. 364–369. ACM Press, New York (1986)Google Scholar
  9. 9.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)zbMATHCrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Dolev, D., Strong, H.R.: Polynomial algorithms for multiple processor agreement. In: Proceedings of the 14th Annual ACM Symposium on Theory of Computing (STOC 1982), pp. 401–407 (1982)Google Scholar
  13. 13.
    Dolev, D., Strong, H.R.: Authenticated algorithms for Byzantine agreement. SIAM Journal on Computing 12(4), 656–666 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. Distributed Computing 1, 26–39 (1986)zbMATHCrossRefGoogle Scholar
  15. 15.
    Fitzi, M., Gisin, N., Maurer, U.: Quantum solution to the Byzantine agreement problem. Physical Review Letters 87(21), 7901–7901 (2001)CrossRefGoogle Scholar
  16. 16.
    Fitzi, M., Gisin, N., Maurer, U.M., von Rotz, O.: Unconditional Byzantine agreement and multi-party computation secure against dishonest minorities from scratch. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 482–501. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    Fitzi, M., Maurer, U.: From partial consistency to global broadcast. In: 32nd Annual Symposium on Theory of Computing, STOC 2000, pp. 494–503. ACM, New York (2000)CrossRefGoogle Scholar
  18. 18.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC 1987), pp. 218–229. ACM Press, New York (1987)Google Scholar
  19. 19.
    Lamport, L.: Constructing digital signatures from a one-way function. Technical Report SRI-CSL-98, SRI International Computer Science Laboratory (1979) Google Scholar
  20. 20.
    Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)zbMATHCrossRefGoogle Scholar
  21. 21.
    Maurer, U.: Secret key agreement by public discussion. IEEE Transaction on Information Theory 39(3), 733–742 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Maurer, U.M.: Information-theoretically secure secret-key agreement by NOT authenticated public discussion. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 209–225. Springer, Heidelberg (1997)Google Scholar
  23. 23.
    Maurer, U.M., Wolf, S.: Secret-key agreement over unauthenticated public channels—Part I: Definitions and a completeness result. IEEE Transactions on Information Theory 49, 822–831 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Maurer, U.M., Wolf, S.: Secret-key agreement over unauthenticated public channels—Part II: The simulatability condition. IEEE Transactions on Information Theory 49, 832–838 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Pfitzmann, B., Waidner, M.: Information-theoretic pseudosignatures and Byzantine agreement for t >= n/3. Technical Report RZ 2882 (#90830), IBM Research (1996)Google Scholar
  26. 26.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 73–85 (1989)Google Scholar
  27. 27.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 1982), pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Matthias Fitzi
    • 1
  • Stefan Wolf
    • 2
  • Jürg Wullschleger
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaDavisUSA
  2. 2.Département d’Informatique et R.O.Université de MontréalCanada

Personalised recommendations