Abstract
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.
Chapter PDF
Similar content being viewed by others
References
Beaver, D.: Multiparty protocols tolerating half faulty processors. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 560–572. Springer, Heidelberg (1990)
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)
Blahut, R.E.: Principles and practice of information theory. Addison-Wesley, Reading (1988)
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)
Chaum, D.: The Dining Cryptographers Problem: Unconditional sender and recipient untraceability. Journal of Cryptology 1(1), 65–75 (1988)
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)
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)
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)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)
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)
Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)
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)
Dolev, D., Strong, H.R.: Authenticated algorithms for Byzantine agreement. SIAM Journal on Computing 12(4), 656–666 (1983)
Fischer, M.J., Lynch, N.A., Merritt, M.: Easy impossibility proofs for distributed consensus problems. Distributed Computing 1, 26–39 (1986)
Fitzi, M., Gisin, N., Maurer, U.: Quantum solution to the Byzantine agreement problem. Physical Review Letters 87(21), 7901–7901 (2001)
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)
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)
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)
Lamport, L.: Constructing digital signatures from a one-way function. Technical Report SRI-CSL-98, SRI International Computer Science Laboratory (1979)
Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Transactions on Programming Languages and Systems 4(3), 382–401 (1982)
Maurer, U.: Secret key agreement by public discussion. IEEE Transaction on Information Theory 39(3), 733–742 (1993)
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)
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)
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)
Pfitzmann, B., Waidner, M.: Information-theoretic pseudosignatures and Byzantine agreement for t >= n/3. Technical Report RZ 2882 (#90830), IBM Research (1996)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fitzi, M., Wolf, S., Wullschleger, J. (2004). Pseudo-signatures, Broadcast, and Multi-party Computation from Correlated Randomness. In: Franklin, M. (eds) Advances in Cryptology – CRYPTO 2004. CRYPTO 2004. Lecture Notes in Computer Science, vol 3152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28628-8_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-28628-8_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22668-0
Online ISBN: 978-3-540-28628-8
eBook Packages: Springer Book Archive