Constant-Round Multiparty Computation Using a Black-Box Pseudorandom Generator

  • Ivan Damgård
  • Yuval Ishai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3621)


We present a constant-round protocol for general secure multiparty computation which makes a black-box use of a pseudorandom generator. In particular, the protocol does not require expensive zero-knowledge proofs and its communication complexity does not depend on the computational complexity of the underlying cryptographic primitive. Our protocol withstands an active, adaptive adversary corrupting a minority of the parties. Previous constant-round protocols of this type were only known in the semi-honest model or for restricted classes of functionalities.


Pseudorandom Generator Oblivious Transfer Secure Multiparty Computation Output Wire Input Wire 
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.


  1. 1.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. In: Proc. 20th Conference on Computational Complexity (2005)Google Scholar
  2. 2.
    Bar-Ilan, J., Beaver, D.: Non-cryptographic fault-tolerant computing in a constant number of rounds. In: Proc. 8th ACM PODC, pp. 201–209 (1989)Google Scholar
  3. 3.
    Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P.: Security with low communication overhead (extended abstract). In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 62–76. Springer, Heidelberg (1991)Google Scholar
  4. 4.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: Proc. of 22nd STOC, pp. 503–513 (1990)Google Scholar
  5. 5.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proc. of 20th STOC, pp. 1–10 (1988)Google Scholar
  6. 6.
    Cachin, C., Camenisch, J., Kilian, J., Muller, J.: One-round secure computation and secure autonomous mobile agents. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, p. 512. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. of Cryptology 13(1) (2000)Google Scholar
  8. 8.
    Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: FOCS 2001, pp. 136–145 (2001)Google Scholar
  9. 9.
    Cramer, R., Damgård, I.: Secure distributed linear algebra in a constant number of rounds. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 119. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Cramer, R., Damgård, I., Ishai, Y.: Share conversion, pseudorandom secret-sharing and applications to secure computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Cramer, R., Damgård, I., Maurer, U.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Cramer, R., Damgård, I., Nielsen, J.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Feige, U., Fiat, A., Shamir, A.: Zero-Knowledge Proofs of Identity. J. Cryptology 1(2), 77–94 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Feige, U., Kilian, J., Naor, M.: A minimal model for secure computation (extended abstract). In: Proc. 26th STOC, pp. 554–563. ACM, New York (1994)Google Scholar
  16. 16.
    Feldman, P., Micali, S.: An Optimal Algorithm for Synchronous Byzantine Agreement. SIAM. J. Computing 26(2), 873–933 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The Round Complexity of Verifiable Secret Sharing and Secure Multicast. In: Proceedings of the 33rd ACM Symp. on Theory of Computing (STOC 2001), pp. 580–589 (2001)Google Scholar
  18. 18.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: On 2-round secure multiparty computation. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, p. 178. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  19. 19.
    Gilboa, N., Ishai, Y.: Compressing cryptographic resources. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, p. 591. Springer, Heidelberg (1999)Google Scholar
  20. 20.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game (extended abstract). In: Proc. of 19th STOC, pp. 218–229 (1987)Google Scholar
  21. 21.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Hirt, M., Maurer, U.M.: Robustness for Free in Unconditional Multi-party Computation. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 101–118. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  23. 23.
    Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: Proc. 41st FOCS, pp. 294–304 (2000)Google Scholar
  24. 24.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of 21st Annual ACM Symposium on the Theory of Computing, pp. 44–61 (1989)Google Scholar
  25. 25.
    Katz, J., Ostrovsky, R.: Round-Optimal Secure Two-Party Computation. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 335–354. Springer, Heidelberg (2004)Google Scholar
  26. 26.
    Katz, J., Ostrovsky, R., Smith, A.: Round Efficiency of Multi-party Computation with a Dishonest Majority. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 578–595. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  27. 27.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Proc. 20th STOC, pp. 20–31 (1988)Google Scholar
  28. 28.
    Lindell, Y.: Parallel Coin-Tossing and Constant-Round Secure Two-Party Computation. J. Cryptology 16(3), 143–184 (2003); Preliminary version in Crypto 2001 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: Sequential composition of protocols without simultaneous termination. In: Proc. PODC 2002, pp. 203–212 (2002)Google Scholar
  30. 30.
    Lindell, Y., Pinkas, B.: A Proof of Yao’s Protocol for Secure Two-Party Computation. Cryptology ePrint Archive, Report 2004/175 (2004)Google Scholar
  31. 31.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proc. STOC 2001, pp. 590–599 (2001)Google Scholar
  32. 32.
    Naor, M., Pinkas, B., Sumner, R.: Privacy preserving auctions and mechanism design. In: Proc. 1st ACM Conference on Electronic Commerce, pp. 129–139 (1999)Google Scholar
  33. 33.
    Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: Proc. STOC 2004, pp. 232–241 (2004)Google Scholar
  34. 34.
    Pass, R., Rosen, A.: Bounded-Concurrent Secure Two-Party Computation in a Constant Number of Rounds. In: FOCS 2003 (2003)Google Scholar
  35. 35.
    Rabin, T., Ben-Or, M.: Verifiable Secret Sharing and Multiparty Protocols with Honest Majority. In: Proc. 21st STOC, pp. 73–85. ACM, New York (1989)Google Scholar
  36. 36.
    Reingold, O., Trevisan, L., Vadhan, S.P.: Notions of Reducibility between Cryptographic Primitives. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 1–20. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  37. 37.
    Rogaway, P.: The Round Complexity of Secure Protocols. PhD thesis, MIT (June 1991)Google Scholar
  38. 38.
    Shamir, A.: How to share a secret. Commun. ACM 22(6), 612–613 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Tate, S.R., Xu, K.: On garbled circuits and constant round secure function evaluation. CoPS Lab Technical Report 2003-02, University of North Texas (2003)Google Scholar
  40. 40.
    Yao, A.C.: How to generate and exchange secrets. In: Proc. 27th FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ivan Damgård
    • 1
  • Yuval Ishai
    • 2
  1. 1.Aarhus University 
  2. 2.Technion 

Personalised recommendations