Scalable Secure Multiparty Computation

  • Ivan Damgård
  • Yuval Ishai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4117)


We present the first general protocol for secure multiparty computation which is scalable, in the sense that the amortized work per player does not grow, and in some natural settings even vanishes, with the number of players. Our protocol is secure against an active adversary which may adaptively corrupt up to some constant fraction of the players. The protocol can be implemented in a constant number rounds assuming the existence of a “computationally simple” pseudorandom generator, or in a small non-constant number of rounds assuming an arbitrary pseudorandom generator.


Linear Code Pseudorandom Generator Replication Pattern Secure Multiparty Computation Output 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.: Cryptography in NC 0. In: Proc. FOCS 2004, pp. 165–175 (2004)Google Scholar
  2. 2.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Computationally private randomizing polynomials and their applications. In: Proc. CCC 2005, pp. 260–274 (2005)Google Scholar
  3. 3.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: On Pseudorandom Generators with Linear Stretch in NC0 . In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 260–271. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Barkol, O., Ishai, Y.: Secure Computation of Constant-Depth Circuits with Applications to Database Search Problems. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 395–411. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Beaver, D.: Efficient Multiparty Protocols Using Circuit Randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992)Google Scholar
  6. 6.
    Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P.: Security with low communication overhead. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 62–76. Springer, Heidelberg (1991)Google Scholar
  7. 7.
    Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols (extended abstract). In: Proc. STOC 1990, pp. 503–513 (1990)Google Scholar
  8. 8.
    Beerliová-Trubíniová, Z., Hirt, M.: Efficient Multi-party Computation with Dispute Control. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 305–328. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proc. STOC 1988, pp. 1–10 (1988)Google Scholar
  10. 10.
    Canetti, R.: Security and composition of multiparty cryptographic protocols. J. of Cryptology 13(1), 143–202 (2000)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Canetti, R.: Universally Composable Security: A New Paradigm for Cryptographic Protocols. In: Proc. FOCS 2001, pp. 136–145 (2001)Google Scholar
  12. 12.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols (extended abstract). In: Proc. STOC 1988, pp. 11–19 (1988)Google Scholar
  13. 13.
    Cleve, R.: Limits on the Security of Coin Flips when Half the Processors Are Faulty (Extended Abstract). In: Proc. STOC 1986, pp. 364–369 (1986)Google Scholar
  14. 14.
    Cramer, R., Damgård, I.B., 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
  15. 15.
    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
  16. 16.
    Damgård, I.B., Ishai, Y.: Constant-Round Multiparty Computation Using a Black-Box Pseudorandom Generator. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 378–394. Springer, Heidelberg (2005)Google Scholar
  17. 17.
    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
  18. 18.
    Even, S., Goldreich, O., Lempel, A.: A Randomized Protocol for Signing Contracts. Communications of the ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Feldman, P., Micali, S.: An Optimal Algorithm for Synchronous Byzantine Agreement. SIAM. J. Computing 26(2), 873–933 (1997)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Franklin, M.K., Haber, S.: Joint Encryption and Message-Efficient Secure Computation. In: Proc. Crypto 1993, pp. 266-277 (1993) (Full version in Journal of Cyptoglogy 9(4): 217-232 (1996))Google Scholar
  21. 21.
    Franklin, M.K., Yung, M.: Communication Complexity of Secure Computation. In: Proc. STOC 1992, pp. 699–710 (1992)Google Scholar
  22. 22.
    Gennaro, R., Ishai, Y., Kushilevitz, E., Rabin, T.: The Round Complexity of Verifiable Secret Sharing and Secure Multicast. In: Proc. STOC 2001, pp. 580–589 (2001)Google Scholar
  23. 23.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game (extended abstract). In: Proc. STOC 1987, pp. 218–229 (1987)Google Scholar
  24. 24.
    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
  25. 25.
    Hirt, M., Maurer, U.M., Przydatek, B.: Efficient Secure Multi-party Computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  26. 26.
    Hirt, M., Nielsen, J.B.: Upper Bounds on the Communication Complexity of Optimally Resilient Cryptographic Multiparty Computation. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 79–99. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Hirt, M., Nielsen, J.B.: Robust Multiparty Computation with Linear Communication Complexity. These proceedingsGoogle Scholar
  28. 28.
    Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: Proc. FOCS 2000, pp. 294–304 (2000)Google Scholar
  29. 29.
    Jakobsson, M., Juels, A.: Mix and Match: Secure Function Evaluation via Ciphertexts. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 162–177. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  30. 30.
    Katz, J., Koo, C.-Y.: On Expected Constant-Round Protocols for Byzantine Agreement. These proceedingsGoogle Scholar
  31. 31.
    Lindell, Y., Lysyanskaya, A., Rabin, T.: Sequential composition of protocols without simultaneous termination. In: Proc. PODC 2002, pp. 203–212 (2002)Google Scholar
  32. 32.
    Mossel, E., Shpilka, A., Trevisan, L.: On ε-biased generators in NC0. In: Proc. FOCS 2003, pp. 136–145 (2003)Google Scholar
  33. 33.
    Naor, J., Naor, M.: Small-bias probability spaces: Efficient constructions and applications. SIAM J. Comput. 22(4), 838–856 (1993) (Preliminary version in Proc. STOC 1990)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: Proc. STOC 2001, pp. 590–599 (2001)Google Scholar
  35. 35.
    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
  36. 36.
    Shamir, A.: How to share a secret. Commun. ACM 22(6), 612–613 (1979)MATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Yao, A.C.: How to generate and exchange secrets. In: Proc. FOCS 1986, pp. 162–167 (1986)Google Scholar
  38. 38.
    Zhang, Z., Liu, M.-l., Xiao, L.: Parallel Multi-party Computation from Linear Multi-secret Sharing Schemes. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 156–173. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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