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Constant-Round Black-Box Construction of Composable Multi-Party Computation Protocol

  • Susumu Kiyoshima
  • Yoshifumi Manabe
  • Tatsuaki Okamoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8349)

Abstract

We present the first general MPC protocol that satisfies the following: (1) the construction is black-box, (2) the protocol is universally composable in the plain model, and (3) the number of rounds is constant. The security of our protocol is proven in angel-based UC security under the assumption of the existence of one-way functions that are secure against sub-exponential-time adversaries and constant-round semi-honest oblivious transfer protocols that are secure against quasi-polynomial-time adversaries. We obtain the MPC protocol by constructing a constant-round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions that are secure against sub-exponential-time adversaries. To justify the use of such a sub-exponential hardness assumption in obtaining our constant-round CCA-secure commitment scheme, we show that if black-box reductions are used, there does not exist any constant-round CCA-secure commitment scheme under any falsifiable polynomial-time hardness assumptions.

Keywords

Commitment Scheme Oblivious Transfer Hiding Property Hardness Assumption Round Complexity 
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.

References

  1. 1.
    Barak, B., Sahai, A.: How to play almost any mental game over the net—concurrent composition via super-polynomial simulation. In: FOCS, pp. 543–552 (2005)Google Scholar
  2. 2.
    Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136–145 (2001)Google Scholar
  3. 3.
    Canetti, R., Fischlin, M.: Universally composable commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge. In: STOC, pp. 235–244 (2000)Google Scholar
  5. 5.
    Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-box concurrent zero-knowledge requires (almost) logarithmically many rounds. SIAM J. Comput. 32(1), 1–47 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Canetti, R., Kushilevitz, E., Lindell, Y.: On the limitations of universally composable two-party computation without set-up assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 68–86. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: FOCS, pp. 541–550 (2010)Google Scholar
  8. 8.
    Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: STOC, pp. 494–503 (2002)Google Scholar
  9. 9.
    Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Black-box construction of a non-malleable encryption scheme from any semantically secure one. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 427–444. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: Simple, black-box constructions of adaptively secure protocols. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 387–402. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Garg, S., Goyal, V., Jain, A., Sahai, A.: Concurrently secure computation in constant rounds. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 99–116. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: STOC, pp. 99–108 (2011)Google Scholar
  14. 14.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game or a completeness theorem for protocols with honest majority. In: STOC. pp. 218–229 (1987)Google Scholar
  15. 15.
    Goyal, V.: Constant round non-malleable protocols using one way functions. In: STOC, pp. 695–704 (2011)Google Scholar
  16. 16.
    Goyal, V.: Non-black-box simulation in the fully concurrent setting. In: STOC, pp. 221–230 (2013)Google Scholar
  17. 17.
    Goyal, V., Lin, H., Pandey, O., Pass, R., Sahai, A.: Round-efficient concurrently composable secure computation via a robust extraction lemma. Cryptology ePrint Archive, Report 2012/652 (2012), http://eprint.iacr.org/
  18. 18.
    Haitner, I.: Semi-honest to malicious oblivious transfer - the black-box way. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 412–426. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Haitner, I., Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-box constructions of protocols for secure computation. SIAM J. Comput. 40(2), 225–266 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-box constructions for secure computation. In: STOC, pp. 99–108 (2006)Google Scholar
  21. 21.
    Lin, H.: Concurrent Security. Ph.D. thesis, Cornell University (2011)Google Scholar
  22. 22.
    Lin, H., Pass, R.: Non-malleability amplification. In: STOC, pp. 189–198 (2009)Google Scholar
  23. 23.
    Lin, H., Pass, R.: Black-box constructions of composable protocols without set-up. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 461–478. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  25. 25.
    Malkin, T., Moriarty, R., Yakovenko, N.: Generalized environmental security from number theoretic assumptions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 343–359. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  26. 26.
    Micciancio, D., Ong, S.J., Sahai, A., Vadhan, S.: Concurrent zero knowledge without complexity assumptions. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 1–20. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  27. 27.
    Naor, M.: Bit commitment using pseudorandomness. J. Cryptology 4(2), 151–158 (1991)CrossRefzbMATHGoogle Scholar
  28. 28.
    Naor, M.: On cryptographic assumptions and challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  29. 29.
    Pass, R.: Simulation in quasi-polynomial time, and its application to protocol composition. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 160–176. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  30. 30.
    Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: STOC, pp. 232–241 (2004)Google Scholar
  31. 31.
    Pass, R., Lin, H., Venkitasubramaniam, M.: A unified framework for UC from only OT. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 699–717. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  32. 32.
    Pass, R., Venkitasubramaniam, M.: On constant-round concurrent zero-knowledge. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 553–570. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  33. 33.
    Pass, R., Wee, H.: Black-box constructions of two-party protocols from one-way functions. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 403–418. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  34. 34.
    Pass, R., Wee, H.: Constant-round non-malleable commitments from sub-exponential one-way functions. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 638–655. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  35. 35.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS, pp. 366–375 (2002)Google Scholar
  36. 36.
    Prabhakaran, M., Sahai, A.: New notions of security: Achieving aniversal composability without trusted setup. In: STOC, pp. 242–251 (2004)Google Scholar
  37. 37.
    Wee, H.: Black-box, round-efficient secure computation via non-malleability amplification. In: FOCS, pp. 531–540 (2010)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Susumu Kiyoshima
    • 1
  • Yoshifumi Manabe
    • 2
  • Tatsuaki Okamoto
    • 1
  1. 1.NTT Secure Platform LaboratoriesJapan
  2. 2.Kogakuin UniversityJapan

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