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What Security Can We Achieve Within 4 Rounds?

  • Carmit HazayEmail author
  • Muthuramakrishnan Venkitasubramaniam
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9841)

Abstract

Katz and Ostrovsky (Crypto 2004) proved that five rounds are necessary for stand-alone general black-box constructions of secure two-party protocols and at least four rounds are necessary if only one party needs to receive the output. Recently, Ostrovsky, Richelson and Scafuro (Crypto 2015) proved optimality of this result by showing how to realize arbitrary functionalities in four rounds where only one party receives the output via a black-box construction (and an extension to five rounds where both parties receive the output). In this paper we study the question of what security is achievable for stand-alone two-party protocols within four rounds.

We first provide a four-round two-party protocol for coin-tossing that achieves 1 / p-simulation security (i.e. simulation fails with probability at most \(1/p+{\mathsf{negl}}\)), in the presence of malicious corruptions. Next, we provide a four-round two-party protocol for general functionalities, where both parties receive the output, that achieves 1 / p-security in the presence of malicious adversaries corrupting one of the parties, and full security in the presence of non-aborting malicious adversaries corrupting the other party.

Next, we provide a three-round oblivious-transfer protocol, that achieves 1 / p-simulation security against arbitrary malicious senders, while simultaneously guaranteeing a meaningful notion of privacy against malicious corruptions of either party.

Finally, we show that the simulation-based security guarantees for our three-round protocols are optimal by proving that 1 / p-simulation security is impossible to achieve against both parties in three rounds or less when requiring some minimal guarantees on the privacy of their inputs.

Keywords

Secure computation Coin-tossing Oblivious transfer Round complexity 

References

  1. 1.
    Asokan, N., Shoup, V., Waidner, M.: Optimistic fair exchange of digital signatures. IEEE J. Sel. Areas Commun. 18(4), 593–610 (2000)CrossRefzbMATHGoogle Scholar
  2. 2.
    Aumann, Y., Lindell, Y.: Security against covert adversaries: efficient protocols for realistic adversaries. J. Cryptol. 23(2), 281–343 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Barak, B., Sahai, A.: How to play almost any mental game over the net - concurrent composition via super-polynomial simulation. IACR Cryptology ePrint Archive 2005:106 (2005)Google Scholar
  4. 4.
    Beaver, D.: Foundations of secure interactive computing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 377–391. Springer, Heidelberg (1992)Google Scholar
  5. 5.
    Bentov, I., Kumaresan, R.: How to use bitcoin to design fair protocols. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 421–439. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  6. 6.
    Blum, M.: How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, USA, pp. 1444–1451Google Scholar
  7. 7.
    Cleve, R.: Limits on the security of coin flips when half the processors are faulty (extended abstract). In: STOC, pp. 364–369 (1986)Google Scholar
  8. 8.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Garay, J.A., Katz, J., Tackmann, B., Zikas, V.: How fair is your protocol? A utility-based approach to protocol optimality. In: PODC, pp. 281–290 (2015)Google Scholar
  10. 10.
    Garg, S., Mukherjee, P., Pandey, O., Polychroniadou, A.: The exact round complexity of secure computation. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 448–476. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49896-5_16 CrossRefGoogle Scholar
  11. 11.
    Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    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
  13. 13.
    Gordon, S.D., Katz, J.: Partial fairness in secure two-party computation. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 157–176. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Halevi, S., Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. J. Cryptol. 25(1), 158–193 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hazay, C., Venkitasubramaniam, M.: What security can we achieve in 4-rounds? IACR Cryptology ePrint Arch. 2015, 797 (2015). http://eprint.iacr.org/2015/797 Google Scholar
  17. 17.
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Prabhakaran, M., Sahai, A.: Efficient non-interactive secure computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 406–425. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    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)CrossRefGoogle Scholar
  19. 19.
    Lindell, Y.: Parallel coin-tossing and constant-round secure two-party computation. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, p. 171. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    Micali, S.: Simple and fast optimistic protocols for fair electronic exchange. In: PODC, pp. 12–19 (2003)Google Scholar
  21. 21.
    Micali, S., Pass, R., Rosen, A.: Input-indistinguishable computation. In: FOCS, pp. 367–378 (2006)Google Scholar
  22. 22.
    Micali, S., Rogaway, P.: Secure computation. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 392–404. Springer, Heidelberg (1992)Google Scholar
  23. 23.
    Moran, T., Naor, M., Segev, G.: An optimally fair coin toss. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 1–18. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Naor, M., Pinkas, B.: Efficient oblivious transfer protocols. In: SODA, pp. 448–457 (2001)Google Scholar
  25. 25.
    Ostrovsky, R., Richelson, S., Scafuro, A.: Round-optimal black-box two-party computation. IACR Cryptology ePrint Archive 2015:553 (2015)Google Scholar
  26. 26.
    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
  27. 27.
    Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
  28. 28.
    Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  29. 29.
    Prabhakaran, M., Sahai, A.: New notions of security: achieving universal composability without trusted setup. In: STOC, pp. 242–251 (2004)Google Scholar
  30. 30.
    Yao, AC.-C.: How to generate and exchange secrets (extended abstract). In: FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Carmit Hazay
    • 1
    Email author
  • Muthuramakrishnan Venkitasubramaniam
    • 2
  1. 1.Faculty of EngineeringBar-Ilan UniversityRamat GanIsrael
  2. 2.University of RochesterRochesterUSA

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