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Concurrent Zero Knowledge in the Bounded Player Model

  • Vipul Goyal
  • Abhishek Jain
  • Rafail Ostrovsky
  • Silas Richelson
  • Ivan Visconti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

In this paper we put forward the Bounded Player Model for secure computation. In this new model, the number of players that will ever be involved in secure computations is bounded, but the number of computations is not a priori bounded. Indeed, while the number of devices and people on this planet can be realistically estimated and bounded, the number of computations these devices will run can not be realistically bounded. Further, we note that in the bounded player model, in addition to no a priori bound on the number of sessions, there is no synchronization barrier, no trusted party, and simulation must be performed in polynomial time.

In this setting, we achieve concurrent Zero Knowledge (cZK) with sub-logarithmic round complexity. Our security proof is (necessarily) non-black-box, our simulator is “straight-line” and works as long as the number of rounds is ω(1).

We further show that unlike previously studied relaxations of the standard model (e.g., bounded number of sessions, timing assumptions, super-polynomial simulation), concurrent-secure computation is still impossible to achieve in the Bounded Player model. This gives evidence that our model is “closer” to the standard model than previously studied models, and study of this model might shed light on constructing round efficient concurrent zero-knowledge in the standard model as well.

Keywords

Proof System Commitment Scheme Argument System Common Reference String Random Tape 
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.
    Agrawal, S., Goyal, V., Jain, A., Prabhakaran, M., Sahai, A.: New Impossibility Results for Concurrent Composition and a Non-interactive Completeness Theorem for Secure Computation. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 443–460. Springer, Heidelberg (2012)Google Scholar
  2. 2.
    Barak, B.: How to go beyond the black-box simulation barrier. In: FOCS, pp. 106–115 (2001)Google Scholar
  3. 3.
    Barak, B., Goldreich, O.: Universal arguments and their applications. In: IEEE Conference on Computational Complexity, pp. 194–203 (2002)Google Scholar
  4. 4.
    Barak, B., Lindell, Y.: Strict polynomial-time in simulation and extraction. In: STOC, pp. 484–493 (2002)Google Scholar
  5. 5.
    Barak, B., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero knowledge. In: FOCS, pp. 345–354 (2006)Google 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, pp. 1444–1451 (1987)Google Scholar
  7. 7.
    Blum, M., Santis, A.D., Micali, S., Persiano, G.: Noninteractive zero-knowledge. SIAM J. Comput. 20(6), 1084–1118 (1991)MathSciNetCrossRefzbMATHGoogle 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.
    Canetti, R.: Universally composable signature, certification, and authentication. In: CSFW (2004)Google Scholar
  10. 10.
    Canetti, R., Goldreich, O., Goldwasser, S., Micali, S.: Resettable zero-knowledge (extended abstract). In: STOC, pp. 235–244 (2000)Google Scholar
  11. 11.
    Canetti, R., Kilian, J., Petrank, E., Rosen, A.: Black-box concurrent zero-knowledge requires \(\stackrel{\sim}{\Omega}(\log n)\) rounds. In: STOC, pp. 570–579 (2001)Google Scholar
  12. 12.
    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
  13. 13.
    Di Crescenzo, G., Ostrovsky, R.: On Concurrent Zero-Knowledge with Pre-processing (Extended Abstract). In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 485–502. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Di Crescenzo, G., Persiano, G., Visconti, I.: Constant-Round Resettable Zero Knowledge with Concurrent Soundness in the Bare Public-Key Model. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 237–253. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Di Crescenzo, G., Visconti, I.: Concurrent Zero Knowledge in the Public-Key Model. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 816–827. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. In: STOC, pp. 409–418 (1998)Google Scholar
  17. 17.
    Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: FOCS, pp. 308–317 (1990)Google Scholar
  18. 18.
    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
  19. 19.
    Garg, S., Kumarasubramanian, A., Ostrovsky, R., Visconti, I.: Impossibility Results for Static Input Secure Computation. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 424–442. Springer, Heidelberg (2012)Google Scholar
  20. 20.
    Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for np. J. Cryptology 9(3), 167–190 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: STOC, pp. 291–304 (1985)Google Scholar
  22. 22.
    Goyal, V., Jain, A., Ostrovsky, R., Richelson, S., Visconti, I.: Concurrent zero knowledge in the bounded player model. IACR Cryptology ePrint Archive 2012, 279 (2012)Google Scholar
  23. 23.
    Kidron, D., Lindell, Y.: Impossibility results for universal composability in public-key models and with fixed inputs. J. Cryptology 24(3), 517–544 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Kilian, J., Micali, S., Ostrovsky, R.: Minimum resource zero-knowledge proofs (extended abstract). In: FOCS, pp. 474–479 (1989)Google Scholar
  25. 25.
    Kilian, J., Petrank, E.: Concurrent and resettable zero-knowledge in poly-loalgorithm rounds. In: STOC, pp. 560–569 (2001)Google Scholar
  26. 26.
    Lin, H., Pass, R., Venkitasubramaniam, M.: A unified framework for concurrent security: universal composability from stand-alone non-malleability. In: STOC, pp. 179–188 (2009)Google Scholar
  27. 27.
    Lindell, Y.: Lower Bounds for Concurrent Self Composition. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 203–222. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Micali, S., Pass, R.: Precise zero knowledge (2007)Google Scholar
  29. 29.
    Micali, S., Reyzin, L.: Soundness in the Public-Key Model. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 542–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  30. 30.
    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
  31. 31.
    Pass, R.: Bounded-concurrent secure multi-party computation with a dishonest majority. In: STOC, pp. 232–241 (2004)Google Scholar
  32. 32.
    Pass, R., Rosen, A.: New and improved constructions of non-malleable cryptographic protocols. In: STOC, pp. 533–542 (2005)Google Scholar
  33. 33.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS, pp. 366–375 (2002)Google Scholar
  34. 34.
    Richardson, R., Kilian, J.: On the Concurrent Composition of Zero-Knowledge Proofs. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 415–431. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  35. 35.
    Santis, A.D., Persiano, G.: Zero-knowledge proofs of knowledge without interaction. In: FOCS, pp. 427–436. IEEE Computer Society (1992)Google Scholar
  36. 36.
    Scafuro, A., Visconti, I.: On Round-Optimal Zero Knowledge in the Bare Public-Key Model. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 153–171. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  37. 37.
    Visconti, I.: Efficient Zero Knowledge on the Internet. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 22–33. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Vipul Goyal
    • 1
  • Abhishek Jain
    • 2
  • Rafail Ostrovsky
    • 3
  • Silas Richelson
    • 3
  • Ivan Visconti
    • 4
  1. 1.Microsoft ResearchIndia
  2. 2.MIT and Boston UniversityUSA
  3. 3.UCLAUSA
  4. 4.University of SalernoItaly

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