Journal of Cryptology

, Volume 32, Issue 2, pp 393–434 | Cite as

Non-black-box Simulation in the Fully Concurrent Setting, Revisited

  • Susumu KiyoshimaEmail author


We give a new proof of the existence of \(O(n^{\epsilon })\)-round public-coin concurrent zero-knowledge arguments for \(\mathcal {NP}\), where \(\epsilon >0\) is an arbitrary constant. The security is proven in the plain model under the assumption that collision-resistant hash functions exist. The existence of such concurrent zero-knowledge arguments was previously proven by Goyal (STOC’13) in the plain model under the same assumption. In the proof, we use a new variant of the non-black-box simulation technique of Barak (FOCS’01). An important property of our simulation technique is that the simulator runs in a “straight-line” manner in the fully concurrent setting. Compared with the simulation technique of Goyal, which also has such a property, the analysis of our simulation technique is (arguably) simpler.


Zero-knowledge proofs Concurrent zero-knowledge Non-black-box simulation 



The author greatly thanks the anonymous reviewers of Journal of Cryptology and TCC 2015 for their useful comments about the presentation of this paper. I also thank an anonymous reviewer of TCC 2015 for pointing out an error that I made in an earlier version of this paper.


  1. 1.
    S. Arora, S. Safra, Probabilistic checking of proofs: a new characterization of np. J. ACM, 45(1), 70–122 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    B. Barak, How to go beyond the black-box simulation barrier, in FOCS, pp. 106–115 (2001)Google Scholar
  3. 3.
    G. Brassard, D. Chaum, C. Crépeau, Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Bellare, O. Goldreich, On defining proofs of knowledge, in CRYPTO, pp. 390–420 (1992)Google Scholar
  5. 5.
    B. Barak, O. Goldreich, Universal arguments and their applications. SIAM J. Comput. 38(5), 1661–1694 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    B. Barak, O. Goldreich, S. Goldwasser, Y. Lindell, Resettably-sound zero-knowledge and its applications, in FOCS, pp. 116–125 (2001)Google Scholar
  7. 7.
    M. Blum, How to prove a theorem so no one else can claim it, in The International Congress of Mathematicians, pp. 1444–1451 (1986)Google Scholar
  8. 8.
    N. Bitansky, O. Paneth, From the impossibility of obfuscation to a new non-black-box simulation technique, in FOCS, pp. 223–232 (2012)Google Scholar
  9. 9.
    N. Bitansky, O. Paneth, On the impossibility of approximate obfuscation and applications to resettable cryptography, in STOC, pp. 241–250 (2013)Google Scholar
  10. 10.
    N. Bitansky, O. Paneth, On non-black-box simulation and the impossibility of approximate obfuscation. SIAM J. Comput 44(5), 1325–1383 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Bellare, B.S. Yee, Forward-security in private-key cryptography, in CT-RSA, pp. 1–18 (2003)Google Scholar
  12. 12.
    R. Canetti, O. Goldreich, S. Goldwasser, S. Micali, Resettable zero-knowledge, in STOC, pp. 235–244 (2000)Google Scholar
  13. 13.
    R. Canetti, J. Kilian, E. Petrank, A. Rosen, Black-box concurrent zero-knowledge requires (almost) logarithmically many rounds. SIAM J. Comput. 32(1), 1–47 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    R. Canetti, H. Lin, O. Paneth, Public-coin concurrent zero-knowledge in the global hash model, in TCC, pp. 80–99 (2013)Google Scholar
  15. 15.
    K.-M. Chung, H. Lin, R. Pass, Constant-round concurrent zero knowledge from P-certificates, in FOCS, pp. 50–59 (2013)Google Scholar
  16. 16.
    K.-M. Chung, H. Lin, R. Pass, Constant-round concurrent zero-knowledge from indistinguishability obfuscation, in CRYPTO, pp. 287–307 (2015)Google Scholar
  17. 17.
    Y. Deng, V. Goyal, A. Sahai, Resolving the simultaneous resettability conjecture and a new non-black-box simulation strategy, in FOCS, pp. 251–260 (2009)Google Scholar
  18. 18.
    C. Dwork, M. Naor, A. Sahai, Concurrent zero-knowledge. J. ACM 51(6), 851–898 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    U. Feige, A. Shamir, Witness indistinguishable and witness hiding protocols, in STOC, pp. 416–426 (1990)Google Scholar
  20. 20.
    V. Goyal, D. Gupta, A. Sahai, Concurrent secure computation via non-black box simulation, in CRYPTO, pp. 23–42 (2015)Google Scholar
  21. 21.
    O. Goldreich, H. Krawczyk, On the composition of zero-knowledge proof systems. SIAM J. Comput. 25(1), 169–192 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186–208 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    O. Goldreich, S. Micali, A. Wigderson, Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38(3), 691–729 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    V. Goyal, Non-black-box simulation in the fully concurrent setting, in STOC, pp. 221–230 (2013)Google Scholar
  25. 25.
    J. Htad, R. Impagliazzo, L.A. Levin, M. Luby, A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    J. Kilian, E. Petrank, Concurrent and resettable zero-knowledge in poly-loalgorithm rounds, in STOC, pp. 560–569 (2001)Google Scholar
  27. 27.
    S. Micali, Computationally sound proofs. SIAM J. Comput. 30(4), 1253–1298 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    M. Naor, Bit commitment using pseudorandomness. J. Cryptol. 4(2), 151–158 1991.CrossRefzbMATHGoogle Scholar
  29. 29.
    O. Pandey, M. Prabhakaran, A. Sahai, Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for NP, in TCC, pp. 638–667 (2015)Google Scholar
  30. 30.
    R. Pass, A. Rosen, New and improved constructions of non-malleable cryptographic protocols, in STOC, pp. 533–542 (2005)Google Scholar
  31. 31.
    M. Prabhakaran, A. Rosen, A. Sahai, Concurrent zero knowledge with logarithmic round-complexity, in FOCS, pp. 366–375 (2002)Google Scholar
  32. 32.
    R. Pass, A. Rosen, W.-L. D. Tseng, Public-coin parallel zero-knowledge for NP. J. Cryptol. 26(1), 1–10 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    R. Pass, W.-L.D. Tseng, D. Wikstrm, On the composition of public-coin zero-knowledge protocols, in CRYPTO, pp. 160–176 (2009)Google Scholar
  34. 34.
    R. Richardson, J. Kilian, On the concurrent composition of zero-knowledge proofs, in EUROCRYPT, pp. 415–431 (1999)Google Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

Personalised recommendations