Advertisement

Statistical Concurrent Non-malleable Zero-Knowledge from One-Way Functions

  • Susumu Kiyoshima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9216)

Abstract

Concurrent non-malleable zero-knowledge (\(\mathrm {CNMZK}\)) protocols are zero-knowledge protocols that are secure even when the adversary interacts with multiple provers and verifiers simultaneously. Recently, the first statistical \(\mathrm {CNMZK}\) argument for \(\mathcal {NP}\) was constructed by Orlandi et al. (TCC’14) under the DDH assumption.

In this paper, we construct a statistical \(\mathrm {CNMZK}\) argument for \(\mathcal {NP}\) assuming only the existence of one-way functions. The security is proven via black-box simulation, and the round complexity is \(\mathsf {poly}(n)\). Under the existence of collision-resistant hash functions, the round complexity can be reduced to \(\omega (\log n)\), which is essentially optimal for black-box concurrent zero-knowledge.

Keywords

Hybrid Simulator Commitment Scheme Main Thread Negligible Probability Hiding Property 
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., Prabhakaran, M., Sahai, A.: Concurrent non-malleable zero knowledge. In: FOCS, pp. 345–354 (2006)Google Scholar
  2. 2.
    Blum, M.: How to prove a theorem so no one else can claim it. In: International Congress of Mathematicians, pp. 1444–1451 (1987)Google Scholar
  3. 3.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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
  5. 5.
    Damgård, I., Pedersen, T.P., Pfitzmann, B.: Statistical secrecy and multibit commitments. IEEE Trans. Inf. Theory 44(3), 1143–1151 (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. J. ACM 51(6), 851–898 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Goyal, V., Lin, H., Pandey, O., Pass, R., Sahai, A.: Round-efficient concurrently composable secure computation via a robust extraction lemma. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part I. LNCS, vol. 9014, pp. 260–289. Springer, Heidelberg (2015) Google Scholar
  9. 9.
    Goyal, V., Moriarty, R., Ostrovsky, R., Sahai, A.: Concurrent statistical zero-knowledge arguments for NP from one way functions. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 444–459. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  10. 10.
    Haitner, I., Nguyen, M.-H., Ong, S.J., Reingold, O., Vadhan, S.P.: Statistically hiding commitments and statistical zero-knowledge arguments from any one-way function. SIAM J. Comput. 39(3), 1153–1218 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kiyoshima, S.: Round-efficient black-box construction of composable multi-party computation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 351–368. Springer, Heidelberg (2014) Google Scholar
  13. 13.
    Kiyoshima, S., Manabe, Y., Okamoto, T.: Constant-round black-box construction of composable multi-party computation protocol. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 343–367. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  14. 14.
    Lin, H., Pass, R.: Concurrent non-malleable zero knowledge with adaptive inputs. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 274–292. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    Lin, H., Pass, R., Tseng, W.-L.D., Venkitasubramaniam, M.: Concurrent non-malleable zero knowledge proofs. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 429–446. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  17. 17.
    Micciancio, D., Ong, S.J., Sahai, A., Vadhan, S.P.: 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
  18. 18.
    Naor, M.: Bit commitment using pseudorandomness. J. Cryptol. 4(2), 151–158 (1991)CrossRefzbMATHGoogle Scholar
  19. 19.
    Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC, pp. 33–43 (1989)Google Scholar
  20. 20.
    Orlandi, C., Ostrovsky, R., Rao, V., Sahai, A., Visconti, I.: Statistical concurrent non-malleable zero knowledge. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 167–191. Springer, Heidelberg (2014) CrossRefGoogle Scholar
  21. 21.
    Ostrovsky, R., Pandey, O., Visconti, I.: Efficiency preserving transformations for concurrent non-malleable zero knowledge. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 535–552. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  22. 22.
    Pass, R., Rosen, A.: New and improved constructions of non-malleable cryptographic protocols. In: STOC, pp. 533–542 (2005)Google Scholar
  23. 23.
    Pass, R., Tseng, W.-L.D., Venkitasubramaniam, M.: Concurrent zero knowledge, revisited. J. Cryptol. 27(1), 45–46 (2012)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Prabhakaran, M., Rosen, A., Sahai, A.: Concurrent zero knowledge with logarithmic round-complexity. In: FOCS, pp. 366–375 (2002)Google Scholar
  26. 26.
    Venkitasubramaniam, M.: On adaptively secure protocols. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 455–475. Springer, Heidelberg (2014) Google Scholar

Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  1. 1.NTT Secure Platform LaboratoriesTokyoJapan

Personalised recommendations