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Automata, Languages and Programming pp 271–280Cite as

Non-interactive Zero-Knowledge: A Low-Randomness Characterization of NP (Extended Abstract)

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Abstract

We show that any language L in NP has a non-interactive zero-knowledge proof system which uses Θ(log(1/s) + n ∈) random bits, where s is the soundness error, n the length of the input and ε can be any constant > 0. In order to achieve this result, we formulate and investigate the problem of randomness-efficient error reduction for non-interactive zero-knowledge proofs, which generalizes the analogue and well-studied problem for BPP computation.

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References

  1. M. Ajtai, J. Komlos, and E. Szemeredi, Deterministic Simulation in Logspace, Proc. of STOC 87.

    Google Scholar 

  2. M. Ben-Or, S. Goldwasser, J. Kilian and A. Wigderson, Multi-Prover Interactive Proofs: How to Remove Intractability Assumptions, Proc. of STOC 88.

    Google Scholar 

  3. M. Blum, A. De Santis, S. Micali, and G. Persiano, Non-Interactive Zero-Knowledge, SIAM Journal of Computing, vol. 20, no. 6, Dec 1991, pp. 1084–1118.

    Article  Google Scholar 

  4. M. Blum, P. Feldman, and S. Micali, Non-Interactive Zero-Knowledge and Applications, Proc. of STOC 88.

    Google Scholar 

  5. M. Blum and S. Micali, How to Generate Cryptographically Strong Sequence of Pseudo-Random Bits, SIAM J. on Computing, vol. 13, no. 4, 1984, pp. 850–864.

    Article  MathSciNet  Google Scholar 

  6. J. Boyar and R. Peralta, Short Discreet Proofs, Proc. of EUROCRYPT 96.

    Google Scholar 

  7. A. Cohen and A. Wigderson, Dispersers, Deterministic Amplification and Weak Random Sources, Proc. of FOCS 89.

    Google Scholar 

  8. I. Damgaard, Non-interactive circuit-based proofs and non-interactive perfect zero-knowledge with preprocessing, Proc. of EUROCRYPT 92.

    Google Scholar 

  9. A. De Santis, G. Di Crescenzo, and G. Persiano, The Knowledge Complexity of Quadratic Residuosity Languages, in Theoretical Computer Science, Vol. 132, pp. 291–317 (1994).

    Article  MathSciNet  Google Scholar 

  10. A. De Santis, G. Di Crescenzo, and G. Persiano, Randomness-Efficient Non-Interactive Zero-Knowledge, Proc. of ICALP 97.

    Google Scholar 

  11. A. De Santis and M. Yung, Cryptographic applications of the meta-proof and the many-prover systems, Proc. of CRYPTO 90.

    Google Scholar 

  12. G. Di Crescenzo, Recycling Random Bits for Composed Perfect Zero-Knowledge, Proc. of EUROCRYPT 95.

    Google Scholar 

  13. U. Feige, S. Goldwasser, L. Lovasz, S. Safra and M. Szegedy, Approximating Clique is Almost NP-complete, Proc. of FOCS 91.

    Google Scholar 

  14. U. Feige, D. Lapidot, and A. Shamir, Multiple Non-Interactive Zero-Knowledge Proofs Based on a Single Random String, Proc. of STOC 90.

    Google Scholar 

  15. Gillman, A Chernoff Bound for Random Walks on Expanders, Proc. of STOC 93.

    Google Scholar 

  16. M. Garey e D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness, W.H. Freeman & Co., New York, 1979.

    MATH  Google Scholar 

  17. O. Goldreich, S. Micali, and A. Wigderson, Proofs that Yield Nothing but their Validity or All Languages in NP Have Zero-Knowledge Proof Systems, Journal of the ACM, vol. 38, n. 1, 1991, pp. 691–729.

    MathSciNet  MATH  Google Scholar 

  18. O. Goldreich and Y. Oren, Definitions and Properties of Zero-Knowledge Proof Systems, Journal of Cryptology, vol. 7, 1994, pp. 1–32.

    Article  MathSciNet  Google Scholar 

  19. S. Goldwasser, and S. Micali, Probabilistic Encryption, in Journal of Computer and System Sciences, vol. 28, n. 2, 1984, pp. 270–299.

    Article  MathSciNet  Google Scholar 

  20. S. Goldwasser, S. Micali, and C. Rackoff, The Knowledge Complexity of Interactive Proof-Systems, SIAM J. on Computing, vol. 18, n. 1, 1989.

    Google Scholar 

  21. R. Impagliazzo and D. Zuckerman, How to Recycle Random Bits, Proc. of FOCS 89.

    Google Scholar 

  22. J. Kilian, On the complexity of bounded-interaction and non-interactive zero-knowledge proofs, Proc. of FOCS 94.

    Google Scholar 

  23. J. Kilian, and E. Petrank, An efficient zero-knowledge proof system for NP under general assumptions, Journal of Cryptology, vol. 11, n. 1, pp. 1–28.

    Google Scholar 

  24. M. Luby and A. Wigderson, Pairwise Independence and Derandomization, ICSI Technical Report TR-95-035.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Universitá di Salerno, 84081, Baronissi, SA, Italy

    A. De Santis & G. Persiano

  2. Telcordia Technologies, Morristown, NJ, USA

    G. Di Crescenzo

Authors
  1. A. De Santis
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  2. G. Persiano
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  3. G. Di Crescenzo
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07, Prague 8 - Liben, Czech Republic

    Jirí Wiedermann

  2. ILLC-WINS-University of Amsterdam, Plantage Muidergracht 24, 1018, TV, Amsterdam, The Netherlands

    Peter van Emde Boas

  3. BRICS, Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, DK, 8000, Aarhus C, Denmark

    Mogens Nielsen

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© 1999 Springer-Verlag Berlin Heidelberg

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De Santis, A., Persiano, G., Di Crescenzo, G. (1999). Non-interactive Zero-Knowledge: A Low-Randomness Characterization of NP (Extended Abstract). In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_24

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  • DOI: https://doi.org/10.1007/3-540-48523-6_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66224-2

  • Online ISBN: 978-3-540-48523-0

  • eBook Packages: Springer Book Archive

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