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Randomness-Optimal Characterization of Two NP Proof Systems

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Randomization and Approximation Techniques in Computer Science (RANDOM 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2483))

Abstract

We investigate quantitative aspects of randomness in two types of proof systems for NP: two-round public-coin witness-indistinguishable proof systems and non-interactive zero-knowledge proof systems. Our main results are the following:

  • • if NP has a 2-round public-coin witness-indistinguishable proof system then it has one using Θx(n ∈ + log(1/s)) random bits,

  • • if NP has a non-interactive zero-knowledge proof system then it has one using Θ(n ∈ +log(1/s)) random bits,

  • where s is the soundness error, n the length of the input, and ∈ can be any constant < 0. These results only assume that NP ≠ average-BPP. As a consequence, assuming the existence of one-way functions, both classes of proof systems are characterized by the same randomness complexity as BPP algorithms.

In order to achieve these results, we formulate and investigate the problem of randomness-efficient error reduction for two-round public-coin witness-indistinguishable proofs and improve some of our previous results in [13] on randomness-efficient non-interactive zero-knowledge proofs.

Part of this work done while visiting Università di Salerno.

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Author information

Authors and Affiliations

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

    Alfredo De Santis & Giuseppe Persiano

  2. Telcordia Technologies Inc., Morristown, NJ, 07960, USA

    Giovanni Di Crescenzo

Authors
  1. Alfredo De Santis
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  2. Giovanni Di Crescenzo
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  3. Giuseppe Persiano
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Editor information

Editors and Affiliations

  1. Centre Universitaire d’Informatique, University of Geneva, 24, Rue Général Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  2. Harvard University, DEAS, Maxwell Dworkin 337, 33 Oxford Street, Cambridge, MA, 02138, USA

    Salil Vadhan

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© 2002 Springer-Verlag Berlin Heidelberg

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De Santis, A., Di Crescenzo, G., Persiano, G. (2002). Randomness-Optimal Characterization of Two NP Proof Systems. In: Rolim, J.D.P., Vadhan, S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45726-7_15

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  • DOI: https://doi.org/10.1007/3-540-45726-7_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44147-2

  • Online ISBN: 978-3-540-45726-8

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