Randomness-Optimal Characterization of Two NP Proof Systems

  • Alfredo De Santis
  • Giovanni Di Crescenzo
  • Giuseppe Persiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


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.


Proof System Random String Commitment Scheme Randomness Complexity Reference String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Alfredo De Santis
    • 1
  • Giovanni Di Crescenzo
    • 2
  • Giuseppe Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissi, SAItaly
  2. 2.Telcordia Technologies Inc.MorristownUSA

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