Zero-Knowledge Proofs via Polynomial Representations

  • Giovanni Di Crescenzo
  • Vadym Fedyukovych
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)

Abstract

Under the existence of commitment schemes with homomorphic properties, we construct a constant-round zero-knowledge proof system for an \(\mathcal NP\)-complete language that requires a number of commitments that is sublinear in the size of the (best known) witness verification predicate. The overall communication complexity improves upon best known results for the specific \(\mathcal NP\)-complete language [1,2] and results that could be obtained using zero-knowledge proof systems for the entire \(\mathcal NP\) class (most notably, [3,2,4]). Perhaps of independent interest, our techniques build a proof system after reducing the theorem to be proved to statements among low-degree polynomials over large fields and using Schwartz-Zippel lemma to prove polynomial identities among committed values.

Keywords

Communication Complexity Proof System Polynomial Identity Security Parameter Commitment Scheme 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Giovanni Di Crescenzo
    • 1
  • Vadym Fedyukovych
    • 2
  1. 1.Applied Communication SciencesUSA
  2. 2.GlobalLogicKievUkraine

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