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)


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.


Communication Complexity Proof System Polynomial Identity Security Parameter Commitment Scheme 
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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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