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Zero-Knowledge Proofs via Polynomial Representations

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Mathematical Foundations of Computer Science 2012 (MFCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7464))

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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.

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Author information

Authors and Affiliations

  1. Applied Communication Sciences, New Jersey, USA

    Giovanni Di Crescenzo

  2. GlobalLogic, Kiev, Ukraine

    Vadym Fedyukovych

Authors
  1. Giovanni Di Crescenzo
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  2. Vadym Fedyukovych
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  2. Department of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Vladimiro Sassone

  3. Institute of Theoretical Computer Science, ETH Zürich, CAB H 39.2, Universitätstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Di Crescenzo, G., Fedyukovych, V. (2012). Zero-Knowledge Proofs via Polynomial Representations. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_31

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  • DOI: https://doi.org/10.1007/978-3-642-32589-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32588-5

  • Online ISBN: 978-3-642-32589-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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