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Randomness-efficient non-interactive zero knowledge

Extended abstract
  • Alfredo De Santis
  • Giovanni Di Crescenzo
  • Pino Persiano
Session 18: Cryptography
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1256)

Abstract

The model of Non-Interactive Zero-Knowledge allows to obtain minimal interaction between prover and verifier in a zero-knowledge proof if a public random string is available to both parties. In this paper we investigate upper bounds for the length of the random string for proving one and many statements, obtaining the following results:
  • We show how to prove in non-interactive perfect zero-knowledge any polynomial number of statements using a random string of fixed length, that is, not depending on the number of statements. Previously, such a result was known only in the case of computational zero-knowledge.

  • Under the quadratic residuosity assumption, we show how to prove any NP statement in non-interactive zero-knowledge on a random string of length (nk), where n is the size of the statement and k is the security parameter, which improves the previous best construction by a factor of (k).

Keywords

Proof System Security Parameter Random String Quadratic Residue Quadratic Character 
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 1997

Authors and Affiliations

  • Alfredo De Santis
    • 1
  • Giovanni Di Crescenzo
    • 2
  • Pino Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissiItaly
  2. 2.Computer Science and Engineering DepartmentUniversity of California at San DiegoLa JollaUSA

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