On NC1 Boolean Circuit Composition of Non-interactive Perfect Zero-Knowledge

  • Alfredo De Santis
  • Giovanni Di Crescenzo
  • Giuseppe Persiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3153)


Non-Interactive Perfect Zero-Knowledge (NIPZK) and Perfect Zero-Knowledge (PZK) are the class of languages having a Perfect Zero-Knowledge proof system in the non-interactive and interactive model, respectively.

In this paper we present new techniques for Boolean Circuit Compositions of NIPZK and PZK, and significantly enlarge the class of known languages having such proofs. Our main result is that all NC1 circuit compositions over a certain class of languages (that includes for example quadratic residuosity languages) have NIPZK proofs. Previous results only applied to single threshold gates and certain CNF formulae.

We also extend the class of known languages in PZK by allowing compositions over random self-reducible languages with respect to polynomial-size monotone circuits with fan-out >1 and certain additional restrictions on the allowed gates. Previous results only applied to polynomial-size formulae (that is, circuits with fan-out =1).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alfredo De Santis
    • 1
  • Giovanni Di Crescenzo
    • 2
  • Giuseppe Persiano
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissiItaly
  2. 2.Telcordia TechnologiesPiscatawayUSA

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