On the existence of 3-round zero-knowledge protocols

  • Satoshi Hada
  • Toshiaki Tanaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1462)


In this paper, we construct a 3-round zero-knowledge protocol for any NP language. Goldreich and Krawczyk proved that a 3-round black-box simulation zero-knowledge protocol exists only for BPP languages. However, there is no contradiction here. That is, our proposed protocol achieves a weaker notion of zero-knowledge: auxiliary-input non-uniform zero-knowledge. Since this notion has not been investigated in the literature, we classify several zero-knowledge notions including it and discuss the relationships among them. Our main contribution is to provide a non-black-box simulation technique. It is based on a novel computational assumption related to the Diffie-Hellman problem. Although this assumption is strong and non-standard, its non-standard nature seems essential for our simulation technique.


Zero-knowledge interactive proof Diffie-Hellman problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Satoshi Hada
    • 1
  • Toshiaki Tanaka
    • 1
  1. 1.KDD R&D LaboratoriesSaitamaJapan

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