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A Low Communication Competitive Interactive Proof System for Promised Quadratic Residuosity

  • Toshiya Itoh
  • Masafumi Hoshi
  • Shigeo Tsujii
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 773)

Abstract

A notion of “competitive” interactive proof systems is defined by Bellare and Goldwasser as a natural extension of a problem whether computing a witness w of xL is harder than deciding xL for a language L\( L{\mathbf{ }} \in {\mathbf{ }}\mathcal{N}\mathcal{P} \) . It is widely believed that quadratic residuosity (QR) does not have a competitive interactive proof system. Bellare and Goldwasser however introduced a notion of “representative” of Z N* and showed that there exists a competitive interactive proof system for promised QR, i.e., the moduli N is guaranteed to be the product of k = O(loglog|N|) distinct odd primes. In this paper, we consider how to reduce the communication complexity of a competitive interactive proof system for promised QR and how to relax the constraint on k from O(loglog|N|) to O(log|N|). To do this, we introduce a notion of “dominant” of Z N* and show that promised QR with the constraint that k = O(log|N|) has a competitive interactive proof system with considerably low communication complexity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Toshiya Itoh
    • 1
  • Masafumi Hoshi
    • 1
  • Shigeo Tsujii
    • 2
  1. 1.Department of Information Processing, Interdisciplinary Graduate School of Science and EngineeringTokyo Institute of TechnologyYokohamaJapan
  2. 2.Department of Electrical and Electronic Engineering, Disciplinary Graduate School of Science and EngineeringTokyo Institute of TechnologyTokyoJapan

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