The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes

  • Tatsuaki Okamoto
  • David Pointcheval
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1992)

Abstract

This paper introduces a novel class of computational problems, the gap problems, which can be considered as a dual to the class of the decision problems. We show the relationship among inverting problems, decision problems and gap problems. These problems find a nice and rich practical instantiation with the Diffie-Hellman problems. Then, we see how the gap problems find natural applications in cryptography, namely for proving the security of very efficientsc hemes, but also for solving a more than 10-year old open security problem: the Chaum's undeniable signature.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tatsuaki Okamoto
    • 1
  • David Pointcheval
    • 2
  1. 1.NTT LabsJapan
  2. 2.Déptd'Informat iqueENS - CNRSParis Cedex 05France

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