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

  • Authors:
  • Tatsuaki Okamoto;David Pointcheval

  • Affiliations:
  • -;-

  • Venue:
  • PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
  • Year:
  • 2001

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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.