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

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 efficient schemes, but also for solving a more than 10-year old open security problem: the Chaum’s undeniable signature.

• Type: Conference
• Year: 2001
• Where: PKC
• Authors: Tatsuaki Okamoto, David Pointcheval
• Keywords: Computational Problems, Cryptology, Decision Problems, Gap Problems, PKC 2001