Basing non-interactive zero-knowledge on (Enhanced) trapdoor permutations: The state of the art

Abstract

The purpose of this article is to correct the inaccurate account of this subject that is provided in our two-volume work Foundation of Cryptography. Specifically, as pointed out by Jonathan Katz, it seems that the construction of Non-Interactive Zero-Knowledge proofs for NP requires the existence of a doubly-enhanced collection of trapdoor permutations (to be defined below). We stress that the popular candidate collections of trapdoor permutations do satisfy this doubly-enhanced condition. In fact, any collection of trapdoor permutations that has dense and easily recognizable domain satisfies this condition. © 2011 Springer-Verlag Berlin Heidelberg.