A randomized protocol for signing contracts
Communications of the ACM
RSA and Rabin functions: certain parts are as hard as the whole
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A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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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.