How to construct random functions
Journal of the ACM (JACM)
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Universal one-way hash functions and their cryptographic applications
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Public-key cryptosystems provably secure against chosen ciphertext attacks
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Cryptographic defense against traffic analysis
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Synthesizers and their application to the parallel construction of pseudo-random functions
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Multiple NonInteractive Zero Knowledge Proofs Under General Assumptions
SIAM Journal on Computing
SIAM Journal on Computing
Unique Signatures and Verifiable Random Functions from the DH-DDH Separation
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Proving Security Against Chosen Cyphertext Attacks
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Invariant Signatures and Non-Interactive Zero-Knowledge Proofs are Equivalent (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Efficient Construction of (Distributed) Verifiable Random Functions
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A Forward-Secure Public-Key Encryption Scheme
Journal of Cryptology
SIAM Journal on Computing
Derandomization in Cryptography
SIAM Journal on Computing
How to generate cryptographically strong sequences of pseudo random bits
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Feistel Networks Made Public, and Applications
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Simulatable VRFs with applications to multi-theorem NIZK
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Bounded CCA2-secure encryption
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
A verifiable random function with short proofs and keys
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Non-interactive zaps and new techniques for NIZK
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Construction of a non-malleable encryption scheme from any semantically secure one
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Non-interactive opening for ciphertexts encrypted by shared keys
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Constructing verifiable random functions with large input spaces
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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Verifiable random functions (VRFs), introduced by Micali, Rabin and Vadhan, are pseudorandom functions in which the owner of the seed produces a public-key that constitutes a commitment to all values of the function and can then produce, for any input x , a proof that the function has been evaluated correctly on x , preserving pseudorandomness for all other inputs. No public-key (even a falsely generated one) should allow for proving more than one value per input. VRFs are both a natural and a useful primitive, and previous works have suggested a variety of constructions and applications. Still, there are many open questions in the study of VRFs, especially their relation to more widely studied cryptographic primitives and constructing them from a wide variety of cryptographic assumptions. In this work we define a natural relaxation of VRFs that we call weak verifiable random functions, where pseudorandomness is required to hold only for randomly selected inputs. We conduct a study of weak VRFs, focusing on applications, constructions, and their relationship to other cryptographic primitives. We show: Constructions. We present constructions of weak VRFs based on a variety of assumptions, including general assumptions such as (enhanced) trapdoor permutations, as well as constructions based on specific number-theoretic assumptions such as the Diffie-Hellman assumption in bilinear groups. Separations. Verifiable random functions (both weak and standard) cannot be constructed from one-way permutations in a black-box manner. This constitutes the first result separating (standard) VRFs from any cryptographic primitive. Applications. Weak VRFs capture the essence of constructing non-interactive zero-knowledge proofs for all NP languages.