How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
How to construct random functions
Journal of the ACM (JACM)
How to generate factored random numbers
SIAM Journal on Computing - Special issue on cryptography
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
Minimum disclosure proofs of knowledge
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on 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
Journal of the ACM (JACM)
Bit commitment using pseudo-randomness (extended abstract)
CRYPTO '89 Proceedings on Advances in cryptology
SIAM Journal on Computing
Algorithmic number theory
Adaptive zero knowledge and computational equivocation (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Non-interactive and non-malleable commitment
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Multiple non-interactive zero knowledge proofs based on a single random string
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Zero-knowledge proofs of knowledge without interaction
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Robust Non-interactive Zero Knowledge
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient and Non-interactive Non-malleable Commitment
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Min-round Resettable Zero-Knowledge in the Public-Key Model
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Mutually Independent Commitments
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Towards a Theory of Extractable Functions
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
An Observation on Non-Malleable Witness-Indistinguishability and Non-Malleable Zero-Knowledge
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Universally Composable Adaptive Priced Oblivious Transfer
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
On non-interactive zero-knowledge proofs of knowledge in the shared random string model
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the feasibility of consistent computations
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Practical Internet voting system
Journal of Network and Computer Applications
Resource-based corruptions and the combinatorics of hidden diversity
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Establishing relationships between primitives is an important area in the foundations of Cryptography. In this paper we consider the primitive of non-interactive zero-knowledge proofs of knowledge, namely, methods for writing a proof that on input x the prover knows y such that relation R(x, y) holds. These proofs have important applications for the construction of cryptographic protocols, as cryptosystems and signatures that are secure under strong types of attacks. They were first defined in [10], where a sufficient condition for the existence of such proofs for all NP relations was given. In this paper we show, perhaps unexpectedly, that such condition, based on a variant of publickey cryptosystems, is also necessary. Moreover, we present an alternative and natural condition, based on a variant of commitment schemes, which we show to be necessary and sufficient as well for the construction of such proofs. Such equivalence also allows us to improve known results on the construction of such proofs under the hardness of specific computational problems. Specifically, we show that assuming the hardness of factoring Blum integers is sufficient for such constructions.