How to construct random functions
Journal of the ACM (JACM)
Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
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
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
The relationship between public key encryption and oblivious transfer
FOCS '00 Proceedings of the 41st 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
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
The Impossibility of Basing One-Way Permutations on Central Cryptographic Primitives
Journal of Cryptology
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
Computational Complexity
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Security preserving amplification of hardness
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Single database private information retrieval implies oblivious transfer
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On hardness amplification of one-way functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
On the complexity of parallel hardness amplification for one-way functions
TCC'06 Proceedings of the Third conference on Theory of Cryptography
On the power of nonuniformity in proofs of security
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Almost all the important cryptographic protocols we have today base their security on unproven assumptions, which all imply NP $\ne$ P, and thus having unconditional proofs of their security seems far beyond our reach. One research effort then is to identify more basic primitives and prove the security of these protocols by reductions to the security of these primitives. However, in doing so, one often observes some security loss in the form that the security of the protocols is measured against weaker adversaries, e.g., adversaries with a smaller running time. Is such a security loss avoidable? We study two of the most basic cryptographic reductions: hardness amplification of one-way functions and constructing pseudorandom generators from one-way functions. We show that when they are done in a certain black-box way, such a security loss is in fact unavoidable.