How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
The complexity of promise problems with applications to public-key cryptography
Information and Control
Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
On the theory of average case complexity
Journal of Computer and System Sciences
Random-self-reducibility of complete sets
SIAM Journal on Computing
On the existence of pseudorandom generators
SIAM Journal on Computing
The power of adaptiveness and additional queries in random-self-reductions
Computational Complexity
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
P-selective sets and reducing search to decision vs. self-reducibility
Journal of Computer and System Sciences
Security-preserving hardness-amplification for any regular one-way function
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Constant-Round Coin-Tossing with a Man in the Middle or Realizing the Shared Random String Model
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Stronger Separations for Random-Self-Reducibility, Rounds, and Advice
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
How to Go Beyond the Black-Box Simulation Barrier
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On Worst-Case to Average-Case Reductions for NP Problems
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On interactive proofs with a laconic prover
Computational Complexity
Worst-Case to Average-Case Reductions Based on Gaussian Measures
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Reducing complexity assumptions for statistically-hiding commitment
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Foundations and Trends® in Theoretical Computer Science
Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword
Computational Complexity
Worst-Case to Average-Case Reductions Revisited
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the (Im)Possibility of Arthur-Merlin Witness Hiding Protocols
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Towards non-black-box lower bounds in cryptography
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Limits of provable security from standard assumptions
Proceedings of the forty-third annual ACM symposium on Theory of computing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On efficient zero-knowledge PCPs
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Black-box reductions and separations in cryptography
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
On the power of nonuniformity in proofs of security
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Unprovable security of perfect NIZK and non-interactive non-malleable commitments
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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We consider the possibility of basing one-way functions on NP-Hardness; that is, we study possible reductions from a worst-case decision problem to the task of average-case inverting a polynomial-time computable function f. Our main findings are the following two negative results:If given y one can efficiently compute |f-1(y)| then the existence of a (randomized) reduction of NP to the task of inverting f implies that coNP ⊆ AM. Thus, it follows that such reductions cannot exist unless coNP ⊆ AM. For any function f, the existence of a (randomized) non-adaptive reduction of NP to the task of average-case inverting f implies that coNP ⊆ AM.Our work builds upon and improves on the previous works of Feigenbaum and Fortnow (SIAM Journal on Computing, 1993) and Bogdanov and Trevisan (44th FOCS, 2003), while capitalizing on the additional "computational structure" of the search problem associated with the task of inverting polynomial-time computable functions. We believe that our results illustrate the gain of directly studying the context of one-way functions rather than inferring results for it from a the general study of worst-case to average-case reductions.