How to construct random functions
Journal of the ACM (JACM)
Average case complete problems
SIAM Journal on Computing
Random instances of a graph coloring problem are hard
STOC '88 Proceedings of the twentieth 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
Journal of Computer and System Sciences
Random-self-reducibility of complete sets
SIAM Journal on Computing
Designing programs that check their work
Journal of the ACM (JACM)
BPP has subexponential time simulations unless EXPTIME has publishable proofs
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 = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
SIAM Journal on Computing
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION
On Worst-Case to Average-Case Reductions for NP Problems
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
List-Decoding Using The XOR Lemma
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness amplification within NP
Journal of Computer and System Sciences - Special issue on computational complexity 2002
Worst-Case to Average-Case Reductions Based on Gaussian Measures
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
Uniform hardness versus randomness tradeoffs for Arthur-Merlin games
Computational Complexity
On uniform amplification of hardness in NP
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
If NP Languages are Hard on the Worst-Case Then It is Easy to Find Their Hard Instances
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Journal of the ACM (JACM)
Using Nondeterminism to Amplify Hardness
SIAM Journal on Computing
Distinguishing SAT from Polynomial-Size Circuits, through Black-Box Queries
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
Worst-case vs. algorithmic average-case complexity in the polynomial-time hierarchy
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Limitations of Hardness vs. Randomness under Uniform Reductions
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Combinatorial Optimization Using Electro-Optical Vector by Matrix Multiplication Architecture
OSC '09 Proceedings of the 2nd International Workshop on Optical SuperComputing
Relativized worlds without worst-case to average-case reductions for NP
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Nanotechnology based optical solution for NP-hard problems
OSC'10 Proceedings of the Third international conference on Optical supercomputing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
ACM Transactions on Computation Theory (TOCT)
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We prove that if NP $${\nsubseteq}$$ BPP, i.e., if SAT is worst-case hard, then for every probabilistic polynomial-time algorithm trying to decide SAT, there exists some polynomially samplable distribution that is hard for it. That is, the algorithm often errs on inputs from this distribution. This is the first worst-case to average-case reduction for NP of any kind. We stress however, that this does not mean that there exists one fixed samplable distribution that is hard for all probabilistic polynomial-time algorithms, which is a pre-requisite assumption needed for one-way functions and cryptography (even if not a sufficient assumption). Nevertheless, we do show that there is a fixed distribution on instances of NP-complete languages, that is samplable in quasi-polynomial time and is hard for all probabilistic polynomial-time algorithms (unless NP is easy in the worst case).Our results are based on the following lemma that may be of independent interest: Given the description of an efficient (probabilistic) algorithm that fails to solve SAT in the worst case, we can efficiently generate at most three Boolean formulae (of increasing lengths) such that the algorithm errs on at least one of them.