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
Average case complete problems
SIAM Journal on Computing
NP is as easy as detecting unique solutions
Theoretical Computer Science
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
Many hard examples for resolution
Journal of the ACM (JACM)
Average case complexity under the universal distribution equals worst-case complexity
Information Processing Letters
On the theory of average case complexity
Journal of Computer and System Sciences
Random-self-reducibility of complete sets
SIAM Journal on Computing
Amplification of weak learning under the uniform distribution
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Journal of Computer and System Sciences
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
On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the complexity of unsatisfiability proofs for random k-CNF formulas
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
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
The Asymptotic Order of the Random k -SAT Threshold
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Cryptocomplexity and NP-Completeness
Proceedings of the 7th Colloquium on Automata, Languages and Programming
On Polynomial-Factor Approximations to the Shortest Lattice Vector Length
SIAM Journal on Discrete Mathematics
New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On the cryptocomplexity of knapsack systems
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
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
Using nondeterminism to amplify hardness
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Worst-Case to Average-Case Reductions Based on Gaussian Measures
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Almost Perfect Lattices, the Covering Radius Problem, and Applications to Ajtai's Connection Factor
SIAM Journal on Computing
On uniform amplification of hardness in NP
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on 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)
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On basing one-way functions on NP-hardness
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Witnesses for non-satisfiability of dense random 3CNF formulas
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 1
Foundations of Cryptography: Volume 1
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword
Computational Complexity
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An Infinitely-Often One-Way Function Based on an Average-Case Assumption
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Structural Complexity of AvgBPP
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
Average case complexity, revisited
Studies in complexity and cryptography
On an optimal randomized acceptor for graph nonisomorphism
Information Processing Letters
Optimal acceptors and optimal proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
An encoding invariant version of polynomial time computable distributions
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Relativized Worlds without Worst-Case to Average-Case Reductions for NP
ACM Transactions on Computation Theory (TOCT)
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Encoding Invariance in Average Case Complexity
Theory of Computing Systems
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We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain specific (but somewhat artificial) NP problem is easy-on-average with respect to the uniform distribution, then all problems in NP are easy-on-average with respect to all samplable distributions. Applying the theory to natural distributional problems remain an outstanding open question. We review some natural distributional problems whose average-case complexity is of particular interest and that do not yet fit into this theory. A major open question is whether the existence of hard-on-average problems in NP can be based on the P ≠ NP assumption or on related worst-case assumptions. We review negative results showing that certain proof techniques cannot prove such a result. While the relation between worst-case and average-case complexity for general NP problems remains open, there has been progress in understanding the relation between different "degrees" of average-case complexity. We discuss some of these "hardness amplification" results.