Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Information Processing Letters
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
Journal of Computer and System Sciences
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
On Pseudorandom Generators in NC
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Error Reduction for Extractors
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Optimal Randomizer Efficiency in the Bounded-Storage Model
Journal of Cryptology
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Random Structures & Algorithms
Verifying and decoding in constant depth
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
SIAM Journal on Computing
Deterministic Extractors for Bit-Fixing Sources by Obtaining an Independent Seed
SIAM Journal on Computing
Extracting Randomness Using Few Independent Sources
SIAM Journal on Computing
SIAM Journal on Computing
Cryptography with constant computational overhead
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
New algorithms for finding irreducible polynomials over finite fields
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Randomness-efficient oblivious sampling
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
How to get more mileage from randomness extractors
Random Structures & Algorithms
A 2-Source Almost-Extractor for Linear Entropy
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
Extractors for Three Uneven-Length Sources
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
Goldreich's One-Way Function Candidate and Myopic Backtracking Algorithms
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Extractors And Rank Extractors For Polynomial Sources
Computational Complexity
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Towards a Study of Low-Complexity Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Extractors for Low-Weight Affine Sources
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
On the Security of Goldreich's One-Way Function
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Extractors Using Hardness Amplification
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Extractors for a Constant Number of Polynomially Small Min-Entropy Independent Sources
SIAM Journal on Computing
Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors
Journal of the ACM (JACM)
Simple extractors via constructions of cryptographic pseudo-random generators
Theoretical Computer Science
2-Source Extractors under Computational Assumptions and Cryptography with Defective Randomness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Simple Affine Extractors Using Dimension Expansion
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors
Journal of Computer and System Sciences
Deterministic extractors for small-space sources
Journal of Computer and System Sciences
The Complexity of Distributions
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Improved Constructions of Three Source Extractors
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
A New Approach to Affine Extractors and Dispersers
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Bounded-Depth Circuits Cannot Sample Good Codes
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Extractors for Circuit Sources
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Affine extractors over prime fields
Combinatorica
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
Pseudorandomness
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We consider the problem of extracting randomness from sources that are efficiently samplable, in the sense that each output bit of the sampler only depends on some small number d of the random input bits. As our main result, we construct a deterministic extractor that, given any d-local source with min-entropy k on n bits, extracts Ω(k2/nd) bits that are 2−nΩ(1)-close to uniform, provided d ≤ o(log n) and k ≥ n2/3+γ (for arbitrarily small constants γ 0). Using our result, we also improve a result of Viola [2010] who proved a 1/2 − O(1/log n) statistical distance lower bound for o(log n)-local samplers trying to sample input-output pairs of an explicit boolean function, assuming the samplers use at most n + n1−δ random bits for some constant δ 0. Using a different function, we simultaneously improve the lower bound to 1/2 − 2−nΩ(1) and eliminate the restriction on the number of random bits.