How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Journal of Computer and System Sciences
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
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
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
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Lower bounds on the efficiency of generic cryptographic constructions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the distribution of the number of roots of polynomials and explicit weak designs
Random Structures & Algorithms
Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors
Journal of Cryptology
Optimal Randomizer Efficiency in the Bounded-Storage Model
Journal of Cryptology
Computational Complexity: A Quantitative Perspective (North-Holland Mathematical Studies)
Computational Complexity: A Quantitative Perspective (North-Holland Mathematical Studies)
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
Computational Complexity
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
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Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-correcting codes and that are very simple and efficient. For example, one extractor produces each output bit separately in O(log2n) time. These extractors work for weak sources with min entropy λ n, for arbitrary constant λ0, have seed length O(log2n), and their output length is ≈ nλ/3.