Journal of Computer and System Sciences
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
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
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extracting randomness: a survey and new constructions
Journal of Computer and System Sciences
Tight bounds for depth-two superconcentrators
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Expanders that Beat the Eigenvalue Bound: Explicit Construction andApplications
Expanders that Beat the Eigenvalue Bound: Explicit Construction andApplications
Computing with very weak random sources
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Exposure-resilient functions and all-or-nothing transforms
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On the error parameter of dispersers
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Random selection with an adversarial majority
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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We present a general method to reduce the error of any extractor. Our method works particularly well in the case that the original extractor extracts up to a constant fraction of the source min-entropy and achieves a polynomially small error. In that case, we are able to reduce the error to (almost) any \math, using only \math additional truly random bits (while keeping the other parameters of the original extractor more or less the same). In other cases (e.g. when the original extractor extracts all the min-entropy or achieves only a constant error) our method is not optimal but it is still quite efficient and leads to improved constructions of extractors.Using our method, we are able to improve almost all known extractors in the case where the error required is relatively small (e.g. less than polynomially small error). In particular, we apply our method to the new extractors of [Tre99,RRV99] to get improved constructions in almost all cases. Specifically, we obtain extractors that work for sources of any min-entropy on strings of length n which: (a) extract any \math fraction of the min-entropy using \math truly random bits (\math), (b) extract any constant fraction of the min-entropy using \math truly random bits, and (c) extract all the min-entropy using \math truly random bits.