Extractors and pseudorandom generators
Journal of the ACM (JACM)
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
Approximation of boolean functions by combinatorial rectangles
Theoretical Computer Science
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
Does privacy require true randomness?
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Uniform derandomization from pathetic lower bounds
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Separating sources for encryption and secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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We show how to simulate any BPP algorithm in polynomial time by using a weak random source of r bits and min-entropy $r^{\gamma}$ for any $\gamma 0$. This follows from a more general result about sampling with weak random sources. Our result matches an information-theoretic lower bound and solves a question that has been open for some years. The previous best results were a polynomial time simulation of RP [M. Saks, A. Srinivasan, and S. Zhou, Proc. 27th ACM Symp. on Theory of Computing, 1995, pp. 479--488] and a quasi-polynomial time simulation of BPP [A. Ta-Shma, Proc. 28th ACM Symp. on Theory of Computing, 1996, pp. 276--285].Departing significantly from previous related works, we do not use extractors; instead, we use the OR-disperser of Saks, Srinivasan, and Zhou in combination with a tricky use of hitting sets borrowed from [Andreev, Clementi, and Rolim, J. ACM, 45 (1998), pp. 179--213].