Combinatorica - Theory of Computing
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth 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
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the complexity of approximating the VC dimension
Journal of Computer and System Sciences - Complexity 2001
On the (non)Universality of the One-Time Pad
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the Impossibility of Private Key Cryptography with Weakly Random Keys
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extracting Randomness via Repeated Condensing
SIAM Journal on Computing
Extractors for a constant number of polynomially small min-entropy independent sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth 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
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Generating Quasi-Random Sequences From Slightly-Random Sources
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Dispersers, deterministic amplification, and weak random sources
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Extractors and lower bounds for locally samplable sources
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
The size Ramsey number of a directed path
Journal of Combinatorial Theory Series B
Improving the Hadamard extractor
Theoretical Computer Science
Properties and applications of boolean function composition
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We present new explicit constructions of deterministic randomness extractors, dispersers and related objects. We say that a distribution X on binary strings of length n is a δ-source if X assigns probability at most 2−δn to any string of length n. For every δ0, we construct the following poly(n)-time computable functions: 2-source disperser: D:({0, 1}n)2 → {0, 1} such that for any two independent δ-sources X1,X2 we have that the support of D(X1,X2) is {0, 1}. Bipartite Ramsey graph: Let N=2n. A corollary is that the function D is a 2-coloring of the edges of KN,N (the complete bipartite graph over two sets of N vertices) such that any induced subgraph of size Nδ by Nδ is not monochromatic. 3-source extractor: E:({0, 1}n)3→ {0, 1} such that for any three independent δ-sources X1,X2,X3 we have that E(X1,X2,X3) is o(1)-close to being an unbiased random bit. No previous explicit construction was known for either of these for any δ A component in these results is a new construction of condensers that may be of independent interest: This is a function C:{0, 1}n → ({0, 1}n/c)d (where c and d are constants that depend only on δ) such that for every δ-source X one of the output blocks of C(X) is (exponentially close to) a 0.9-source. (This result was obtained independently by Ran Raz.) The constructions are quite involved and use as building blocks other new and known objects. A recurring theme in these constructions is that objects that were designed to work with independent inputs, sometimes perform well enough with correlated, high entropy inputs. The construction of the disperser is based on a new technique which we call “the challenge-response mechanism” that (in some sense) allows “identifying high entropy regions” in a given pair of sources using only one sample from the two sources.