Generating quasi-random sequences from semi-random sources
Journal of Computer and System Sciences
Combinatorica - Theory of Computing
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Extracting randomness: a survey and new constructions
Journal of Computer and System Sciences
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
Deterministic Extractors for Affine Sources over Large Fields
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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
Independent Unbiased Coin Flips From A Correlated Biased Source: A Finite State Markov Chain
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
How to get more mileage from randomness extractors
Random Structures & Algorithms
Increasing the Output Length of Zero-Error Dispersers
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 Low-Weight Affine Sources
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors
Journal of the ACM (JACM)
Deterministic extractors for small-space sources
Journal of Computer and System Sciences
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
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
| Hi-index | 5.23 |
In this paper we construct a strong randomness extractor with two independent @?-bit input distributions with min entropies b"X,b"Y,b"X+b"Y@? (the probability of any particular output is upper bounded by 2^-^b^"^X and 2^-^b^"^Y, respectively). For b"X,b"Y@?@?-1, our extractor produces one bit which is by the factor of 2 closer to the uniform distribution, when compared to the Hadamard extractor. What is more, this distance drops to zero if at least one of the min entropies raises to @?. This is in sharp contrast to the Hadamard extractor which fails to produce even a single unbiased bit, even if one of the input distributions is uniform. We also extend our construction to produce k bits of output with a bias that is by the factor of 3/2 smaller than that of the corresponding Hadamard extractor and retains the ability to produce unbiased bits if one of the input distributions is uniform. The strongness property of the extractor is maintained in both cases, however, in the multi-bit scenario the bias is increased by the factor of 3/2.