## Extracting all the Randomness and Reducing the Error in Trevisan's Extractors (1999)

### Cached

### Download Links

- [www.wisdom.weizmann.ac.il]
- [www.wisdom.weizmann.ac.il]
- [theory.lcs.mit.edu]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proceedings of the 31st Annual ACM Symposium on Theory of Computing |

Citations: | 78 - 16 self |

### BibTeX

@INPROCEEDINGS{Raz99extractingall,

author = {Ran Raz and Omer Reingold and Salil Vadhan},

title = {Extracting all the Randomness and Reducing the Error in Trevisan's Extractors},

booktitle = {In Proceedings of the 31st Annual ACM Symposium on Theory of Computing},

year = {1999},

pages = {149--158}

}

### Years of Citing Articles

### OpenURL

### Abstract

We give explicit constructions of extractors which work for a source of any min-entropy on strings of length n. These extractors can extract any constant fraction of the min-entropy using O(log² n) additional random bits, and can extract all the min-entropy using O(log³ n) additional random bits. Both of these constructions use fewer truly random bits than any previous construction which works for all min-entropies and extracts a constant fraction of the min-entropy. We then improve our second construction and show that we can reduce the entropy loss to 2 log(1=") +O(1) bits, while still using O(log³ n) truly random bits (where entropy loss is defined as [(source min-entropy) + (# truly random bits used) (# output bits)], and " is the statistical difference from uniform achieved). This entropy loss is optimal up to a constant additive term. our...