### Abstract

Given two independent weak random sources X, Y, with the same length l and min-entropies bx,by whose sum is greater than l + Ω(polylog(l/ε)), we construct a deterministic two-source extractor (aka "blender") that extracts max(bx,by) + (bx + by - l - 41og(1/ε)) bits which are ε-close to uniform. In contrast, best previously published construction [4] extracted at most 1/2(b
_{x}+b
_{y}-l-2 log(1/ε)) bits. Our main technical tool is a construction of a strong two-source extractor that extracts (b
_{x}+b
_{y}-l)-2log(1/ε) bits which are ε-close to being uniform and independent of one of the sources (aka "strong blender"), so that they can later be reused as a seed to a seeded extractor. Our strong two-source extractor construction improves the best previously published construction of such strong blenders [7] by a factor of 2, applies to more sources X and Y, and is considerably simpler than the latter. Our methodology also unifies several of the previous two-source extractor constructions from the literature.

Original language | English (US) |
---|---|

Pages (from-to) | 334-344 |

Number of pages | 11 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 3122 |

State | Published - 2004 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*3122*, 334-344.

**Improved randomness extraction from two independent sources.** / Dodis, Yevgeniy; Elbaz, Ariel; Oliveira, Roberto; Raz, Ran.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 3122, pp. 334-344.

}

TY - JOUR

T1 - Improved randomness extraction from two independent sources

AU - Dodis, Yevgeniy

AU - Elbaz, Ariel

AU - Oliveira, Roberto

AU - Raz, Ran

PY - 2004

Y1 - 2004

N2 - Given two independent weak random sources X, Y, with the same length l and min-entropies bx,by whose sum is greater than l + Ω(polylog(l/ε)), we construct a deterministic two-source extractor (aka "blender") that extracts max(bx,by) + (bx + by - l - 41og(1/ε)) bits which are ε-close to uniform. In contrast, best previously published construction [4] extracted at most 1/2(b x+b y-l-2 log(1/ε)) bits. Our main technical tool is a construction of a strong two-source extractor that extracts (b x+b y-l)-2log(1/ε) bits which are ε-close to being uniform and independent of one of the sources (aka "strong blender"), so that they can later be reused as a seed to a seeded extractor. Our strong two-source extractor construction improves the best previously published construction of such strong blenders [7] by a factor of 2, applies to more sources X and Y, and is considerably simpler than the latter. Our methodology also unifies several of the previous two-source extractor constructions from the literature.

AB - Given two independent weak random sources X, Y, with the same length l and min-entropies bx,by whose sum is greater than l + Ω(polylog(l/ε)), we construct a deterministic two-source extractor (aka "blender") that extracts max(bx,by) + (bx + by - l - 41og(1/ε)) bits which are ε-close to uniform. In contrast, best previously published construction [4] extracted at most 1/2(b x+b y-l-2 log(1/ε)) bits. Our main technical tool is a construction of a strong two-source extractor that extracts (b x+b y-l)-2log(1/ε) bits which are ε-close to being uniform and independent of one of the sources (aka "strong blender"), so that they can later be reused as a seed to a seeded extractor. Our strong two-source extractor construction improves the best previously published construction of such strong blenders [7] by a factor of 2, applies to more sources X and Y, and is considerably simpler than the latter. Our methodology also unifies several of the previous two-source extractor constructions from the literature.

UR - http://www.scopus.com/inward/record.url?scp=20544433132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20544433132&partnerID=8YFLogxK

M3 - Article

VL - 3122

SP - 334

EP - 344

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -