Improved randomness extraction from two independent sources

Yevgeniy Dodis, Ariel Elbaz, Roberto Oliveira, Ran Raz

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)334-344
Number of pages11
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3122
StatePublished - 2004

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Entropy
Randomness
Extractor
Seeds
Seed
Methodology

ASJC Scopus subject areas

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

Cite this

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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.",
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AU - Dodis, Yevgeniy

AU - Elbaz, Ariel

AU - Oliveira, Roberto

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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.

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