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(bx+by-l-2 log(1/ε)) bits. Our main technical tool is a construction of a strong two-source extractor that extracts (bx+by-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. © Springer-Verlag 2004.
CITATION STYLE
Dodis, Y., Elbaz, A., Oliveira, R., & Raz, R. (2004). Improved randomness extraction from two independent sources. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3122, 334–344. https://doi.org/10.1007/978-3-540-27821-4_30
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