Abstract
Given two independent weak random sources X,Y, with the same length ℓ and min-entropies b X , b Y whose sum is greater than \(\ell+ \Omega(\mbox{\sf polylog}(\ell/\varepsilon))\), we construct a deterministic two-source extractor (aka “blender”) that extracts max (b X ,b Y ) + (b X + b Y − − ℓ − − 4log(1/ε)) bits which are ε-close to uniform. In contrast, best previously published construction [4] extracted at most \(\frac{1}{2}(b_X + b_Y -- \ell -- 2\log(1/\varepsilon))\) 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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Dodis, Y., Elbaz, A., Oliveira, R., Raz, R. (2004). Improved Randomness Extraction from Two Independent Sources. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. RANDOM APPROX 2004 2004. Lecture Notes in Computer Science, vol 3122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27821-4_30
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DOI: https://doi.org/10.1007/978-3-540-27821-4_30
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