Deterministic Extraction from Weak Random Sources
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Deterministic Extraction from Weak Random Sources - Preamble
Preface Roughly speaking, a deterministic extractor is a function that 'extracts' almost perfect random bits from a 'weak random source'-a distribution that contains some entropy but is far from being truly random. In this book we explicitly construct deterministic extractors and related objects for various types of sources. A basic theme in this book is a methodology of recycling randomness th...
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Randomness is used in many places in our daily lives. Some examples are gambling, statistics, algorithms, cryptography etc. For such applications one typically assumes a supply of completely unbiased and independent randim bits. This raises the problem of where to get these assumed random bits from. We could try and use natural sources of randomness such as sun spots, the stock market or the we...
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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 − 4 log(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 l...
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