Extractors for Three Uneven-Length Sources
نویسندگان
چکیده
We construct an efficient 3-source extractor that requires one of the sources to be significantly shorter than the min-entropy of the other two sources. Our extractors work even when the longer, n-bit sources have min-entropy n and the shorter source has min-entropy log n. Previous constructions for independent sources with min-entropy n required Θ(1/γ) sources [Rao06]. Our construction relies on lossless condensers [GUV07] based on Parvaresh-Vardy codes [PV05], as well as on a 2-source extractor for a block source and general source [BRSW06].
منابع مشابه
Quantum-Proof Extractors: Optimal up to Constant Factors
We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence O(log(n/ǫ)) on the input length n and error ǫ. Our extractors support any min-entropy k = Ω(log n+ log(1/ǫ)) and extract m = (1− α)k bits that are ǫ-close to uniform, for any desired constant α > 0. Previous constructions had a quadratically worse seed length or were restricted to very...
متن کاملDeterministic 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...
متن کاملSimple Extractors via Constructions of Cryptographic Pseudo-random Generators
Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-co...
متن کاملLecture 15: Simulating Bpp -high Min-entropy Sources 1 Simulating Bpp Using Sv-sources
It’s easy to check that any specific string of length n has probability at most (1 − δ), hence SV-sources are n log 1 1−δ -sources. Also recall that SV-sources are (k, l) block sources where k = l log 1 1−δ . Suppose δ = log 1 1−δ , then k = δl. Take a hash-based extractor E : {0, 1} × {0, 1} → {0, 1}. Here, our weak-source is a SVsource over the strings of length n and suppose k = n log 1 1−δ ...
متن کاملVariable-Length Extractors: Efficiently Extracting Randomness from Weak Stochastic Processes
The topic of generating random bits from imperfect random sources was studied extensively. Existing work provides solutions that are based on the concept of a fixed-length extractor; namely, an algorithm that gets a fixed number of random bits from a source and generates random bits. Typically, the number of random bits extracted using fixed-length extractors is upperbounded by the min-entropy....
متن کامل