NDLI: Sparse extractor families for all the entropy

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Sparse extractor families for all the entropy

Content Provider	Semantic Scholar
Author	Bogdanov, Andrej Guo, Siyao
Copyright Year	2018
Abstract	We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without any assumption on the underlying distribution beyond a min-entropy requirement. We give two simple constructions of sparse extractor families, which are collections of sparse functions such that for any distribution X on inputs of sufficiently high min-entropy, the output of most functions from the collection on a random input chosen from X is statistically close to uniform. For strong extractor families (i.e., functions in the family do not take additional randomness) we give upper and lower bounds on the sparsity that are tight up to a constant factor for a wide range of min-entropies. We then prove that for some min-entropies weak extractor families can achieve better sparsity. We show how this construction can be used towards more efficient parallel transformation of (non-uniform) one-way functions into pseudorandom generators. More generally, sparse extractor families can be used instead of pairwise independence in various randomized or nonuniform settings where preserving locality (i.e., parallelism) is of interest. andrejb@cse.cuhk.edu.hk. Department of Computer Science and Engineering and Institute for Theoretical Computer Science and Communications, Chinese University of Hong Kong. Work supported by grants RGC GRF CUHK410309 and CUHK410111. † syguo@cse.cuhk.edu.hk. Department of Computer Science and Engineering, Chinese University of Hong Kong.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://export.arxiv.org/pdf/1207.6260
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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