Sparse extractor families for all the entropy
Refereed conference paper presented and published in conference proceedings


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AbstractWe 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. These 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 input 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 sparsity or preserving locality (i.e., parallelism) is of interest. © 2013 ACM.
All Author(s) ListBogdanov A., Guo S.
Name of Conference2013 4th ACM Conference on Innovations in Theoretical Computer Science, ITCS 2013
Start Date of Conference09/01/2013
End Date of Conference12/01/2013
Place of ConferenceBerkeley, CA
Country/Region of ConferenceUnited States of America
Detailed descriptionorganized by ACM,
Year2013
Month2
Day11
Pages553 - 560
ISBN9781450318594
LanguagesEnglish-United Kingdom
Keywordsparallel cryptography, random matrices, randomness extraction

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