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Extractors for LowWeight A#ne Sources Institute for Advanced Study

Summary: Extractors for Low­Weight A#ne Sources
Anup Rao #
Institute for Advanced Study
November 19, 2007
We give polynomial time computable extractors for low­weight a#nce sources. A distribution
is a#ne if it samples a random points from some unknown low dimensional subspace of F n
2 . A
distribution is low weight a#ne if the corresponding linear space has a basis of low­weight vectors.
Low­weight a#ne sources are thus a generalization of the well studied models of bit­fixing sources
(which are just weight 1 a#ne sources).
For universal constants c, #, our extractors can extract almost all the entropy from weight k #
a#ne sources of dimension k, as long as k > log c
n, with error 2
-k##3# . This gives new extractors
for low entropy bit­fixing sources with exponentially small error, a parameter that is important for
the application of these extractors to cryptography.
Our techniques involve constructing new condensers for a#ne somewhere random sources.
Keywords: Extractors, A#ne Sources, Exposure Resilient Cryptography


Source: Anderson, Richard - Department of Computer Science and Engineering, University of Washington at Seattle


Collections: Computer Technologies and Information Sciences