Extractors for Low-Weight Affine Sources

Anup Rao
2009 2009 24th Annual IEEE Conference on Computational Complexity  
We give polynomial time computable extractors for low-weight affince sources. A distribution is affine if it samples a random points from some unknown low dimensional subspace of F n 2 . A distribution is low weight affine if the corresponding linear space has a basis of low-weight vectors. Low-weight affine sources are thus a generalization of the well studied models of bit-fixing sources (which are just weight 1 affine sources). For universal constants c, , our extractors can extract almost
more » ... an extract almost all the entropy from weight k affine sources of dimension k, as long as k > log c n, with error 2 −k Ω(1) . This gives new extractors for low entropy bit-fixing 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 affine somewhere random sources.
doi:10.1109/ccc.2009.36 dblp:conf/coco/Rao09 fatcat:e6ml6i7uivdbhfln7fnsyushqq