Extractors for Low-Weight Affine Sources

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 Fn 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 all the entropy from weight k affine sources of dimension k, as long as k > logc n, with error 2-k(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.

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Anup Rao
• Keywords: Affine Sources, Algorithms, COCO 2009, Low Weight Affine, Low-weight Affine Sources