Name
Abstract | ||
|---|---|---|
We give polynomial time computable extractors for \emph{low-weight affince sources}. A distribution is affine if it samples a randompoints from some unknown low dimensional subspace of $\mathbb{F}_2^n$. A distribution is low weight affine if the corresponding linear spacehas 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 $c,\epsilon$, our extractors can extract almost allthe entropy from weight $k^{\epsilon}$ affine sources of dimension $k$, as long as $k \log ^c n$, with error $2^{-k^{\Omega(1)}}$. In particular, our results give 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 \emph{condensers} for \emph{affine somewhere random sources}. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/CCC.2009.36 | IEEE Conference on Computational Complexity |
Keywords | DocType | Volume |
polynomial time | Journal | 15 |
Issue | ISSN | Citations |
015 | 1093-0159 | 13 |
PageRank | References | Authors |
0.95 | 9 | 1 |