Deterministic extractors

We study constructions of deterministic extractors for various specialized classes of sources. Deterministic extractors for a class of sources are functions such that for any random source in the class, the output of the extractor is close to uniform. Thus, we can transform weak randomness into true randomness that can be used in applications. For example, the true randomness we extract can be used in cryptographic protocols, such as generating cryptographic keys. Other applications include distributed computing and randomized algorithms. We have examined some of the most general and interesting classes of sources for which we can construct such extractors. For each class, our goal is to construct extractors with exponentially small error that extract as much of the min-entropy in the source as possible and that work even when the min-entropy in the source is small. In particular, we construct extractors for sources that only have access to a small amount of space. This construction is based on a construction for independent sources, which are sources consisting of a number of independent smaller sources. We also give results for oblivious bit-fixing and symbol-fixing sources. In such sources some of the bits (or symbols) are fixed and then the rest are chosen uniformly at random. These results also have an application in the area of exposure-resilient cryptography, giving adaptive All-Or-Nothing-Transforms. We also have results on non-oblivious bit-fixing sources and affine sources.