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Showing 1 to 6 of 6 for “"Randomness extractors"”.
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The method of multiplicities
… correcting codes, pseudorandom generators and randomness extractors. Somewhat strikingly, polynomials have also been found to be a powerful tool in the analysis of combinatorial parameters of objects that have some algebraic structure. This method of analysis has found applications in works on …
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Maintaining secrecy when information leakage is unavoidable
… tools from complexity theory known as randomness extractors.
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Kakeya sets and the method of multiplicities
… results, of interest in combinatorics and randomness extraction. 1. We show that every Kakeya set (a set of points that contains a line in every direction) in F' must be of size at least qn/2n. This bound is tight to within a 2 + o(1) factor for every n as q -- oc, compared to previous …
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Algebraic methods in randomness and pseudorandomness
Algebra and randomness come together rather nicely in computation. A central example of this relationship in action is the Schwartz-Zippel lemma and its application to the fast randomized checking of polynomial identities. In this thesis, we further this relationship in two ways: (1) by compiling …
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Seedless Extractors
Randomness is a powerful tool, exploited almost everywhere in computer science – from cryptography, to distributed computing, to algorithm design and more. Unfortunately, most of these applications require access to perfectly uniform bits, while randomness harvested from nature (e.g., atmospheric …
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Sparse graph codes for compression, sensing, and secrecy
… because they provide a method for constructing randomness extractors. Finally, we use several well-known isoperimetric inequalities (Harper's inequality, Azuma's inequality, and the Gaussian Isoperimetric inequality) in our analysis of the duality between lossy source coding and channel coding.