Affine dispersers from subspace polynomials

An affine disperser over Fn 2 for sources of dimension d is a function f : Fn 2 F2 such that for any affine space S Fn 2 of dimension at least d, we have {f(s) : s S} = F2. Affine dispersers have been considered in the context of deterministic extraction of randomness from structured sources of imperfect randomness. Previously, explicit constructions of affine dispersers were known for every d = (n), due to Barak et. al. [2] and Bourgain [10] (the latter in fact gives stronger objects called affine extractors). In this work we give the first explicit affine dispersers for sublinear dimension. Specifically, our dispersers work even when d = (n4/5 ). The main novelty in our construction lies in the method of proof, which relies on elementary properties of subspace polynomials. In contrast, the previous works mentioned above relied on sum-product theorems for finite fields. Categories and Subject Descriptors G.3 [Mathematics of Computing]: Probability and Statistics--Random number gen...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Eli Ben-Sasson, Swastik Kopparty
• Keywords: Affine Space, Algorithms, Explicit Affine Dispersers, Objects Called Affine, STOC 2009