A PRG for boolean PTF of degree 2 with seed length subpolynomial in ϵ and logarithmic in n

We construct and analyze a pseudorandom generator for degree 2 boolean polynomial threshold functions. Random constructions achieve the optimal seed length of O(log n+ log 1/epsilon), however the best known explicit construction of [8] uses a seed length of O(log n . epsilon(-8)). In this work we give an explicit construction that uses a seed length of O(log n+(1/epsilon)(o(1))). Note that this improves the seed length substantially and that the dependence on the error epsilon is additive and only grows subpolynomially as opposed to the previously known multiplicative polynomial dependence. Our generator uses dimensionality reduction on a Nisan-Wigderson based pseudorandom generator given by Lu, Kabanets [18].