A PRG for Boolean PTF of Degree 2 with Seed Length Subpolynomial in epsilon and Logarithmic in n

Abstract

We construct and analyze a pseudorandom generator for degree 2 boolean polynomial threshold functions. Random constructions achieve the optimal seed length of [EQUATION], however the best known explicit construction of [8] uses a seed length of O(log n · ϵ−8). In this work we give an explicit construction that uses a seed length of [EQUATION]. Note that this improves the seed length substantially and that the dependence on the error ϵ 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].