On the Complexity of Non-adaptively Increasing the Stretch of Pseudorandom Generators

We study the complexity of black-box constructions of linearstretch pseudorandom generators starting from a 1-bit stretch oracle generator G. We show that there is no construction which makes nonadaptive queries to G and then just outputs bits of the answers. The result extends to constructions that both work in the non-uniform setting and are only black-box in the primitive G (not the proof of correctness), in the sense that any such construction implies NP/poly 6= P/poly. We then argue that not much more can be obtained using our techniques: via a modification of an argument of Reingold, Trevisan, and Vadhan (TCC ’04), we prove in the non-uniform setting that there is a construction which only treats the primitive G as black-box, has polynomial stretch, makes non-adaptive queries to the oracle G, and outputs an affine function (i.e., parity or its complement) of the oracle query answers.