Constant-Error Pseudorandomness Proofs from Hardness Require Majority

Abstract

Research in the 1980s and 1990s showed how to construct a pseudorandom generator from a function that is hard to compute on more than 99% of the inputs. A more recent line of works showed, however, that if the generator has small error, then the proof of correctness cannot be implemented in subclasses of TC 0 , and hence the construction cannot be applied to the known hardness results. This article considers a typical class of pseudorandom generator constructions, and proves an analogous result for the case of large error.