On worst-case to average-case reductions for NP problems

We show that if an NP-complete problem has a non-adaptive self-corrector with respect to a distribution that can be sampled then coNP is contained in AM/poly and the polynomial hierarchy collapses to the third level. Feigenbaum and Fortnow show the same conclusion under the stronger assumption that an NP-complete problem has a non-adaptive random self-reduction. Our result shows it is impossible (using non-adaptive reductions) to base the average-case hardness of a problem in NP or the security of a one-way function on the worst-case complexity of an NP-complete problem (unless the polynomial hierarchy collapses).