No better ways to generate hard NP instances than picking uniformly at random
Russell Impagliazzo, Levin L.A · 1990
Distributed NP (DNP) problems are ones supplied with probability distributions of instances. It is shown that every DNP problem complete for P-time computable distributions is also complete for all distributions that can be sampled. This result makes the concept of average-case NP completeness robust and the question of the average-case complexity of complete DNP problems a natural alternative to P=?NP. Similar techniques yield a connection between cryptography and learning theory.