Black-Box Separations and Their Adaptability to the Non-uniform Model

Oracle separation methods are used in cryptography to rule out black-box reductions between cryptographic primitives. It is sufficient to find an oracle relative to which the base primitive exists but there are no secure instances of the constructed primitive. It is often beyond our current reach to construct a fixed oracle with such properties because it is difficult to prove the existence of secure base primitives. To overcome this gap, randomized oracles are used to create random base primitives that are secure on average. After that, a fixed oracle is extracted from the probability distribution by using non-constructive probabilistic arguments and the countability of the set of adversaries. Such extraction only applies to uniform reductions because the set of non-uniform adversaries is not countable. We study how to adapt oracle separation results to the non-uniform model. The known separation techniques are capable of ruling out the so-called fully black-box reductions and a certain strong form of semi black-box reductions also in the non-uniform model. We study how to go beyond the barrier of strong semi black-box reductions and show that this is possible by using random oracles with auxiliary advice. For that end, we prove a conjecture of Unruh (2007) about pre-sampling being a sufficient substitute for advice for any oracle distribution.