Abstract: Compressed oracles (Zhandry, Crypto 2019) are a powerful technique to reason about quantum random oracles, enabling a sort of lazy sampling in the presence of superposition queries. A long-standing open question is whether a similar technique can also be used to reason about random (efficiently invertible) permutations.
In this work, we make a step towards answering this question. We first define the compressed permutation oracle and illustrate its use. While the soundness of this technique (i.e., the indistinguishability from a random permutation) remains a conjecture, we show a curious 2-for-1 theorem: If we use the compressed permutation oracle methodology to show that some construction (e.g., Luby-Rackoff) implements a random permutation (or strong qPRP), then we get the fact that this methodology is actually sound for free.
Permalink: http://www.ut.ee/~unruh/publications/towards-cpo.html