Abstract: We study the quantum query complexity of finding a collision for a function f whose outputs are chosen according to a distribution with min-entropy k. We prove that $Ω(2^{k/9})$ quantum queries are necessary to find a collision for function f. This is needed in some security proofs in the quantum random oracle model (e.g. the Fujisaki-Okamoto transform).
Permalink: http://www.ut.ee/~unruh/publications/collision.html