Quantum Collision-Resistance of Non-Uniformly Distributed Functions (PQCrypto 2016)
Ehsan Ebrahimi Targhi, Gelo Noel Tabia, Dominique Unruh
[ eprint | official ]

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).