Quantum Collision-Finding in Non-Uniform Random Functions.

We study quantum attacks on finding a collision in a non-uniform random function whose outputs are drawn according to a distribution of min-entropy k. This can be viewed as showing generic security of hash functions under relaxed assumptions in contrast to the standard heuristic of assuming uniformly random outputs. It is useful in analyzing quantum security of the Fujisaki-Okamoto transformation [31]. In particular, our results close a gap left open in [30].