## CryptoDB

### Paper: On Finding Quantum Multi-collisions

Authors: Qipeng Liu Mark Zhandry DOI: 10.1007/978-3-030-17659-4_7 (login may be required) Search ePrint Search Google A k-collision for a compressing hash function H is a set of k distinct inputs that all map to the same output. In this work, we show that for any constant k, $\varTheta \left( N^{\frac{1}{2}(1-\frac{1}{2^k-1})}\right)$ quantum queries are both necessary and sufficient to achieve a k-collision with constant probability. This improves on both the best prior upper bound (Hosoyamada et al., ASIACRYPT 2017) and provides the first non-trivial lower bound, completely resolving the problem.
##### BibTeX
@article{eurocrypt-2019-29385,
title={On Finding Quantum Multi-collisions},
booktitle={Advances in Cryptology – EUROCRYPT 2019},
series={Advances in Cryptology – EUROCRYPT 2019},
publisher={Springer},
volume={11478},
pages={189-218},
doi={10.1007/978-3-030-17659-4_7},
author={Qipeng Liu and Mark Zhandry},
year=2019
}