Paper 2018/1096 Original: eprint.iacr.org/2018/1096 ↗
On Finding Quantum Multi-collisions
Abstract
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 $k$, $\Theta\left(N^{\frac{1}{2}(1-\frac{1}{2^k-1})}\right)$ 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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2019-02-27: last updated
- 2018-11-15: published
- Short URL
- https://ia.cr/2018/1096
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/1096,
author = {Qipeng Liu and Mark Zhandry},
title = {On Finding Quantum Multi-collisions},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/1096},
year = {2018},
url = {https://eprint.iacr.org/2018/1096}
}