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**2018/1096**

**Title:**

On Finding Quantum Multi-collisions

**Authors:**
Qipeng Liu, Mark Zhandry

**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.

**ePrint:**
https://eprint.iacr.org/2018/1096

**Talk: **https://www.youtube.com/watch?v=tpS_JuQWG-4

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