Cryptology ePrint Archive: Report 2018/1096

On Finding Quantum Multi-collisions

Qipeng Liu and 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.

Category / Keywords: foundations / quantum cryptography

Date: received 12 Nov 2018

Contact author: qipengl at cs princeton edu

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Version: 20181115:160446 (All versions of this report)

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