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, (Formula presented) 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.
Cite
CITATION STYLE
Liu, Q., & Zhandry, M. (2019). On finding quantum multi-collisions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11478 LNCS, pp. 189–218). Springer Verlag. https://doi.org/10.1007/978-3-030-17659-4_7
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