On finding quantum multi-collisions

Qipeng Liu; Mark Zhandry

doi:10.1007/978-3-030-17659-4_7

On finding quantum multi-collisions

Qipeng Liu, Mark Zhandry

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

13 Scopus citations

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.

Original language	English (US)
Title of host publication	Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Editors	Vincent Rijmen, Yuval Ishai
Publisher	Springer Verlag
Pages	189-218
Number of pages	30
ISBN (Print)	9783030176587
DOIs	https://doi.org/10.1007/978-3-030-17659-4_7
State	Published - 2019
Event	38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 - Darmstadt, Germany Duration: May 19 2019 → May 23 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11478 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019
Country/Territory	Germany
City	Darmstadt
Period	5/19/19 → 5/23/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-17659-4_7

Cite this

Liu, Q., & Zhandry, M. (2019). On finding quantum multi-collisions. In V. Rijmen, & Y. Ishai (Eds.), Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (pp. 189-218). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11478 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-17659-4_7

Liu, Qipeng ; Zhandry, Mark. / On finding quantum multi-collisions. Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. editor / Vincent Rijmen ; Yuval Ishai. Springer Verlag, 2019. pp. 189-218 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

author = "Qipeng Liu and Mark Zhandry",

note = "Funding Information: Acknowledgements. This work is supported in part by NSF. Opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF. Publisher Copyright: {\textcopyright} International Association for Cryptologic Research 2019.; 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019 ; Conference date: 19-05-2019 Through 23-05-2019",

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Liu, Q & Zhandry, M 2019, On finding quantum multi-collisions. in V Rijmen & Y Ishai (eds), Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11478 LNCS, Springer Verlag, pp. 189-218, 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2019, Darmstadt, Germany, 5/19/19. https://doi.org/10.1007/978-3-030-17659-4_7

On finding quantum multi-collisions. / Liu, Qipeng; Zhandry, Mark.
Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. ed. / Vincent Rijmen; Yuval Ishai. Springer Verlag, 2019. p. 189-218 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11478 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N1 - Funding Information: Acknowledgements. This work is supported in part by NSF. Opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF. Publisher Copyright: © International Association for Cryptologic Research 2019.

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AB - 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.

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T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Liu Q, Zhandry M. On finding quantum multi-collisions. In Rijmen V, Ishai Y, editors, Advances in Cryptology – EUROCRYPT 2019 - 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Springer Verlag. 2019. p. 189-218. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-17659-4_7

On finding quantum multi-collisions

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