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On the necessity of collapsing for post-quantum and quantum commitments
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Dall'Agnol, Marcel and Spooner, Nicholas (2023) On the necessity of collapsing for post-quantum and quantum commitments. In: 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023), Aveiro, Portugal, 24-28 Jul 2023, 266 2:1-2:23. ISBN 9783959772839. ISSN 1868-8969.
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Official URL: https://drops.dagstuhl.de/opus/volltexte/2023/1831...
Abstract
Collapse binding and collapsing were proposed by Unruh (Eurocrypt '16) as post-quantum strengthenings of computational binding and collision resistance, respectively. These notions have been very successful in facilitating the "lifting" of classical security proofs to the quantum setting. A basic and natural question remains unanswered, however: are they the weakest notions that suffice for such lifting?
In this work we answer this question in the affirmative by giving a classical commit-and-open protocol which is post-quantum secure if and only if the commitment scheme (resp. hash function) used is collapse binding (resp. collapsing). We also generalise the definition of collapse binding to quantum commitment schemes, and prove that the equivalence carries over when the sender in this commit-and-open protocol communicates quantum information.
As a consequence, we establish that a variety of "weak" binding notions (sum binding, CDMS binding and unequivocality) are in fact equivalent to collapse binding, both for post-quantum and quantum commitments.
Finally, we prove a "win-win" result, showing that a post-quantum computationally binding commitment scheme that is not collapse binding can be used to build an equivocal commitment scheme (which can, in turn, be used to build one-shot signatures and other useful quantum primitives). This strengthens a result due to Zhandry (Eurocrypt '19) showing that the same object yields quantum lightning.
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
Library of Congress Subject Headings (LCSH): | Quantum cryptography , Data encryption (Computer science), Computational complexity | ||||
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) | ||||
Publisher: | Schloss Dagstuhl — Leibniz-Zentrum für Informatik | ||||
Place of Publication: | Dagstuhl, Germany | ||||
ISBN: | 9783959772839 | ||||
ISSN: | 1868-8969 | ||||
Official Date: | 18 July 2023 | ||||
Dates: |
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Volume: | 266 | ||||
Page Range: | 2:1-2:23 | ||||
Article Number: | 2 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 2 November 2023 | ||||
Date of first compliant Open Access: | 6 November 2023 | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023) | ||||
Type of Event: | Conference | ||||
Location of Event: | Aveiro, Portugal | ||||
Date(s) of Event: | 24-28 Jul 2023 | ||||
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