Zero-Knowledge Proofs of Quantumness

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no"> <link href="/css/bootstrap/css/bootstrap.min.css" rel="stylesheet"> <script src="/css/bootstrap/js/bootstrap.bundle.min.js"></script> <title>Zero-Knowledge Proofs of Quantumness</title> <link rel="stylesheet" href="/css/iacrcc.css"> <link rel="icon" type="image/png" href="/favicon.ico"> <style> div.authorname { font-weight: 500; margin-bottom: .3rem; } div.author { margin-bottom: 1rem; } span.keyword { font-weight: 500; } span.keyword a { color: black; } div.reference { margin-bottom: .5rem; } ol.bib li:before { margin-left: -1.5rem; content: "[" counter(bcounter) "] "; margin-right: .5rem; } ol.bib { list-style: none; counter-reset: bcounter; } ol.bib li { counter-increment: bcounter; margin-bottom: .5rem; } .card-header { background-color: #d1e7dd !important; } .authorlist { /* border: 1px solid #aaa; padding: 1rem; margin-bottom: 1rem; background-color: white;*/ } </style> <script> MathJax = { tex: { inlineMath: [['$', '$'], ['\$', '\$']], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEnvironments: false, processEscapes: true }, "HTML-CSS": { linebreaks: { automatic: true } } }; </script> <script id="MathJax-script" async src="/js/mathjax/tex-chtml.js"></script> <link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"> <meta name="DC.Creator.PersonalName" content="Duong Hieu Phan"> <meta name="DC.Creator.PersonalName" content="Weiqiang Wen"> <meta name="DC.Creator.PersonalName" content="Xingyu Yan"> <meta name="DC.Creator.PersonalName" content="Jinwei Zheng"> <meta name="DC.Date.created" content="2025-01-13 16:12:07"> <meta name="DC.Date.dateSubmitted" content="2024-10-08"> <meta name="DC.Date.dateAccepted" content="2024-12-03"> <meta name="DC.Description" xml:lang="en" lang="en" content="<p> With the rapid development of quantum computers, proofs of quantumness have recently become an interesting and intriguing research direction. However, in all current schemes for proofs of quantumness, quantum provers almost invariably face the risk of being maliciously exploited by classical verifiers. In fact, through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. In other words, malicious verifiers can break some schemes (that quantum provers are not aware of) through interaction with quantum provers. All this is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness.</p><p>To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent any malicious verifier from exploiting quantum advantage. Interestingly, we find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes.</p><p>Due to some technical reason, it appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. Intuitively, this helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof.</p><p>Specifically, the two principle proofs of quantumness schemes: Shor's factoring-based scheme and learning with errors-based scheme in [Brakerski et al, FOCS, 2018], can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Notably, the zero-knowledge proofs of quantumness can be viewed as an enhanced security notion for proofs of quantumness. To prevent malicious verifiers from exploiting the quantum device's capabilities or knowledge, it is advisable to transition existing proofs of quantumness schemes to this framework whenever feasible. </p>"> <meta name="DC.Format" content="application/pdf"> <meta name="DC.Identifier.DOI" content="10.62056/ayiv4fe-3"> <meta name="DC.Identifier.URI" content="https://cic.iacr.org/p/1/4/24"> <meta name="DC.Language" content="en"> <meta name="DC.Rights" content="Copyright (c) 2023 held by author(s)"> <meta name="DC.Rights" content="https://creativecommons.org/licenses/by/4.0/"> <meta name="DC.Source" content="IACR Communications in Cryptology"> <meta name="DC.Source.ISSN" content="3006-5496"> <meta name="DC.Source.Issue" content="4"> <meta name="DC.Source.Volume" content="1"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Quantum cryptography"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Zero-knowledge"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Proofs of quantumness."> <meta name="DC.Title" content="Zero-Knowledge Proofs of Quantumness"> <meta name="DC.Type" content="Text.Serial.Journal"> <meta name="DC.Type.articleType" content="Articles"> <meta name="citation_journal_title" content="IACR Communications in Cryptology"> <meta name="citation_journal_abbrev" content="CiC"> <meta name="citation_issn" content="3006-5496"><meta name="citation_author" content="Duong Hieu Phan"> <meta name="citation_author_institution" content="LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris"> <meta name="citation_author" content="Weiqiang Wen"> <meta name="citation_author_institution" content="LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris"> <meta name="citation_author" content="Xingyu Yan"> <meta name="citation_author_institution" content="State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876"> <meta name="citation_author_institution" content="School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing, 100081"> <meta name="citation_author" content="Jinwei Zheng"> <meta name="citation_author_institution" content="LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris"> <meta name="citation_title" content="Zero-Knowledge Proofs of Quantumness"> <meta name="citation_language" content="en"> <meta name="citation_date" content="2025-01-13"> <meta name="citation_volume" content="1"> <meta name="citation_issue" content="4"> <meta name="citation_doi" content="10.62056/ayiv4fe-3"> <meta name="citation_abstract_html_url" content="https://cic.iacr.org/p/1/4/24"> <meta name="citation_keywords" xml:lang="en" lang="en" content="Quantum cryptography"><meta name="citation_keywords" xml:lang="en" lang="en" content="Zero-knowledge"><meta name="citation_keywords" xml:lang="en" lang="en" content="Proofs of quantumness."> <meta name="citation_pdf_url" content="https://cic.iacr.org/p/1/4/24/pdf"> </head> <body> <noscript> <h1 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class="authorlist collapse"> <div class="author"> <div class="authorname">Duong Hieu Phan <a target="_blank" href="https://orcid.org/0000-0003-1136-4064"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris, France<br> <span class="font-monospace">hieu dot phan at telecom-paris dot fr</span> </div> </div> <div class="author"> <div class="authorname">Weiqiang Wen <a target="_blank" href="https://orcid.org/0000-0001-5272-2572"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris, France<br> <span class="font-monospace">weiqiang dot wen at telecom-paris dot fr</span> </div> </div> <div class="author"> <div class="authorname">Xingyu Yan <a target="_blank" href="https://orcid.org/0000-0001-9147-6554"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China<br> School of Cyberspace Science and Technology, Beijing Institute of Technology, Beijing, 100081, China<br> <span class="font-monospace">yanxy2020 at bupt dot edu dot cn</span> </div> </div> <div class="author"> <div class="authorname">Jinwei Zheng </div> <div class="ms-4 mb-2"> LTCI, Telecom Paris, Institut Polytechnique de Paris, Paris, France<br> <span class="font-monospace">jinwei dot zheng at telecom-paris dot fr</span> </div> </div> </div> <div class="mb-3"> <strong class="fs-4">Keywords: </strong> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Quantum cryptography" title="Quantum cryptography"><a href="/search?q=Quantum%20cryptography">Quantum cryptography</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Zero-knowledge" title="Zero-knowledge"><a href="/search?q=Zero-knowledge">Zero-knowledge</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Proofs of quantumness." title="Proofs of quantumness."><a href="/search?q=Proofs%20of%20quantumness.">Proofs of quantumness.</a></span> </div> <h3 class="mt-4">Abstract</h3> <p><p> With the rapid development of quantum computers, proofs of quantumness have recently become an interesting and intriguing research direction. However, in all current schemes for proofs of quantumness, quantum provers almost invariably face the risk of being maliciously exploited by classical verifiers. In fact, through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. In other words, malicious verifiers can break some schemes (that quantum provers are not aware of) through interaction with quantum provers. All this is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness.</p><p>To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent any malicious verifier from exploiting quantum advantage. Interestingly, we find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes.</p><p>Due to some technical reason, it appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. Intuitively, this helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof.</p><p>Specifically, the two principle proofs of quantumness schemes: Shor's factoring-based scheme and learning with errors-based scheme in [Brakerski et al, FOCS, 2018], can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Notably, the zero-knowledge proofs of quantumness can be viewed as an enhanced security notion for proofs of quantumness. To prevent malicious verifiers from exploiting the quantum device's capabilities or knowledge, it is advisable to transition existing proofs of quantumness schemes to this framework whenever feasible. </p></p> <h3 class="mb-3">References</h3> <div class="d-flex"> <div style="min-width:9rem;">[AA11]</div> <div><div id="ref-aaronson2011computational" class="bibitem">Scott Aaronson and Alex Arkhipov. 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JOUR AU - Phan, Duong AU - Wen, Weiqiang AU - Yan, Xingyu AU - Zheng, Jinwei PY - 2025 TI - Zero-Knowledge Proofs of Quantumness JF - IACR Communications in Cryptology JA - CIC VL - 1 IS - 4 DO - 10.62056/ayiv4fe-3 UR - https://doi.org/10.62056/ayiv4fe-3 AB - <p> With the rapid development of quantum computers, proofs of quantumness have recently become an interesting and intriguing research direction. However, in all current schemes for proofs of quantumness, quantum provers almost invariably face the risk of being maliciously exploited by classical verifiers. In fact, through malicious strategies in interaction with quantum provers, classical verifiers could solve some instances of hard problems that arise from the specific scheme in use. In other words, malicious verifiers can break some schemes (that quantum provers are not aware of) through interaction with quantum provers. All this is due to the lack of formalization that prevents malicious verifiers from extracting useful information in proofs of quantumness.</p><p>To address this issue, we formalize zero-knowledge proofs of quantumness. Intuitively, the zero-knowledge property necessitates that the information gained by the classical verifier from interactions with the quantum prover should not surpass what can be simulated using a simulated classical prover interacting with the same verifier. As a result, the new zero-knowledge notion can prevent any malicious verifier from exploiting quantum advantage. Interestingly, we find that the classical zero-knowledge proof is sufficient to compile some existing proofs of quantumness schemes into zero-knowledge proofs of quantumness schemes.</p><p>Due to some technical reason, it appears to be more general to require zero-knowledge proof on the verifier side instead of the prover side. Intuitively, this helps to regulate the verifier's behavior from malicious to be honest-but-curious. As a result, both parties will play not only one role in the proofs of quantumness but also the dual role in the classical zero-knowledge proof.</p><p>Specifically, the two principle proofs of quantumness schemes: Shor's factoring-based scheme and learning with errors-based scheme in [Brakerski et al, FOCS, 2018], can be transformed into zero-knowledge proofs of quantumness by requiring an extractable non-interactive zero-knowledge argument on the verifier side. Notably, the zero-knowledge proofs of quantumness can be viewed as an enhanced security notion for proofs of quantumness. To prevent malicious verifiers from exploiting the quantum device's capabilities or knowledge, it is advisable to transition existing proofs of quantumness schemes to this framework whenever feasible. </p> ER -</pre> <button id="riscopy" class="btn btn-sm btn-primary" aria-label="Copy to clipboard" onclick="copyMetadata('riscopy', 'ris')">Copy to clipboard</button> <button id="risdownload" class="ms-3 btn btn-sm btn-primary" aria-label="Download RIS file" onclick="sendCitation('ris')">Download .ris file</button> </div> <div class="tab-pane" id="text-pane" role="tabpanel" aria-labelledby="text-tab" tabindex="0"> <div class="w-75" id="textcitation">Duong Hieu Phan, Weiqiang Wen, Xingyu Yan, and Jinwei Zheng, Zero-Knowledge Proofs of Quantumness. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 4, Jan 13, 2025, doi: 10.62056/ayiv4fe-3.</div> <button id="textcopy" class="btn btn-sm btn-primary mt-3" aria-label="Copy to clipboard" onclick="copyMetadata('textcopy', 'textcitation')">Copy to clipboard</button> </div> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-secondary" data-bs-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="modal fade" id="citationsModal" tabindex="-1" aria-labelledby="citationsModalLabel" aria-hidden="true"> <div class="modal-dialog modal-dialog-scrollable modal-lg"> <div class="modal-content"> <div class="modal-header"> <h1 class="modal-title fs-3">Known citations</h1> <button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button> </div> <div class="modal-body p-4"> <p> We do not crawl the web, so we are only able to identify citations from papers that are registered with a DOI in crossref.org and the publisher reports their citations to crossref, and crossref can identify a DOI from the reference. 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Zero-Knowledge Proofs of Quantumness