Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies

<!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>Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies</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="Giacomo Borin"> <meta name="DC.Creator.PersonalName" content="Yi-Fu Lai"> <meta name="DC.Creator.PersonalName" content="Antonin Leroux"> <meta name="DC.Date.created" content="2025-01-13 16:12:07"> <meta name="DC.Date.dateSubmitted" content="2024-07-09"> <meta name="DC.Date.dateAccepted" content="2024-12-03"> <meta name="DC.Description" xml:lang="en" lang="en" content="<p> We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing the limitations of existing isogeny-based ring signatures.</p><p> First, we present an efficient concrete distinguisher for the SQIsign simulator when the signing key is provided using one transcript. This shows that turning SQIsign into an efficient full anonymous ring signature requires some new ideas.</p><p> Second, we propose a variant of SQIsign (Asiacrypt'20) that is resistant to the distinguisher attack with only a x1.4 increase in size and we render it to a ring signature, that we refer to as Erebor. This variant introduces a new zero-knowledge assumption that ensures full anonymity. The efficiency of Erebor remains comparable to that of SQIsign, with only a proportional increase due to the ring size. This results in a signature size of 0.71 KB for 4 users and 1.41 KB for 8 users, making it the most compact post-quantum ring signature for up to 29 users.</p><p> Third, we revisit the GPS signature scheme (Asiacrypt'17), developing efficient subroutines to make the scheme more efficient and significantly reduce the resulting signature size. By integrating our scheme with the paradigm by Beullens, Katsumata, and Pintore (Asiacrypt’20), we achieve an efficient logarithmic ring signature, that we call Durian, resulting in a signature size of 9.87 KB for a ring of size 1024.</p>"> <meta name="DC.Format" content="application/pdf"> <meta name="DC.Identifier.DOI" content="10.62056/ava3zivrzn"> <meta name="DC.Identifier.URI" content="https://cic.iacr.org/p/1/4/4"> <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.Title" content="Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies"> <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="Giacomo Borin"> <meta name="citation_author_institution" content="IBM Research - Zurich"> <meta name="citation_author_institution" content="University of Zurich"> <meta name="citation_author" content="Yi-Fu Lai"> <meta name="citation_author_institution" content="Ruhr University Bochum"> <meta name="citation_author" content="Antonin Leroux"> <meta name="citation_author_institution" content="DGA Maitrise de l'information"> <meta name="citation_author_institution" content="Université de Rennes"> <meta name="citation_title" content="Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies"> <meta name="citation_language" content="en"> <meta name="citation_date" content="2025-01-13"> <meta 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mt-2 d-flex justify-content-between flex-column flex-lg-row"> <div>Giacomo Borin, Yi-Fu Lai, Antonin Leroux</div> <button role="button" aria-expanded="false" aria-controls="authorlist" class="ms-4 btn me-3 dropdown-toggle" data-bs-toggle="collapse" data-bs-target="#authorlist">Author Info</button> </div> <div id="authorlist" class="authorlist collapse"> <div class="author"> <div class="authorname">Giacomo Borin <a target="_blank" href="https://orcid.org/0009-0001-7311-3802"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> IBM Research - Zurich, Rüschlikon, Switzerland<br> University of Zurich, Zurich, Switzerland<br> <span class="font-monospace">erebor at gbor dot in</span> </div> </div> <div class="author"> <div class="authorname">Yi-Fu Lai <a target="_blank" href="https://orcid.org/0000-0002-1346-9372"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> Ruhr University Bochum, Bochum, Germany<br> <span class="font-monospace">yi-fu dot lai at rub dot de</span> </div> </div> <div class="author"> <div class="authorname">Antonin Leroux <a target="_blank" href="https://orcid.org/0009-0002-3737-0075"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> DGA Maitrise de l'information, Bruz, France<br> Université de Rennes, Rennes, France<br> <span class="font-monospace">antonin dot leroux at polytechnique dot org</span> </div> </div> </div> <h3 class="mt-4">Abstract</h3> <p><p> We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing the limitations of existing isogeny-based ring signatures.</p><p> First, we present an efficient concrete distinguisher for the SQIsign simulator when the signing key is provided using one transcript. This shows that turning SQIsign into an efficient full anonymous ring signature requires some new ideas.</p><p> Second, we propose a variant of SQIsign (Asiacrypt'20) that is resistant to the distinguisher attack with only a x1.4 increase in size and we render it to a ring signature, that we refer to as Erebor. This variant introduces a new zero-knowledge assumption that ensures full anonymity. The efficiency of Erebor remains comparable to that of SQIsign, with only a proportional increase due to the ring size. This results in a signature size of 0.71 KB for 4 users and 1.41 KB for 8 users, making it the most compact post-quantum ring signature for up to 29 users.</p><p> Third, we revisit the GPS signature scheme (Asiacrypt'17), developing efficient subroutines to make the scheme more efficient and significantly reduce the resulting signature size. By integrating our scheme with the paradigm by Beullens, Katsumata, and Pintore (Asiacrypt’20), we achieve an efficient logarithmic ring signature, that we call Durian, resulting in a signature size of 9.87 KB for a ring of size 1024.</p></p> <h3 class="mb-3">References</h3> <div class="d-flex"> <div style="min-width:9rem;">[AABN02]</div> <div><div id="ref-EC:AABN02" class="bibitem">Michel Abdalla, Jee Hea An and Mihir Bellare, and Chanathip Namprempre. From Identification to Signatures via the Fiat-Shamir Transform: Minimizing Assumptions for Security and Forward-Security. In Lars R. Knudsen, editor, <em>EUROCRYPT 2002</em>, volume 2332 of <em>LNCS</em>, pages 418–433. 2002. Springer, Heidelberg. 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DOI: <a href="https://doi.org/10.1007/978-3-030-51280-4_25">10.1007/978-3-030-51280-4_25</a></div></div> </div> <div class="text-end mb-4"> <a href="https://scholar.google.com/scholar?hl=en&q=Tsz+Hon+Yuen+Shifeng+Sun+Joseph+K.+Liu+Man+Ho+Au+Muhammed+F.+Esgin+Qingzhao+Zhang+Dawu+Gu+RingCT+3.0+for+Blockchain+Confidential+Transaction%3A+Shorter+Size+and+Stronger+Security+2020" target="_blank" class="ms-3">Google Scholar</a> <a href="https://eprint.iacr.org/search?relevance=on&authors=Tsz+Hon+Yuen+Shifeng+Sun+Joseph+K.+Liu+Man+Ho+Au+Muhammed+F.+Esgin+Qingzhao+Zhang+Dawu+Gu&title=RingCT+3.0+for+Blockchain+Confidential+Transaction%3A+Shorter+Size+and+Stronger+Security&submittedafter=2019&submittedbefore=2021" target="_blank" class="ms-3">ePrint</a> </div> </div> <div class="col-12 col-md-4"> <p class="mt-4"> <a class="btn btn-outline-dark" href="/p/1/4/4/pdf"><img alt="PDF" class="icon" src="/images/file-pdf.svg">PDF</a> <img style="margin-left: 1rem;max-width: 1.2rem;" src="/images/open_access.svg" title="Open access" alt="Open access"> </p> <div class="my-4"> <span class="fw-bold me-2">DOI:</span> <a href="https://doi.org/10.62056/ava3zivrzn">https://doi.org/10.62056/ava3zivrzn</a> </div> <div class="card mb-4"> <h5 class="card-header">History</h5> <div class="card-body"> <strong>Submitted</strong>: 2024-07-09<br> <strong>Accepted</strong>: 2024-12-03<br> <strong>Published</strong>: 2025-01-13<br>  <script src="https://crossmark-cdn.crossref.org/widget/v2.0/widget.js"></script> <a data-target="crossmark"><img style="margin-top:4px;" src="https://crossmark-cdn.crossref.org/widget/v2.0/logos/CROSSMARK_Color_horizontal.svg" width="150" /></a>  </div> </div> <div class="card mb-4"> <h5 class="card-header">How to cite</h5> <div class="card-body"> <p>Giacomo Borin, Yi-Fu Lai, and Antonin Leroux, Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 4, Jan 13, 2025, doi: 10.62056/ava3zivrzn. </p> <button type="button" id="citationModalLabel" class="float-end btn btn-outline-dark" data-bs-toggle="modal" data-bs-target="#citationModal"> BibTeX, etc </button> </div> </div> <div class="card mb-4"> <h5 class="card-header">License</h5> <div class="card-body"> <p>Copyright is held by the author(s)</p> <p> This work is licensed under a <a target="_blank" href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution (CC BY)</a> license. </p> </div> </div> </div> </div> <div class="modal fade" id="citationModal" tabindex="-1" aria-labelledby="citationModalLabel" aria-hidden="true"> <div class="modal-dialog modal-xl"> <div class="modal-content"> <div class="modal-header"> <h1 class="modal-title fs-3">How to cite this</h1> <button type="button" class="btn-close" data-bs-dismiss="modal" aria-label="Close"></button> </div> <div class="modal-body p-4"> <ul class="nav nav-tabs" id="myTab" role="tablist"> <li class="nav-item" role="presentation"> <button class="nav-link active" id="bibtex-tab" data-bs-toggle="tab" data-bs-target="#bibtex-pane" type="button" role="tab" aria-controls="bibtex-pane" aria-selected="true">BibTeX</button> </li> <li class="nav-item" role="presentation"> <button class="nav-link" id="ris-tab" data-bs-toggle="tab" data-bs-target="#ris-pane" type="button" role="tab" aria-controls="ris-pane" aria-selected="false">RIS/Endnote/Zotero/Mendeley</button> </li> <li class="nav-item" role="presentation"> <button class="nav-link" id="text-tab" data-bs-toggle="tab" data-bs-target="#text-pane" type="button" role="tab" aria-controls="text-pane" aria-selected="false">Text</button> </li> </ul> <div class="tab-content p-4"> <div class="tab-pane active" id="bibtex-pane" role="tabpanel" aria-labelledby="bibtex-tab" tabindex="0"> <pre id="bib">@article{CiC-1-4-4, author = "Borin, Giacomo and Lai, Yi-Fu and Leroux, Antonin", journal = "{IACR} {C}ommunications in {C}ryptology", publisher = "{I}nternational {A}ssociation for {C}ryptologic {R}esearch", title = "Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies", volume = "1", number = "4", date = "2025-01-13", year = "2025", issn = "3006-5496", doi = "10.62056/ava3zivrzn" } </pre> <button id="bibtexcopy" class="btn btn-sm btn-primary" aria-label="Copy to clipboard" onclick="copyMetadata('bibtexcopy', 'bib')">Copy to clipboard</button> <button id="bibtexdownload" class="ms-3 btn btn-sm btn-primary" aria-label="Download BibTeX .bib file" onclick="sendCitation('bib')">Download .bib file</button> </div> <div class="tab-pane" id="ris-pane" role="tabpanel" aria-labelledby="ris-tab" tabindex="0"> <pre id="ris">TY - JOUR AU - Borin, Giacomo AU - Lai, Yi-Fu AU - Leroux, Antonin PY - 2025 TI - Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies JF - IACR Communications in Cryptology JA - CIC VL - 1 IS - 4 DO - 10.62056/ava3zivrzn UR - https://doi.org/10.62056/ava3zivrzn AB - <p> We construct two efficient post-quantum ring signatures with anonymity against full key exposure from isogenies, addressing the limitations of existing isogeny-based ring signatures.</p><p> First, we present an efficient concrete distinguisher for the SQIsign simulator when the signing key is provided using one transcript. This shows that turning SQIsign into an efficient full anonymous ring signature requires some new ideas.</p><p> Second, we propose a variant of SQIsign (Asiacrypt'20) that is resistant to the distinguisher attack with only a x1.4 increase in size and we render it to a ring signature, that we refer to as Erebor. This variant introduces a new zero-knowledge assumption that ensures full anonymity. The efficiency of Erebor remains comparable to that of SQIsign, with only a proportional increase due to the ring size. This results in a signature size of 0.71 KB for 4 users and 1.41 KB for 8 users, making it the most compact post-quantum ring signature for up to 29 users.</p><p> Third, we revisit the GPS signature scheme (Asiacrypt'17), developing efficient subroutines to make the scheme more efficient and significantly reduce the resulting signature size. By integrating our scheme with the paradigm by Beullens, Katsumata, and Pintore (Asiacrypt’20), we achieve an efficient logarithmic ring signature, that we call Durian, resulting in a signature size of 9.87 KB for a ring of size 1024.</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">Giacomo Borin, Yi-Fu Lai, and Antonin Leroux, Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 4, Jan 13, 2025, doi: 10.62056/ava3zivrzn.</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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Erebor and Durian: Full Anonymous Ring Signatures from Quaternions and Isogenies