Broadcast Encryption using Sum-Product decomposition of Boolean functions

<!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>Broadcast Encryption using Sum-Product decomposition of Boolean functions</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="Aurélien Dupin"> <meta name="DC.Creator.PersonalName" content="Simon Abelard"> <meta name="DC.Date.created" content="2024-04-09 19:26:57"> <meta name="DC.Date.dateSubmitted" content="2024-01-08"> <meta name="DC.Date.dateAccepted" content="2024-03-05"> <meta name="DC.Description" xml:lang="en" lang="en" content="<p> The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.</p><p> Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.</p><p> In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage. </p>"> <meta name="DC.Format" content="application/pdf"> <meta name="DC.Identifier.DOI" content="10.62056/av4fe0iuc"> <meta name="DC.Identifier.URI" content="https://cic.iacr.org/p/1/1/18"> <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="1"> <meta name="DC.Source.Volume" content="1"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Broadcast Encryption"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Boolean Functions"> <meta name="DC.Title" content="Broadcast Encryption using Sum-Product decomposition of Boolean functions"> <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="Aurélien Dupin"> <meta name="citation_author_institution" content="Thales SIX France"> <meta name="citation_author" content="Simon Abelard"> <meta name="citation_author_institution" content="Thales SIX France"> <meta name="citation_title" content="Broadcast Encryption using Sum-Product decomposition of Boolean functions"> <meta name="citation_language" content="en"> <meta name="citation_date" content="2024-04-09"> <meta name="citation_volume" content="1"> <meta name="citation_issue" content="1"> <meta name="citation_doi" content="10.62056/av4fe0iuc"> <meta name="citation_abstract_html_url" content="https://cic.iacr.org/p/1/1/18"> 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flex-lg-row"> <div>Aurélien Dupin, Simon Abelard</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">Aurélien Dupin </div> <div class="ms-4 mb-2"> Thales SIX France, Gennevilliers, France<br> <span class="font-monospace">aurelien dot dupin at thalesgroup dot com</span> </div> </div> <div class="author"> <div class="authorname">Simon Abelard </div> <div class="ms-4 mb-2"> Thales SIX France, Gennevilliers, France<br> <span class="font-monospace">sabelard at protonmail dot com</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="Broadcast Encryption" title="Broadcast Encryption"><a href="/search?q=Broadcast%20Encryption">Broadcast Encryption</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Boolean Functions" title="Boolean Functions"><a href="/search?q=Boolean%20Functions">Boolean Functions</a></span> </div> <h3 class="mt-4">Abstract</h3> <p><p> The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.</p><p> Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.</p><p> In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage. </p></p> <h3 class="mb-3">References</h3> <div class="d-flex"> <div style="min-width:9rem;">[AWY20]</div> <div>Shweta Agrawal, Daniel Wichs, and Shota Yamada. Optimal broadcast encryption from <span class="bibtex-protected">LWE</span> and pairings in the standard model. 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JOUR AU - Dupin, Aurélien AU - Abelard, Simon PY - 2024 TI - Broadcast Encryption using Sum-Product decomposition of Boolean functions JF - IACR Communications in Cryptology JA - CIC VL - 1 IS - 1 DO - 10.62056/av4fe0iuc UR - https://doi.org/10.62056/av4fe0iuc AB - <p> The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.</p><p> Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.</p><p> In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage. </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">Aurélien Dupin and Simon Abelard, Broadcast Encryption using Sum-Product decomposition of Boolean functions. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/av4fe0iuc.</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. That includes (most) articles from Springer and many from ACM, but it excludes citations from USENIX because they don't issue DOIs. It also excludes citations from arxiv and eprint. You may find more citations in <a href="https://scholar.google.com/scholar?hl=en&q=Broadcast+Encryption+using+Sum-Product+decomposition+of+Boolean+functions">Google Scholar</a>. </p> <ol> <li>Oliwer Sobolewski, Konrad Wrona, Adrian Cinal, Gabriel Wechta, Joanna Sliwa, Mateusz Leśniak, Michał Wroński, Miroslaw Kutylowski and Przemysław Kubiak. Quantum-Resistant Key Management for Underwater Acoustic Multicast Communication. <em>MILCOM 2024 - 2024 IEEE Military Communications Conference (MILCOM)</em> (2024), p. 196 DOI: <a href="https://doi.org/10.1109/MILCOM61039.2024.10773852" target="_blank">10.1109/MILCOM61039.2024.10773852</a></li> </ol> </div> <div class="modal-footer"> <button type="button" class="btn btn-secondary" data-bs-dismiss="modal">Close</button> </div> </div> </div> </div> <script> function copyMetadata(buttid, id) { let range = document.createRange(); range.selectNode(document.getElementById(id)); window.getSelection().removeAllRanges(); window.getSelection().addRange(range); document.execCommand('copy'); window.getSelection().removeAllRanges(); const copyTooltip = new bootstrap.Tooltip('#' + buttid, {trigger: 'manual', title: 'Copied!'}); copyTooltip.show(); setTimeout(function() { copyTooltip.dispose(); }, 2000); } function sendCitation(typ) { // typ is 'bib' or 'ris' let data = document.getElementById(typ).innerHTML; atag = document.createElement('a'); atag.setAttribute('href', 'data:text/plain;charset=utf-8,' + encodeURIComponent(data)); atag.setAttribute('download', '1-1-18.' + typ); if (document.createEvent) { let event = document.createEvent('MouseEvents'); event.initEvent('click', true, true); atag.dispatchEvent(event); } else { atag.click(); } } </script> </main> <div class="container-fluid mt-auto" id="pageFooter"> </div> <footer class="text-center footer py-3"> <small> <a href="https://iacr.org/copyright.html">Copyright © 2025</a> <span class="d-none d-md-inline">by the </span><span class="d-md-none">IACR</span> <span class="d-none d-md-inline">International Association for Cryptologic Research</span> <span class="d-none d-md-inline">• </span><br class="d-md-none"> <a href="https://iacr.org/privacy.html">Privacy Policy</a> </small> </footer> <script id="results-template" type="text/x-handlebars-template"> <div class="p-3 shadow" style="margin-bottom:1rem;max-height:70vh;overflow-y:scroll"> <p>{{estimated_results}} results (if more than 100, then refine your query)</p> <ol> {{#each results}} <li role="presentation"><a href="{{url}}">{{title}}</a><br> {{#each authors }}{{this}}{{#unless @last}}, {{/unless}}{{/each}}</li> {{/each}} </ol> </div> </script> <script src="/static/js/handlebars-v4.7.7.js"></script> <script> var theTemplateScript = document.getElementById('results-template').innerHTML; var resultsTemplate = Handlebars.compile(theTemplateScript); var textinput = document.getElementById('searchbox'); // Returns a function, that, as long as it continues to be invoked, will not // be triggered. 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Broadcast Encryption using Sum-Product decomposition of Boolean functions