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Efficient Boolean-to-Arithmetic Mask Conversion in Hardware
<!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>Efficient Boolean-to-Arithmetic Mask Conversion in Hardware</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="Aein Rezaei Shahmirzadi"> <meta name="DC.Creator.PersonalName" content="Michael Hutter"> <meta name="DC.Date.created" content="2024-10-07 15:13:12"> <meta name="DC.Date.dateSubmitted" content="2024-07-09"> <meta name="DC.Date.dateAccepted" content="2024-09-02"> <meta name="DC.Description" xml:lang="en" lang="en" content="<p>Masking schemes are key in thwarting side-channel attacks due to their robust theoretical foundation. Transitioning from Boolean to arithmetic (B2A) masking is a necessary step in various cryptography schemes, including hash functions, ARX-based ciphers, and lattice-based cryptography. While there exists a significant body of research focusing on B2A software implementations, studies pertaining to hardware implementations are quite limited, with the majority dedicated solely to creating efficient Boolean masked adders. In this paper, we present first- and second-order secure hardware implementations to perform B2A mask conversion efficiently without using masked adder structures. We first introduce a first-order secure low-latency gadget that executes a B2A2k in a single cycle. Furthermore, we propose a second-order secure B2A2k gadget that has a latency of only 4 clock cycles. Both gadgets are independent of the input word size k. We then show how these new primitives lead to improved B2Aq hardware implementations that perform a B2A mask conversion of integers modulo an arbitrary number. Our results show that our new gadgets outperform comparable solutions by more than a magnitude in terms of resource requirements and are at least 3 times faster in terms of latency and throughput. All gadgets have been formally verified and proven secure in the glitch-robust PINI security model. We additionally confirm the security of our gadgets on an FPGA platform using practical TVLA tests. </p>"> <meta name="DC.Format" content="application/pdf"> <meta name="DC.Identifier.DOI" content="10.62056/a3c0l2isfg"> <meta name="DC.Identifier.URI" content="https://cic.iacr.org/p/1/3/46"> <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="3"> <meta name="DC.Source.Volume" content="1"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Secure Mask Conversion"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Mixed Boolean Arithmetic (MBA)"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Boolean-to-Arithmetic (B2A)"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Arithmetic-to-Boolean (A2B)"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Side-Channel Analysis"> <meta name="DC.Subject" xml:lang="en" lang="en" content="DPA Countermeasures"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Hardware Implementation"> <meta name="DC.Subject" xml:lang="en" lang="en" content="Physical Security"> <meta name="DC.Title" content="Efficient Boolean-to-Arithmetic Mask Conversion in Hardware"> <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="Aein Rezaei Shahmirzadi"> <meta name="citation_author_institution" content="PQShield"> <meta name="citation_author" content="Michael Hutter"> <meta name="citation_author_institution" content="PQShield"> <meta name="citation_title" content="Efficient Boolean-to-Arithmetic Mask Conversion in Hardware"> <meta name="citation_language" content="en"> <meta name="citation_date" content="2024-10-07"> <meta name="citation_volume" content="1"> <meta name="citation_issue" content="3"> <meta name="citation_doi" content="10.62056/a3c0l2isfg"> <meta name="citation_abstract_html_url" content="https://cic.iacr.org/p/1/3/46"> <meta name="citation_keywords" xml:lang="en" lang="en" content="Secure Mask Conversion"><meta name="citation_keywords" xml:lang="en" lang="en" content="Mixed Boolean Arithmetic (MBA)"><meta name="citation_keywords" xml:lang="en" lang="en" content="Boolean-to-Arithmetic (B2A)"><meta name="citation_keywords" xml:lang="en" lang="en" content="Arithmetic-to-Boolean (A2B)"><meta name="citation_keywords" xml:lang="en" lang="en" content="Side-Channel Analysis"><meta name="citation_keywords" xml:lang="en" lang="en" content="DPA Countermeasures"><meta name="citation_keywords" xml:lang="en" 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Michael Hutter</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">Aein Rezaei Shahmirzadi <a target="_blank" href="https://orcid.org/0000-0002-9549-268X"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> PQShield, Oxford, UK<br> <span class="font-monospace">aein dot shahmirzadi at pqshield dot com</span> </div> </div> <div class="author"> <div class="authorname">Michael Hutter <a target="_blank" href="https://orcid.org/0000-0001-9769-7649"><img alt="ORCID" class="align-baseline orcidIcon" src="/images/orcid.svg"></a> </div> <div class="ms-4 mb-2"> PQShield, Oxford, UK<br> <span class="font-monospace">michael dot hutter at pqshield 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="Secure Mask Conversion" title="Secure Mask Conversion"><a href="/search?q=Secure%20Mask%20Conversion">Secure Mask Conversion</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Mixed Boolean Arithmetic (MBA)" title="Mixed Boolean Arithmetic (MBA)"><a href="/search?q=Mixed%20Boolean%20Arithmetic%20%28MBA%29">Mixed Boolean Arithmetic (MBA)</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Boolean-to-Arithmetic (B2A)" title="Boolean-to-Arithmetic (B2A)"><a href="/search?q=Boolean-to-Arithmetic%20%28B2A%29">Boolean-to-Arithmetic (B2A)</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Arithmetic-to-Boolean (A2B)" title="Arithmetic-to-Boolean (A2B)"><a href="/search?q=Arithmetic-to-Boolean%20%28A2B%29">Arithmetic-to-Boolean (A2B)</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Side-Channel Analysis" title="Side-Channel Analysis"><a href="/search?q=Side-Channel%20Analysis">Side-Channel Analysis</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="DPA Countermeasures" title="DPA Countermeasures"><a href="/search?q=DPA%20Countermeasures">DPA Countermeasures</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Hardware Implementation" title="Hardware Implementation"><a href="/search?q=Hardware%20Implementation">Hardware Implementation</a></span> <span class="badge p-2 text-bg-light keyword ms-2 my-1" alt="Physical Security" title="Physical Security"><a href="/search?q=Physical%20Security">Physical Security</a></span> </div> <h3 class="mt-4">Abstract</h3> <p><p>Masking schemes are key in thwarting side-channel attacks due to their robust theoretical foundation. Transitioning from Boolean to arithmetic (B2A) masking is a necessary step in various cryptography schemes, including hash functions, ARX-based ciphers, and lattice-based cryptography. While there exists a significant body of research focusing on B2A software implementations, studies pertaining to hardware implementations are quite limited, with the majority dedicated solely to creating efficient Boolean masked adders. In this paper, we present first- and second-order secure hardware implementations to perform B2A mask conversion efficiently without using masked adder structures. We first introduce a first-order secure low-latency gadget that executes a B2A2k in a single cycle. Furthermore, we propose a second-order secure B2A2k gadget that has a latency of only 4 clock cycles. Both gadgets are independent of the input word size k. We then show how these new primitives lead to improved B2Aq hardware implementations that perform a B2A mask conversion of integers modulo an arbitrary number. Our results show that our new gadgets outperform comparable solutions by more than a magnitude in terms of resource requirements and are at least 3 times faster in terms of latency and throughput. All gadgets have been formally verified and proven secure in the glitch-robust PINI security model. We additionally confirm the security of our gadgets on an FPGA platform using practical TVLA tests. </p></p> <h3 class="mb-3">References</h3> <div class="d-flex"> <div style="min-width:9rem;">[AHMP10]</div> <div><div id="ref-Aumasson2010SHA3Blake" class="bibitem">Jean-Philippe Aumasson, Luca Henzen, Willi Meier, and Raphael C.-W. Phan. SHA-3 Proposal BLAKE. <a href="https://131002.net/blake">https://131002.net/blake</a>. 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DOI: <a href="https://doi.org/10.1007/978-3-319-64647-3_8">10.1007/978-3-319-64647-3_8</a></div></div> </div> <div class="text-end mb-4"> <a href="https://scholar.google.com/scholar?hl=en&q=Yoo-Seung+Won+Dong-Guk+Han+Efficient+Conversion+Method+from+Arithmetic+to+Boolean+Masking+in+Constrained+Devices+2017" target="_blank" class="ms-3">Google Scholar</a> <a href="https://eprint.iacr.org/search?relevance=on&authors=Yoo-Seung+Won+Dong-Guk+Han&title=Efficient+Conversion+Method+from+Arithmetic+to+Boolean+Masking+in+Constrained+Devices&submittedafter=2016&submittedbefore=2018" 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/1/3/46/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/a3c0l2isfg">https://doi.org/10.62056/a3c0l2isfg</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>: 2024-09-02<br> <strong>Published</strong>: 2024-10-07<br> <!-- begin crossmark --> <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> <!-- end crossmark --> </div> </div> <div class="card mb-4"> <h5 class="card-header">How to cite</h5> <div class="card-body"> <p>Aein Rezaei Shahmirzadi and Michael Hutter, Efficient Boolean-to-Arithmetic Mask Conversion in Hardware. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 3, Oct 07, 2024, doi: 10.62056/a3c0l2isfg. </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-1-3-46, author = "Shahmirzadi, Aein Rezaei and Hutter, Michael", journal = "{IACR} {C}ommunications in {C}ryptology", publisher = "{I}nternational {A}ssociation for {C}ryptologic {R}esearch", title = "Efficient Boolean-to-Arithmetic Mask Conversion in Hardware", volume = "1", number = "3", date = "2024-10-07", year = "2024", issn = "3006-5496", doi = "10.62056/a3c0l2isfg" } </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 - Shahmirzadi, Aein AU - Hutter, Michael PY - 2024 TI - Efficient Boolean-to-Arithmetic Mask Conversion in Hardware JF - IACR Communications in Cryptology JA - CIC VL - 1 IS - 3 DO - 10.62056/a3c0l2isfg UR - https://doi.org/10.62056/a3c0l2isfg AB - <p>Masking schemes are key in thwarting side-channel attacks due to their robust theoretical foundation. Transitioning from Boolean to arithmetic (B2A) masking is a necessary step in various cryptography schemes, including hash functions, ARX-based ciphers, and lattice-based cryptography. While there exists a significant body of research focusing on B2A software implementations, studies pertaining to hardware implementations are quite limited, with the majority dedicated solely to creating efficient Boolean masked adders. In this paper, we present first- and second-order secure hardware implementations to perform B2A mask conversion efficiently without using masked adder structures. We first introduce a first-order secure low-latency gadget that executes a B2A2k in a single cycle. Furthermore, we propose a second-order secure B2A2k gadget that has a latency of only 4 clock cycles. Both gadgets are independent of the input word size k. We then show how these new primitives lead to improved B2Aq hardware implementations that perform a B2A mask conversion of integers modulo an arbitrary number. Our results show that our new gadgets outperform comparable solutions by more than a magnitude in terms of resource requirements and are at least 3 times faster in terms of latency and throughput. All gadgets have been formally verified and proven secure in the glitch-robust PINI security model. We additionally confirm the security of our gadgets on an FPGA platform using practical TVLA tests. </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">Aein Rezaei Shahmirzadi and Michael Hutter, Efficient Boolean-to-Arithmetic Mask Conversion in Hardware. <span class="fst-italic">IACR Communications in Cryptology</span>, vol. 1, no. 3, Oct 07, 2024, doi: 10.62056/a3c0l2isfg.</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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