CINXE.COM
Galois Field Commitment Scheme
<!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/dist/css/bootstrap.min.css" rel="stylesheet"> <title>Galois Field Commitment Scheme</title> <link rel="stylesheet" href="/css/eprint.css?v=10"> <link rel="shortcut icon" href="/favicon.ico" type="image/x-icon" /> <link rel="apple-touch-icon" href="/img/apple-touch-icon-180x180.png" /> <style> a.toggle-open:after { content:' -'; font-weight: 800; } a.toggle-closed:after { content: " ›"; font-weight: 800; } .paper-abstract { white-space: pre-wrap; } #metadata dt { margin-top: 1rem; } #metadata dt + dd { /* gap between dt and first dd */ margin-top: .75rem; } #metadata dd { margin-left: 2rem; } #metadata dd.keywords { padding-bottom: .5rem; } span.authorName { margin-top: .5rem; font-style: italic; } </style> <script> MathJax = { tex: { inlineMath: [['$', '$'], ['\\(', '\\)']], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEnvironments: false }, loader: { load: [ "ui/safe", "ui/lazy", ], }, options: { safeOptions: { allow: { URLs: "none", classes: "safe", cssIDs: "safe", styles: "safe", }, }, } }; </script> <script id="MathJax-script" async src="/js/mathjax/tex-chtml.js"></script> <meta name="citation_title" content="Galois Field Commitment Scheme"> <meta name="citation_author" content="Alexandre Pinto"> <meta name="citation_author" content="André Souto"> <meta name="citation_author" content="Armando Matos"> <meta name="citation_author" content="Luís Antunes"> <meta name="citation_journal_title" content="Cryptology ePrint Archive"> <meta name="citation_publication_date" content="2006"> <meta name="citation_pdf_url" content="https://eprint.iacr.org/2006/410.pdf"> <meta property="og:image" content="https://eprint.iacr.org/img/iacrlogo.png"/> <meta property="og:image:alt" content="IACR logo"/> <meta property="og:url" content="https://eprint.iacr.org/2006/410"> <meta property="og:site_name" content="IACR Cryptology ePrint Archive" /> <meta property="og:type" content="article" /> <meta property="og:title" content="Galois Field Commitment Scheme" /> <meta property="og:description" content="In [3] the authors give the first mathematical formalization of an unconditionally secure commitment scheme. Their construction has some similarities to one used to build authentication codes, so they raise the question whether there is some relation between commitment schemes and authentication schemes. They conjecture that authentication schemes with arbitration can be used, but they stress that the information flows are different. In this paper, we show that there is indeed a relation between unconditionally secure commitment schemes and unconditionally secure authentication schemes, and that an unconditionally secure commitment scheme can be built from such an authentication scheme and an unconditionally secure cipher system. This parallel is then used to analyse a new attack against commitment schemes that is the counterpart of the impersonation attack in an authentication system. To investigate the opposite direction, we start by defining an optimal commitment system and showing that this must be a resolvable design commitment scheme as proposed in the aforementioned paper. Then, a proof is given that the resolvable design commitment schemes are a composition of an authentication system and a cipher system and the conclusion follows that this is the case for all optimal commitment systems. We prove that there is a commitment scheme based on Galois Fields that uses the One-Time Pad as the cipher system, which to our knowledge is new in the literature. The main technique in the proof is the construction of an appropriate design for any n, originating an authentication system that is perfectly secure against deception attacks of levels 0 and 1. The commitment scheme here proposed uses only very simple operations and can be very efficiently implemented both in hardware and software. Finally, we give a brief look at the possibility of building commitment schemes from other primitives." /> <meta property="article:section" content="PROTOCOLS" /> <meta property="article:modified_time" content="2006-11-13T12:01:51+00:00" /> <meta property="article:published_time" content="2006-11-13T12:01:51+00:00" /> <meta property="article:tag" content="Commitment" /> <meta property="article:tag" content="Authentication" /> <meta property="article:tag" content="Unconditional Security" /> <meta property="article:tag" content="Galois Field." /> </head> <body> <noscript> <h1 class="text-center">What a lovely hat</h1> <h4 class="text-center">Is it made out of <a href="https://iacr.org/tinfoil.html">tin foil</a>?</h4> </noscript> <div class="fixed-top" id="topNavbar"> <nav class="navbar navbar-custom navbar-expand-lg"> <div class="container px-0 justify-content-between justify-content-lg-evenly"> <div class="order-0 align-items-center d-flex"> <button class="navbar-toggler btnNoOutline" type="button" data-bs-toggle="collapse" data-bs-target="#navbarContent" aria-controls="navbarContent" aria-expanded="false"> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <a class="d-none me-5 d-lg-inline" href="https://iacr.org/"><img class="iacrlogo" src="/img/iacrlogo_small.png" alt="IACR Logo" style="max-width:6rem;"></a> </div> <a class="ePrintname order-1" href="/"> <span class="longNavName">Cryptology ePrint Archive</span> </a> <div class="collapse navbar-collapse order-3" id="navbarContent"> <ul class="navbar-nav me-auto ms-2 mb-2 mb-lg-0 justify-content-end w-100"> <li class="ps-md-3 nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Papers </a> <ul class="dropdown-menu me-3" aria-labelledby="navbarDropdown"> <span class="text-dark mx-3" style="white-space:nowrap;">Updates from the last:</span> <li><a class="dropdown-item ps-custom" href="/days/7">7 days</a></li> <li><a class="dropdown-item ps-custom" href="/days/31">31 days</a></li> <li><a class="dropdown-item ps-custom" href="/days/183">6 months</a></li> <li><a class="dropdown-item ps-custom" href="/days/365">365 days</a></li> <li><hr class="dropdown-divider"></li> <li><a class="dropdown-item" href="/byyear">Listing by year</a></li> <li><a class="dropdown-item" href="/complete">All papers</a></li> <li><a class="dropdown-item" href="/complete/compact">Compact view</a></li> <li><a class="dropdown-item" href="https://www.iacr.org/news/subscribe">Subscribe</a></li> <li><hr class="dropdown-divider"></li> <li><a class="dropdown-item" href="/citation.html">How to cite</a></li> <li><hr class="dropdown-divider"></li> <li><a class="dropdown-item" href="/rss">Harvesting metadata</a></li> </ul> </li> <li class="ps-md-3 nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="submissionsDropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Submissions </a> <ul class="dropdown-menu me-3" aria-labelledby="submissionsDropdown"> <li><a class="dropdown-item" href="/submit">Submit a paper</a></li> <li><a class="dropdown-item" href="/revise">Revise or withdraw a paper</a></li> <li><a class="dropdown-item" href="/operations.html">Acceptance and publishing conditions</a></li> </ul> </li> <li class="ps-md-3 nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="aboutDropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> About </a> <ul class="dropdown-menu me-3" aria-labelledby="aboutDropdown"> <li><a class="dropdown-item" href="/about.html">Goals and history</a></li> <li><a class="dropdown-item" href="/news.html">News</a></li> <li><a class="dropdown-item" href="/stats">Statistics</a></li> <li><a class="dropdown-item" href="/contact.html">Contact</a></li> </ul> </li> </ul> </div> <div class="dropdown ps-md-2 text-right order-2 order-lg-last"> <button class="btn btnNoOutline" type="button" id="dropdownMenuButton1" data-bs-toggle="dropdown" aria-expanded="false"> <img src="/img/search.svg" class="searchIcon" alt="Search Button"/> </button> <div id="searchDd" class="dropdown-menu dropdown-menu-end p-0" aria-labelledby="dropdownMenuButton1"> <form action="/search" method="GET"> <div class="input-group"> <input id="searchbox" name="q" type="search" class="form-control" autocomplete="off"> <button class="btn btn-secondary border input-group-append ml-2"> Search </button> </div> </form> <div class="ms-2 p-1 d-none"><a href="/search">Advanced search</a></div> </div> </div> </div> </nav> </div> <main id="eprintContent" class="container px-3 py-4 p-md-4"> <div class="row mt-4"> <div class="col-md-7 col-lg-8 pe-md-5"> <h4>Paper 2006/410</h4> <h3 class="mb-3">Galois Field Commitment Scheme</h3> <p class="fst-italic mb-3"> Alexandre Pinto, André Souto, Armando Matos, and Luís Antunes </p> <h5 class="mt-3">Abstract</h5> <p style="white-space: pre-wrap;">In [3] the authors give the first mathematical formalization of an unconditionally secure commitment scheme. Their construction has some similarities to one used to build authentication codes, so they raise the question whether there is some relation between commitment schemes and authentication schemes. They conjecture that authentication schemes with arbitration can be used, but they stress that the information flows are different. In this paper, we show that there is indeed a relation between unconditionally secure commitment schemes and unconditionally secure authentication schemes, and that an unconditionally secure commitment scheme can be built from such an authentication scheme and an unconditionally secure cipher system. This parallel is then used to analyse a new attack against commitment schemes that is the counterpart of the impersonation attack in an authentication system. To investigate the opposite direction, we start by defining an optimal commitment system and showing that this must be a resolvable design commitment scheme as proposed in the aforementioned paper. Then, a proof is given that the resolvable design commitment schemes are a composition of an authentication system and a cipher system and the conclusion follows that this is the case for all optimal commitment systems. We prove that there is a commitment scheme based on Galois Fields that uses the One-Time Pad as the cipher system, which to our knowledge is new in the literature. The main technique in the proof is the construction of an appropriate design for any n, originating an authentication system that is perfectly secure against deception attacks of levels 0 and 1. The commitment scheme here proposed uses only very simple operations and can be very efficiently implemented both in hardware and software. Finally, we give a brief look at the possibility of building commitment schemes from other primitives.</p> </div> <div id="metadata" class="col-md-5 col-lg-4 ps-md-5 mt-4 mt-md-0"> <h5>Metadata</h5> <dl> <dt> Available format(s) </dt> <dd> <a class="btn btn-sm btn-outline-dark" href="/2006/410.pdf"> <img class="icon" src="/img/file-pdf.svg">PDF</a> </dd> <dt>Category</dt> <dd><a href="/search?category=PROTOCOLS"><small class="badge category category-PROTOCOLS">Cryptographic protocols</small></a></dd> <dt>Publication info</dt> <dd>Published elsewhere. Unknown where it was published</dd> <dt>Keywords</dt> <dd class="keywords"><a href="/search?q=Commitment" class="me-2 badge bg-secondary keyword">Commitment</a><a href="/search?q=Authentication" class="me-2 badge bg-secondary keyword">Authentication</a><a href="/search?q=Unconditional%20Security" class="me-2 badge bg-secondary keyword">Unconditional Security</a><a href="/search?q=Galois%20Field." class="me-2 badge bg-secondary keyword">Galois Field.</a></dd> <dt>Contact author(s)</dt> <dd><span class="font-monospace"> alx<span class="obfuscate"> @ </span>dcc fc up pt </span> </dd> <dt>History</dt> <dd>2006-11-13: received</dd> <dt>Short URL</dt> <dd><a href="https://ia.cr/2006/410">https://ia.cr/2006/410</a></dd> <dt>License</dt> <dd><a rel="license" target="_blank" href="https://creativecommons.org/licenses/by/4.0/"> <img class="licenseImg" src="/img/license/CC_BY.svg" alt="Creative Commons Attribution" title="Creative Commons Attribution"><br> <small>CC BY</small> </a> </dd> </dl> </div> </div> <p class="mt-4"><strong>BibTeX</strong> <button id="bibcopy" class="ms-2 btn btn-sm btn-outline-dark" aria-label="Copy to clipboard" onclick="copyBibtex()"> <img src="/img/copy-outline.svg" class="icon">Copy to clipboard</button></p> <pre id="bibtex"> @misc{cryptoeprint:2006/410, author = {Alexandre Pinto and André Souto and Armando Matos and Luís Antunes}, title = {Galois Field Commitment Scheme}, howpublished = {Cryptology {ePrint} Archive, Paper 2006/410}, year = {2006}, url = {https://eprint.iacr.org/2006/410} } </pre> <script> var bibcopy; function triggerTooltip() { console.log('setting tooltip'); } window.onload = triggerTooltip; function copyBibtex() { let range = document.createRange(); range.selectNode(document.getElementById('bibtex')); window.getSelection().removeAllRanges(); window.getSelection().addRange(range); document.execCommand('copy'); window.getSelection().removeAllRanges(); let bibcopy = document.getElementById('bibcopy'); let copyTooltip = new bootstrap.Tooltip(bibcopy, {trigger: 'manual', title: 'Copied!'}); copyTooltip.show(); setTimeout(function() { copyTooltip.dispose(); }, 2000); } </script> </main> <div class="container-fluid mt-auto" id="eprintFooter"> <a href="https://iacr.org/"> <img id="iacrlogo" src="/img/iacrlogo_small.png" class="img-fluid d-block mx-auto" alt="IACR Logo"> </a> <div class="colorDiv"></div> <div class="alert alert-success w-75 mx-auto"> Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. </div> </div> <script src="/css/bootstrap/js/bootstrap.bundle.min.js"></script> <script> var topNavbar = document.getElementById('topNavbar'); if (topNavbar) { document.addEventListener('scroll', function(e) { if (window.scrollY > 100) { topNavbar.classList.add('scrolled'); } else { topNavbar.classList.remove('scrolled'); } }) } </script> </body> </html>