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Why "Fiat-Shamir for Proofs" Lacks a Proof
<!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>Why "Fiat-Shamir for Proofs" Lacks a Proof</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="Why "Fiat-Shamir for Proofs" Lacks a Proof"> <meta name="citation_author" content="Nir Bitansky"> <meta name="citation_author" content="Sanjam Garg"> <meta name="citation_author" content="Daniel Wichs"> <meta name="citation_journal_title" content="Cryptology ePrint Archive"> <meta name="citation_publication_date" content="2012"> <meta name="citation_pdf_url" content="https://eprint.iacr.org/2012/705.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/2012/705"> <meta property="og:site_name" content="IACR Cryptology ePrint Archive" /> <meta property="og:type" content="article" /> <meta property="og:title" content="Why "Fiat-Shamir for Proofs" Lacks a Proof" /> <meta property="og:description" content="The Fiat-Shamir heuristic (CRYPTO '86) is used to convert any 3-message public-coin proof or argument system into a non-interactive argument, by hashing the prover's first message to select the verifier's challenge. It is known that this heuristic is sound when the hash function is modeled as a random oracle. On the other hand, the surprising result of Goldwasser and Kalai (FOCS '03) shows that there exists a computationally sound argument on which the Fiat-Shamir heuristic is never sound, when instantiated with any actual efficient hash function. This leaves us with the following interesting possibility: perhaps there exists a hash function that securely instantiates the Fiat-Shamir heuristic for all 3-message public-coin statistically sound proofs, even if it can fail for some computationally sound arguments. Indeed, the existence of such hash functions has been conjectured by Barak, Lindell and Vadhan (FOCS '03), who also gave a seemingly reasonable and sufficient condition under which such hash functions exist. However, we do not have any provably secure construction of such hash functions, under any standard assumption such as the hardness of DDH, RSA, QR, LWE, etc. In this work we give a broad black-box separation result, showing that the security of such hash functions cannot be proved under virtually any standard cryptographic assumption via a black-box reduction." /> <meta property="article:section" content="FOUNDATIONS" /> <meta property="article:modified_time" content="2012-12-19T21:42:35+00:00" /> <meta property="article:published_time" content="2012-12-18T13:07:28+00:00" /> <meta property="article:tag" content="interactive proofs" /> <meta property="article:tag" content="zero-knowledge" /> </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 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class="fst-italic mb-3"> Nir Bitansky, Sanjam Garg, and Daniel Wichs </p> <h5 class="mt-3">Abstract</h5> <p style="white-space: pre-wrap;">The Fiat-Shamir heuristic (CRYPTO '86) is used to convert any 3-message public-coin proof or argument system into a non-interactive argument, by hashing the prover's first message to select the verifier's challenge. It is known that this heuristic is sound when the hash function is modeled as a random oracle. On the other hand, the surprising result of Goldwasser and Kalai (FOCS '03) shows that there exists a computationally sound argument on which the Fiat-Shamir heuristic is never sound, when instantiated with any actual efficient hash function. This leaves us with the following interesting possibility: perhaps there exists a hash function that securely instantiates the Fiat-Shamir heuristic for all 3-message public-coin statistically sound proofs, even if it can fail for some computationally sound arguments. Indeed, the existence of such hash functions has been conjectured by Barak, Lindell and Vadhan (FOCS '03), who also gave a seemingly reasonable and sufficient condition under which such hash functions exist. However, we do not have any provably secure construction of such hash functions, under any standard assumption such as the hardness of DDH, RSA, QR, LWE, etc. In this work we give a broad black-box separation result, showing that the security of such hash functions cannot be proved under virtually any standard cryptographic assumption via a black-box reduction.</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="/2012/705.pdf"> <img class="icon" src="/img/file-pdf.svg">PDF</a> </dd> <dt>Category</dt> <dd><a href="/search?category=FOUNDATIONS"><small class="badge category category-FOUNDATIONS">Foundations</small></a></dd> <dt>Publication info</dt> <dd>Published elsewhere. A merged version of this work and that of [Dachman-Soled, Jain, Kalai, Lopez-Alt] will appear at TCC 2013.</dd> <dt>Keywords</dt> <dd class="keywords"><a href="/search?q=interactive%20proofs" class="me-2 badge bg-secondary keyword">interactive proofs</a><a href="/search?q=zero-knowledge" class="me-2 badge bg-secondary keyword">zero-knowledge</a></dd> <dt>Contact author(s)</dt> <dd><span class="font-monospace"> danwichs<span class="obfuscate"> @ </span>gmail com </span> </dd> <dt>History</dt> <dd>2012-12-19: last of 2 revisions</dd> <dd>2012-12-18: received</dd> <dd><a rel="nofollow" href="/archive/versions/2012/705">See all versions</a></dd> <dt>Short URL</dt> <dd><a href="https://ia.cr/2012/705">https://ia.cr/2012/705</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:2012/705, author = {Nir Bitansky and Sanjam Garg and Daniel Wichs}, title = {Why "Fiat-Shamir for Proofs" Lacks a Proof}, howpublished = {Cryptology {ePrint} Archive, Paper 2012/705}, year = {2012}, url = {https://eprint.iacr.org/2012/705} } </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>