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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">halo2</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/proofs.html"><strong aria-hidden="true">1.1.</strong> Proof systems</a></li><li class="chapter-item expanded "><a href="../concepts/arithmetization.html"><strong aria-hidden="true">1.2.</strong> UltraPLONK Arithmetization</a></li><li class="chapter-item expanded "><a href="../concepts/cores.html"><strong aria-hidden="true">1.3.</strong> Cores</a></li><li class="chapter-item expanded "><a href="../concepts/chips.html"><strong aria-hidden="true">1.4.</strong> Chips</a></li><li class="chapter-item expanded "><a href="../concepts/gadgets.html"><strong aria-hidden="true">1.5.</strong> Gadgets</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/simple-example.html"><strong aria-hidden="true">2.1.</strong> A simple example</a></li><li class="chapter-item expanded "><a href="../user/lookup-tables.html"><strong aria-hidden="true">2.2.</strong> Lookup tables</a></li><li class="chapter-item expanded "><a href="../user/gadgets.html"><strong aria-hidden="true">2.3.</strong> Gadgets</a></li><li class="chapter-item expanded "><a href="../user/tips-and-tricks.html"><strong aria-hidden="true">2.4.</strong> Tips and tricks</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/proving-system.html"><strong aria-hidden="true">3.1.</strong> Proving system</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/proving-system/multipoint-opening.html"><strong aria-hidden="true">3.1.1.</strong> Multipoint opening argument</a></li><li class="chapter-item expanded "><a href="../design/proving-system/permutation.html"><strong aria-hidden="true">3.1.2.</strong> Permutation argument</a></li><li class="chapter-item expanded "><a href="../design/proving-system/lookup-argument.html"><strong aria-hidden="true">3.1.3.</strong> Lookup argument</a></li><li class="chapter-item expanded "><a href="../design/proving-system/comparison.html"><strong aria-hidden="true">3.1.4.</strong> Comparison to other work</a></li></ol></li><li class="chapter-item expanded "><a href="../design/implementation.html" class="active"><strong aria-hidden="true">3.2.</strong> Implementation</a></li><li class="chapter-item expanded "><a href="../design/gadgets.html"><strong aria-hidden="true">3.3.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/gadgets/sha256.html"><strong aria-hidden="true">3.3.1.</strong> SHA-256</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/gadgets/sha256/table16.html"><strong aria-hidden="true">3.3.1.1.</strong> 16-bit table chip</a></li></ol></li></ol></li></ol></li><li class="chapter-item expanded "><a href="../background.html"><strong aria-hidden="true">4.</strong> Background Material</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../background/fields.html"><strong aria-hidden="true">4.1.</strong> Fields</a></li><li class="chapter-item expanded "><a href="../background/polynomials.html"><strong aria-hidden="true">4.2.</strong> Polynomials</a></li><li class="chapter-item expanded "><a href="../background/groups.html"><strong aria-hidden="true">4.3.</strong> Cryptographic groups</a></li><li class="chapter-item expanded "><a href="../background/curves.html"><strong aria-hidden="true">4.4.</strong> Elliptic curves</a></li><li class="chapter-item expanded "><a href="../background/upa.html"><strong aria-hidden="true">4.5.</strong> UltraPLONK arithmetisation</a></li><li class="chapter-item expanded "><a href="../background/pc-ipa.html"><strong aria-hidden="true">4.6.</strong> Polynomial commitment using inner product argument</a></li><li class="chapter-item expanded "><a href="../background/recursion.html"><strong aria-hidden="true">4.7.</strong> Recursion</a></li></ol></li></ol>
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<h1 class="menu-title">The halo2 Book</h1>
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<h1><a class="header" href="#implementation" id="implementation">Implementation</a></h1>
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<h2><a class="header" href="#proofs-as-opaque-byte-streams" id="proofs-as-opaque-byte-streams">Proofs as opaque byte streams</a></h2>
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<p>In proving system implementations like <code>bellman</code>, there is a concrete <code>Proof</code> struct that
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encapsulates the proof data, is returned by a prover, and can be passed to a verifier.</p>
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<p><code>halo2</code> does not contain any proof-like structures, for several reasons:</p>
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<ul>
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<li>The Proof structures would contain vectors of (vectors of) curve points and scalars.
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This complicates serialization/deserialization of proofs because the lengths of these
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vectors depend on the configuration of the circuit. However, we didn't want to encode
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the lengths of vectors inside of proofs, because at runtime the circuit is fixed, and
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thus so are the proof sizes.</li>
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<li>It's easy to accidentally put stuff into a Proof structure that isn't also placed in the
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transcript, which is a hazard when developing and implementing a proving system.</li>
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<li>We needed to be able to create multiple PLONK proofs at the same time; these proofs
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share many different substructures when they are for the same circuit.</li>
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</ul>
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<p>Instead, <code>halo2</code> treats proof objects as opaque byte streams. Creation and consumption of
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these byte streams happens via the transcript:</p>
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<ul>
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<li>The <code>TranscriptWrite</code> trait represents something that we can write proof components to
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(at proving time).</li>
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<li>The <code>TranscriptRead</code> trait represents something that we can read proof components from
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(at verifying time).</li>
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</ul>
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<p>Crucially, implementations of <code>TranscriptWrite</code> are responsible for simultaneously writing
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to some <code>std::io::Write</code> buffer at the same time that they hash things into the transcript,
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and similarly for <code>TranscriptRead</code>/<code>std::io::Read</code>.</p>
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<p>As a bonus, treating proofs as opaque byte streams ensures that verification accounts for
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the cost of deserialization, which isn't negligible due to point compression.</p>
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