mirror of https://github.com/zcash/halo2.git
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248 lines
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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> PLONKish Arithmetization</a></li><li class="chapter-item expanded "><a href="concepts/chips.html"><strong aria-hidden="true">1.3.</strong> Chips</a></li><li class="chapter-item expanded "><a href="concepts/gadgets.html"><strong aria-hidden="true">1.4.</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/dev-tools.html"><strong aria-hidden="true">2.1.</strong> Developer tools</a></li><li class="chapter-item expanded "><a href="user/simple-example.html"><strong aria-hidden="true">2.2.</strong> A simple example</a></li><li class="chapter-item expanded "><a href="user/lookup-tables.html"><strong aria-hidden="true">2.3.</strong> Lookup tables</a></li><li class="chapter-item expanded "><a href="user/gadgets.html"><strong aria-hidden="true">2.4.</strong> Gadgets</a></li><li class="chapter-item expanded "><a href="user/tips-and-tricks.html"><strong aria-hidden="true">2.5.</strong> Tips and tricks</a></li><li class="chapter-item expanded "><a href="user/wasm-port.html"><strong aria-hidden="true">2.6.</strong> WASM Guide</a></li></ol></li><li class="chapter-item expanded "><a href="dev.html"><strong aria-hidden="true">3.</strong> Developer Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="dev/features.html"><strong aria-hidden="true">3.1.</strong> Feature development</a></li></ol></li><li class="chapter-item expanded "><a href="design.html" class="active"><strong aria-hidden="true">4.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/proving-system.html"><strong aria-hidden="true">4.1.</strong> Proving system</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/proving-system/lookup.html"><strong aria-hidden="true">4.1.1.</strong> Lookup argument</a></li><li class="chapter-item expanded "><a href="design/proving-system/permutation.html"><strong aria-hidden="true">4.1.2.</strong> Permutation argument</a></li><li class="chapter-item expanded "><a href="design/proving-system/circuit-commitments.html"><strong aria-hidden="true">4.1.3.</strong> Circuit commitments</a></li><li class="chapter-item expanded "><a href="design/proving-system/vanishing.html"><strong aria-hidden="true">4.1.4.</strong> Vanishing argument</a></li><li class="chapter-item expanded "><a href="design/proving-system/multipoint-opening.html"><strong aria-hidden="true">4.1.5.</strong> Multipoint opening argument</a></li><li class="chapter-item expanded "><a href="design/proving-system/inner-product.html"><strong aria-hidden="true">4.1.6.</strong> Inner product argument</a></li><li class="chapter-item expanded "><a href="design/proving-system/comparison.html"><strong aria-hidden="true">4.1.7.</strong> Comparison to other work</a></li></ol></li><li class="chapter-item expanded "><a href="design/protocol.html"><strong aria-hidden="true">4.2.</strong> Protocol Description</a></li><li class="chapter-item expanded "><a href="design/implementation.html"><strong aria-hidden="true">4.3.</strong> Implementation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/implementation/proofs.html"><strong aria-hidden="true">4.3.1.</strong> Proofs</a></li><li class="chapter-item expanded "><a href="design/implementation/fields.html"><strong aria-hidden="true">4.3.2.</strong> Fields</a></li><li class="chapter-item expanded "><a href="design/implementation/selector-combining.html"><strong aria-hidden="true">4.3.3.</strong> Selector combining</a></li></ol></li><li class="chapter-item expanded "><a href="design/gadgets.html"><strong aria-hidden="true">4.4.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/gadgets/ecc.html"><strong aria-hidden="true">4.4.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/gadgets/ecc/witnessing-points.html"><strong aria-hidden="true">4.4.1.1.</strong> Witnessing points</a></li><li class="chapter-item expanded "><a href="design/gadgets/ecc/addition.html"><strong aria-hidden="true">4.4.1.2.</strong> Incomplete and complete addition</a></li><li class="chapter-item expanded "><a href="design/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">4.4.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">4.4.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li><li class="chapter-item expanded "><a href="design/gadgets/sinsemilla.html"><strong aria-hidden="true">4.4.2.</strong> Sinsemilla</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/gadgets/sinsemilla/merkle-crh.html"><strong aria-hidden="true">4.4.2.1.</strong> MerkleCRH</a></li></ol></li><li class="chapter-item expanded "><a href="design/gadgets/decomposition.html"><strong aria-hidden="true">4.4.3.</strong> Decomposition</a></li><li class="chapter-item expanded "><a href="design/gadgets/sha256.html"><strong aria-hidden="true">4.4.4.</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">4.4.4.1.</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">5.</strong> Background Material</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="background/fields.html"><strong aria-hidden="true">5.1.</strong> Fields</a></li><li class="chapter-item expanded "><a href="background/polynomials.html"><strong aria-hidden="true">5.2.</strong> Polynomials</a></li><li class="chapter-item expanded "><a href="background/groups.html"><strong aria-hidden="true">5.3.</strong> Cryptographic groups</a></li><li class="chapter-item expanded "><a href="background/curves.html"><strong aria-hidden="true">5.4.</strong> Elliptic curves</a></li><li class="chapter-item expanded "><a href="background/pc-ipa.html"><strong aria-hidden="true">5.5.</strong> Polynomial commitment using inner product argument</a></li><li class="chapter-item expanded "><a href="background/recursion.html"><strong aria-hidden="true">5.6.</strong> Recursion</a></li></ol></li></ol>
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<h1 class="menu-title">The halo2 Book</h1>
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<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css" integrity="sha384-AfEj0r4/OFrOo5t7NnNe46zW/tFgW6x/bCJG8FqQCEo3+Aro6EYUG4+cU+KJWu/X" crossorigin="anonymous">
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<h1 id="design"><a class="header" href="#design">Design</a></h1>
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<h2 id="note-on-language"><a class="header" href="#note-on-language">Note on Language</a></h2>
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<p>We use slightly different language than others to describe PLONK concepts. Here's the
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overview:</p>
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<ol>
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<li>We like to think of PLONK-like arguments as tables, where each column corresponds to a
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"wire". We refer to entries in this table as "cells".</li>
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<li>We like to call "selector polynomials" and so on "fixed columns" instead. We then refer
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specifically to a "selector constraint" when a cell in a fixed column is being used to
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control whether a particular constraint is enabled in that row.</li>
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<li>We call the other polynomials "advice columns" usually, when they're populated by the
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prover.</li>
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<li>We use the term "rule" to refer to a "gate" like
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<span class="katex-display"><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">A</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05017em;">B</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.</span></span></span></span></span>
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<ul>
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<li>TODO: Check how consistent we are with this, and update the code and docs to match.</li>
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</ul>
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</li>
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</ol>
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