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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html" class="active">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"><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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<h1 id="halo2"><a class="header" href="#halo2">halo2</a></h1>
<h2 id="usage"><a class="header" href="#usage">Usage</a></h2>
<p>This repository contains the <a href="halo2_proofs/README.html">halo2_proofs</a> and
<a href="halo2_gadgets/README.html">halo2_gadgets</a> crates, which should be used directly.</p>
<h2 id="minimum-supported-rust-version"><a class="header" href="#minimum-supported-rust-version">Minimum Supported Rust Version</a></h2>
<p>Requires Rust <strong>1.60</strong> or higher.</p>
<p>Minimum supported Rust version can be changed in the future, but it will be done with a
minor version bump.</p>
<h2 id="controlling-parallelism"><a class="header" href="#controlling-parallelism">Controlling parallelism</a></h2>
<p><code>halo2</code> currently uses <a href="https://github.com/rayon-rs/rayon">rayon</a> for parallel computation.
The <code>RAYON_NUM_THREADS</code> environment variable can be used to set the number of threads.</p>
<p>You can disable <code>rayon</code> by disabling the <code>"multicore"</code> feature.
Warning! Halo2 will lose access to parallelism if you disable the <code>"multicore"</code> feature.
This will significantly degrade performance.</p>
<h2 id="license"><a class="header" href="#license">License</a></h2>
<p>Licensed under either of</p>
<ul>
<li>Apache License, Version 2.0, (<a href="LICENSE-APACHE">LICENSE-APACHE</a> or
http://www.apache.org/licenses/LICENSE-2.0)</li>
<li>MIT license (<a href="LICENSE-MIT">LICENSE-MIT</a> or http://opensource.org/licenses/MIT)</li>
</ul>
<p>at your option.</p>
<h3 id="contribution"><a class="header" href="#contribution">Contribution</a></h3>
<p>Unless you explicitly state otherwise, any contribution intentionally
submitted for inclusion in the work by you, as defined in the Apache-2.0
license, shall be dual licensed as above, without any additional terms or
conditions.</p>
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