mirror of https://github.com/zcash/halo2.git
285 lines
22 KiB
HTML
285 lines
22 KiB
HTML
<!DOCTYPE HTML>
|
|
<html lang="en" class="light" dir="ltr">
|
|
<head>
|
|
<!-- Book generated using mdBook -->
|
|
<meta charset="UTF-8">
|
|
<title>SHA-256 - The halo2 Book</title>
|
|
|
|
|
|
<!-- Custom HTML head -->
|
|
|
|
<meta name="description" content="">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1">
|
|
<meta name="theme-color" content="#ffffff">
|
|
|
|
<link rel="icon" href="../../favicon.svg">
|
|
<link rel="shortcut icon" href="../../favicon.png">
|
|
<link rel="stylesheet" href="../../css/variables.css">
|
|
<link rel="stylesheet" href="../../css/general.css">
|
|
<link rel="stylesheet" href="../../css/chrome.css">
|
|
<link rel="stylesheet" href="../../css/print.css" media="print">
|
|
|
|
<!-- Fonts -->
|
|
<link rel="stylesheet" href="../../FontAwesome/css/font-awesome.css">
|
|
<link rel="stylesheet" href="../../fonts/fonts.css">
|
|
|
|
<!-- Highlight.js Stylesheets -->
|
|
<link rel="stylesheet" href="../../highlight.css">
|
|
<link rel="stylesheet" href="../../tomorrow-night.css">
|
|
<link rel="stylesheet" href="../../ayu-highlight.css">
|
|
|
|
<!-- Custom theme stylesheets -->
|
|
|
|
</head>
|
|
<body class="sidebar-visible no-js">
|
|
<div id="body-container">
|
|
<!-- Provide site root to javascript -->
|
|
<script>
|
|
var path_to_root = "../../";
|
|
var default_theme = window.matchMedia("(prefers-color-scheme: dark)").matches ? "navy" : "light";
|
|
</script>
|
|
|
|
<!-- Work around some values being stored in localStorage wrapped in quotes -->
|
|
<script>
|
|
try {
|
|
var theme = localStorage.getItem('mdbook-theme');
|
|
var sidebar = localStorage.getItem('mdbook-sidebar');
|
|
|
|
if (theme.startsWith('"') && theme.endsWith('"')) {
|
|
localStorage.setItem('mdbook-theme', theme.slice(1, theme.length - 1));
|
|
}
|
|
|
|
if (sidebar.startsWith('"') && sidebar.endsWith('"')) {
|
|
localStorage.setItem('mdbook-sidebar', sidebar.slice(1, sidebar.length - 1));
|
|
}
|
|
} catch (e) { }
|
|
</script>
|
|
|
|
<!-- Set the theme before any content is loaded, prevents flash -->
|
|
<script>
|
|
var theme;
|
|
try { theme = localStorage.getItem('mdbook-theme'); } catch(e) { }
|
|
if (theme === null || theme === undefined) { theme = default_theme; }
|
|
var html = document.querySelector('html');
|
|
html.classList.remove('light')
|
|
html.classList.add(theme);
|
|
var body = document.querySelector('body');
|
|
body.classList.remove('no-js')
|
|
body.classList.add('js');
|
|
</script>
|
|
|
|
<input type="checkbox" id="sidebar-toggle-anchor" class="hidden">
|
|
|
|
<!-- Hide / unhide sidebar before it is displayed -->
|
|
<script>
|
|
var body = document.querySelector('body');
|
|
var sidebar = null;
|
|
var sidebar_toggle = document.getElementById("sidebar-toggle-anchor");
|
|
if (document.body.clientWidth >= 1080) {
|
|
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
|
|
sidebar = sidebar || 'visible';
|
|
} else {
|
|
sidebar = 'hidden';
|
|
}
|
|
sidebar_toggle.checked = sidebar === 'visible';
|
|
body.classList.remove('sidebar-visible');
|
|
body.classList.add("sidebar-" + sidebar);
|
|
</script>
|
|
|
|
<nav id="sidebar" class="sidebar" aria-label="Table of contents">
|
|
<div class="sidebar-scrollbox">
|
|
<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"><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" class="active"><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>
|
|
</div>
|
|
<div id="sidebar-resize-handle" class="sidebar-resize-handle">
|
|
<div class="sidebar-resize-indicator"></div>
|
|
</div>
|
|
</nav>
|
|
|
|
<!-- Track and set sidebar scroll position -->
|
|
<script>
|
|
var sidebarScrollbox = document.querySelector('#sidebar .sidebar-scrollbox');
|
|
sidebarScrollbox.addEventListener('click', function(e) {
|
|
if (e.target.tagName === 'A') {
|
|
sessionStorage.setItem('sidebar-scroll', sidebarScrollbox.scrollTop);
|
|
}
|
|
}, { passive: true });
|
|
var sidebarScrollTop = sessionStorage.getItem('sidebar-scroll');
|
|
sessionStorage.removeItem('sidebar-scroll');
|
|
if (sidebarScrollTop) {
|
|
// preserve sidebar scroll position when navigating via links within sidebar
|
|
sidebarScrollbox.scrollTop = sidebarScrollTop;
|
|
} else {
|
|
// scroll sidebar to current active section when navigating via "next/previous chapter" buttons
|
|
var activeSection = document.querySelector('#sidebar .active');
|
|
if (activeSection) {
|
|
activeSection.scrollIntoView({ block: 'center' });
|
|
}
|
|
}
|
|
</script>
|
|
|
|
<div id="page-wrapper" class="page-wrapper">
|
|
|
|
<div class="page">
|
|
<div id="menu-bar-hover-placeholder"></div>
|
|
<div id="menu-bar" class="menu-bar sticky">
|
|
<div class="left-buttons">
|
|
<label id="sidebar-toggle" class="icon-button" for="sidebar-toggle-anchor" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
|
|
<i class="fa fa-bars"></i>
|
|
</label>
|
|
<button id="theme-toggle" class="icon-button" type="button" title="Change theme" aria-label="Change theme" aria-haspopup="true" aria-expanded="false" aria-controls="theme-list">
|
|
<i class="fa fa-paint-brush"></i>
|
|
</button>
|
|
<ul id="theme-list" class="theme-popup" aria-label="Themes" role="menu">
|
|
<li role="none"><button role="menuitem" class="theme" id="light">Light</button></li>
|
|
<li role="none"><button role="menuitem" class="theme" id="rust">Rust</button></li>
|
|
<li role="none"><button role="menuitem" class="theme" id="coal">Coal</button></li>
|
|
<li role="none"><button role="menuitem" class="theme" id="navy">Navy</button></li>
|
|
<li role="none"><button role="menuitem" class="theme" id="ayu">Ayu</button></li>
|
|
</ul>
|
|
<button id="search-toggle" class="icon-button" type="button" title="Search. (Shortkey: s)" aria-label="Toggle Searchbar" aria-expanded="false" aria-keyshortcuts="S" aria-controls="searchbar">
|
|
<i class="fa fa-search"></i>
|
|
</button>
|
|
</div>
|
|
|
|
<h1 class="menu-title">The halo2 Book</h1>
|
|
|
|
<div class="right-buttons">
|
|
<a href="../../print.html" title="Print this book" aria-label="Print this book">
|
|
<i id="print-button" class="fa fa-print"></i>
|
|
</a>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<div id="search-wrapper" class="hidden">
|
|
<form id="searchbar-outer" class="searchbar-outer">
|
|
<input type="search" id="searchbar" name="searchbar" placeholder="Search this book ..." aria-controls="searchresults-outer" aria-describedby="searchresults-header">
|
|
</form>
|
|
<div id="searchresults-outer" class="searchresults-outer hidden">
|
|
<div id="searchresults-header" class="searchresults-header"></div>
|
|
<ul id="searchresults">
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
|
|
<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
|
|
<script>
|
|
document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
|
|
document.getElementById('sidebar').setAttribute('aria-hidden', sidebar !== 'visible');
|
|
Array.from(document.querySelectorAll('#sidebar a')).forEach(function(link) {
|
|
link.setAttribute('tabIndex', sidebar === 'visible' ? 0 : -1);
|
|
});
|
|
</script>
|
|
|
|
<div id="content" class="content">
|
|
<main>
|
|
<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">
|
|
<h1 id="sha-256"><a class="header" href="#sha-256">SHA-256</a></h1>
|
|
<h2 id="specification"><a class="header" href="#specification">Specification</a></h2>
|
|
<p>SHA-256 is specified in <a href="https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf">NIST FIPS PUB 180-4</a>.</p>
|
|
<p>Unlike the specification, we use <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.675em;"></span><span class="mord amsrm">⊞</span></span></span></span> for addition modulo <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">32</span></span></span></span></span></span></span></span></span></span></span></span>, and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span> for
|
|
field addition. <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊕</span></span></span></span> is used for XOR.</p>
|
|
<h2 id="gadget-interface"><a class="header" href="#gadget-interface">Gadget interface</a></h2>
|
|
<p>SHA-256 maintains state in eight 32-bit variables. It processes input as 512-bit blocks,
|
|
but internally splits these blocks into 32-bit chunks. We therefore designed the SHA-256
|
|
gadget to consume input in 32-bit chunks.</p>
|
|
<h2 id="chip-instructions"><a class="header" href="#chip-instructions">Chip instructions</a></h2>
|
|
<p>The SHA-256 gadget requires a chip with the following instructions:</p>
|
|
<pre><pre class="playground"><code class="language-rust"><span class="boring">#![allow(unused)]
|
|
</span><span class="boring">fn main() {
|
|
</span><span class="boring">extern crate halo2_proofs;
|
|
</span><span class="boring">use halo2_proofs::plonk::Error;
|
|
</span><span class="boring">use std::fmt;
|
|
</span><span class="boring">
|
|
</span><span class="boring">trait Chip: Sized {}
|
|
</span><span class="boring">trait Layouter<C: Chip> {}
|
|
</span>const BLOCK_SIZE: usize = 16;
|
|
const DIGEST_SIZE: usize = 8;
|
|
|
|
pub trait Sha256Instructions: Chip {
|
|
/// Variable representing the SHA-256 internal state.
|
|
type State: Clone + fmt::Debug;
|
|
/// Variable representing a 32-bit word of the input block to the SHA-256 compression
|
|
/// function.
|
|
type BlockWord: Copy + fmt::Debug;
|
|
|
|
/// Places the SHA-256 IV in the circuit, returning the initial state variable.
|
|
fn initialization_vector(layouter: &mut impl Layouter<Self>) -> Result<Self::State, Error>;
|
|
|
|
/// Starting from the given initial state, processes a block of input and returns the
|
|
/// final state.
|
|
fn compress(
|
|
layouter: &mut impl Layouter<Self>,
|
|
initial_state: &Self::State,
|
|
input: [Self::BlockWord; BLOCK_SIZE],
|
|
) -> Result<Self::State, Error>;
|
|
|
|
/// Converts the given state into a message digest.
|
|
fn digest(
|
|
layouter: &mut impl Layouter<Self>,
|
|
state: &Self::State,
|
|
) -> Result<[Self::BlockWord; DIGEST_SIZE], Error>;
|
|
}
|
|
<span class="boring">}</span></code></pre></pre>
|
|
<p>TODO: Add instruction for computing padding.</p>
|
|
<p>This set of instructions was chosen to strike a balance between the reusability of the
|
|
instructions, and the scope for chips to internally optimise them. In particular, we
|
|
considered splitting the compression function into its constituent parts (Ch, Maj etc),
|
|
and providing a compression function gadget that implemented the round logic. However,
|
|
this would prevent chips from using relative references between the various parts of a
|
|
compression round. Having an instruction that implements all compression rounds is also
|
|
similar to the Intel SHA extensions, which provide an instruction that performs multiple
|
|
compression rounds.</p>
|
|
|
|
</main>
|
|
|
|
<nav class="nav-wrapper" aria-label="Page navigation">
|
|
<!-- Mobile navigation buttons -->
|
|
<a rel="prev" href="../../design/gadgets/decomposition.html" class="mobile-nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
|
|
<i class="fa fa-angle-left"></i>
|
|
</a>
|
|
|
|
<a rel="next prefetch" href="../../design/gadgets/sha256/table16.html" class="mobile-nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
|
|
<i class="fa fa-angle-right"></i>
|
|
</a>
|
|
|
|
<div style="clear: both"></div>
|
|
</nav>
|
|
</div>
|
|
</div>
|
|
|
|
<nav class="nav-wide-wrapper" aria-label="Page navigation">
|
|
<a rel="prev" href="../../design/gadgets/decomposition.html" class="nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
|
|
<i class="fa fa-angle-left"></i>
|
|
</a>
|
|
|
|
<a rel="next prefetch" href="../../design/gadgets/sha256/table16.html" class="nav-chapters next" title="Next chapter" aria-label="Next chapter" aria-keyshortcuts="Right">
|
|
<i class="fa fa-angle-right"></i>
|
|
</a>
|
|
</nav>
|
|
|
|
</div>
|
|
|
|
|
|
|
|
|
|
<script>
|
|
window.playground_copyable = true;
|
|
</script>
|
|
|
|
|
|
<script src="../../elasticlunr.min.js"></script>
|
|
<script src="../../mark.min.js"></script>
|
|
<script src="../../searcher.js"></script>
|
|
|
|
<script src="../../clipboard.min.js"></script>
|
|
<script src="../../highlight.js"></script>
|
|
<script src="../../book.js"></script>
|
|
|
|
<!-- Custom JS scripts -->
|
|
|
|
|
|
</div>
|
|
</body>
|
|
</html>
|