This commit is contained in:
heeckhau
2023-07-25 10:12:26 +00:00
parent 2aaf3b5b6a
commit 5585ab6528
61 changed files with 10745 additions and 0 deletions

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This file makes sure that Github Pages doesn't process mdBook's output.

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<!DOCTYPE HTML>
<html lang="en" class="sidebar-visible no-js ayu">
<head>
<!-- Book generated using mdBook -->
<meta charset="UTF-8">
<title>Page not found - tlsn-docs</title>
<base href="/">
<!-- 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 -->
<link rel="stylesheet" href="src/css/katex.css">
<link rel="stylesheet" href="src/css/global.css">
</head>
<body>
<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" : "ayu";
</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('no-js')
html.classList.remove('ayu')
html.classList.add(theme);
html.classList.add('js');
</script>
<!-- Hide / unhide sidebar before it is displayed -->
<script>
var html = document.querySelector('html');
var sidebar = null;
if (document.body.clientWidth >= 1080) {
try { sidebar = localStorage.getItem('mdbook-sidebar'); } catch(e) { }
sidebar = sidebar || 'visible';
} else {
sidebar = 'hidden';
}
html.classList.remove('sidebar-visible');
html.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="intro.html">Introduction</a></li><li class="chapter-item expanded affix "><a href="protocol/index.html">Protocol</a></li><li class="chapter-item expanded "><a href="overview.html"><strong aria-hidden="true">1.</strong> Overview</a></li><li class="chapter-item expanded "><a href="protocol/notarization/index.html"><strong aria-hidden="true">2.</strong> Notarization</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">2.1.</strong> TLS Handshake</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="protocol/notarization/key_exchange.html"><strong aria-hidden="true">2.1.1.</strong> Key Exchange</a></li><li class="chapter-item expanded "><a href="protocol/notarization/prf.html"><strong aria-hidden="true">2.1.2.</strong> Symmetric key derivation</a></li></ol></li><li class="chapter-item expanded "><a href="protocol/notarization/encryption.html"><strong aria-hidden="true">2.2.</strong> Encryption</a></li><li class="chapter-item expanded "><a href="protocol/notarization/commitment.html"><strong aria-hidden="true">2.3.</strong> Commitment</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="protocol/notarization/public_data_commitment.html"><strong aria-hidden="true">2.3.1.</strong> Commitment to public data</a></li></ol></li></ol></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.</strong> Selective Disclosure</div></li><li class="chapter-item expanded "><a href="protocol/2pc/garbled_circuits.html"><strong aria-hidden="true">4.</strong> Secure 2-Party Computation</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">4.1.</strong> Garbled Circuits</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="protocol/2pc/deap.html"><strong aria-hidden="true">4.1.1.</strong> Dual Execution with Asymmetric Privacy</a></li></ol></li><li class="chapter-item expanded "><div><strong aria-hidden="true">4.2.</strong> Oblivious Transfer</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">4.3.</strong> Paillier</div></li><li class="chapter-item expanded "><a href="protocol/2pc/mac.html"><strong aria-hidden="true">4.4.</strong> MAC</a></li><li class="chapter-item expanded "><a href="protocol/2pc/ff-arithmetic.html"><strong aria-hidden="true">4.5.</strong> Finite-Field Arithmetic</a></li></ol></li></ol>
</div>
<div id="sidebar-resize-handle" class="sidebar-resize-handle"></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">
<button id="sidebar-toggle" class="icon-button" type="button" title="Toggle Table of Contents" aria-label="Toggle Table of Contents" aria-controls="sidebar">
<i class="fa fa-bars"></i>
</button>
<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">tlsn-docs</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>
<h1 id="document-not-found-404"><a class="header" href="#document-not-found-404">Document not found (404)</a></h1>
<p>This URL is invalid, sorry. Please use the navigation bar or search to continue.</p>
</main>
<nav class="nav-wrapper" aria-label="Page navigation">
<!-- Mobile navigation buttons -->
<div style="clear: both"></div>
</nav>
</div>
</div>
<nav class="nav-wide-wrapper" aria-label="Page navigation">
</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>

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/*
Based off of the Ayu theme
Original by Dempfi (https://github.com/dempfi/ayu)
*/
.hljs {
display: block;
overflow-x: auto;
background: #191f26;
color: #e6e1cf;
}
.hljs-comment,
.hljs-quote {
color: #5c6773;
font-style: italic;
}
.hljs-variable,
.hljs-template-variable,
.hljs-attribute,
.hljs-attr,
.hljs-regexp,
.hljs-link,
.hljs-selector-id,
.hljs-selector-class {
color: #ff7733;
}
.hljs-number,
.hljs-meta,
.hljs-builtin-name,
.hljs-literal,
.hljs-type,
.hljs-params {
color: #ffee99;
}
.hljs-string,
.hljs-bullet {
color: #b8cc52;
}
.hljs-title,
.hljs-built_in,
.hljs-section {
color: #ffb454;
}
.hljs-keyword,
.hljs-selector-tag,
.hljs-symbol {
color: #ff7733;
}
.hljs-name {
color: #36a3d9;
}
.hljs-tag {
color: #00568d;
}
.hljs-emphasis {
font-style: italic;
}
.hljs-strong {
font-weight: bold;
}
.hljs-addition {
color: #91b362;
}
.hljs-deletion {
color: #d96c75;
}

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"use strict";
// Fix back button cache problem
window.onunload = function () { };
// Global variable, shared between modules
function playground_text(playground, hidden = true) {
let code_block = playground.querySelector("code");
if (window.ace && code_block.classList.contains("editable")) {
let editor = window.ace.edit(code_block);
return editor.getValue();
} else if (hidden) {
return code_block.textContent;
} else {
return code_block.innerText;
}
}
(function codeSnippets() {
function fetch_with_timeout(url, options, timeout = 6000) {
return Promise.race([
fetch(url, options),
new Promise((_, reject) => setTimeout(() => reject(new Error('timeout')), timeout))
]);
}
var playgrounds = Array.from(document.querySelectorAll(".playground"));
if (playgrounds.length > 0) {
fetch_with_timeout("https://play.rust-lang.org/meta/crates", {
headers: {
'Content-Type': "application/json",
},
method: 'POST',
mode: 'cors',
})
.then(response => response.json())
.then(response => {
// get list of crates available in the rust playground
let playground_crates = response.crates.map(item => item["id"]);
playgrounds.forEach(block => handle_crate_list_update(block, playground_crates));
});
}
function handle_crate_list_update(playground_block, playground_crates) {
// update the play buttons after receiving the response
update_play_button(playground_block, playground_crates);
// and install on change listener to dynamically update ACE editors
if (window.ace) {
let code_block = playground_block.querySelector("code");
if (code_block.classList.contains("editable")) {
let editor = window.ace.edit(code_block);
editor.addEventListener("change", function (e) {
update_play_button(playground_block, playground_crates);
});
// add Ctrl-Enter command to execute rust code
editor.commands.addCommand({
name: "run",
bindKey: {
win: "Ctrl-Enter",
mac: "Ctrl-Enter"
},
exec: _editor => run_rust_code(playground_block)
});
}
}
}
// updates the visibility of play button based on `no_run` class and
// used crates vs ones available on https://play.rust-lang.org
function update_play_button(pre_block, playground_crates) {
var play_button = pre_block.querySelector(".play-button");
// skip if code is `no_run`
if (pre_block.querySelector('code').classList.contains("no_run")) {
play_button.classList.add("hidden");
return;
}
// get list of `extern crate`'s from snippet
var txt = playground_text(pre_block);
var re = /extern\s+crate\s+([a-zA-Z_0-9]+)\s*;/g;
var snippet_crates = [];
var item;
while (item = re.exec(txt)) {
snippet_crates.push(item[1]);
}
// check if all used crates are available on play.rust-lang.org
var all_available = snippet_crates.every(function (elem) {
return playground_crates.indexOf(elem) > -1;
});
if (all_available) {
play_button.classList.remove("hidden");
} else {
play_button.classList.add("hidden");
}
}
function run_rust_code(code_block) {
var result_block = code_block.querySelector(".result");
if (!result_block) {
result_block = document.createElement('code');
result_block.className = 'result hljs language-bash';
code_block.append(result_block);
}
let text = playground_text(code_block);
let classes = code_block.querySelector('code').classList;
let edition = "2015";
if(classes.contains("edition2018")) {
edition = "2018";
} else if(classes.contains("edition2021")) {
edition = "2021";
}
var params = {
version: "stable",
optimize: "0",
code: text,
edition: edition
};
if (text.indexOf("#![feature") !== -1) {
params.version = "nightly";
}
result_block.innerText = "Running...";
fetch_with_timeout("https://play.rust-lang.org/evaluate.json", {
headers: {
'Content-Type': "application/json",
},
method: 'POST',
mode: 'cors',
body: JSON.stringify(params)
})
.then(response => response.json())
.then(response => {
if (response.result.trim() === '') {
result_block.innerText = "No output";
result_block.classList.add("result-no-output");
} else {
result_block.innerText = response.result;
result_block.classList.remove("result-no-output");
}
})
.catch(error => result_block.innerText = "Playground Communication: " + error.message);
}
// Syntax highlighting Configuration
hljs.configure({
tabReplace: ' ', // 4 spaces
languages: [], // Languages used for auto-detection
});
let code_nodes = Array
.from(document.querySelectorAll('code'))
// Don't highlight `inline code` blocks in headers.
.filter(function (node) {return !node.parentElement.classList.contains("header"); });
if (window.ace) {
// language-rust class needs to be removed for editable
// blocks or highlightjs will capture events
code_nodes
.filter(function (node) {return node.classList.contains("editable"); })
.forEach(function (block) { block.classList.remove('language-rust'); });
code_nodes
.filter(function (node) {return !node.classList.contains("editable"); })
.forEach(function (block) { hljs.highlightBlock(block); });
} else {
code_nodes.forEach(function (block) { hljs.highlightBlock(block); });
}
// Adding the hljs class gives code blocks the color css
// even if highlighting doesn't apply
code_nodes.forEach(function (block) { block.classList.add('hljs'); });
Array.from(document.querySelectorAll("code.hljs")).forEach(function (block) {
var lines = Array.from(block.querySelectorAll('.boring'));
// If no lines were hidden, return
if (!lines.length) { return; }
block.classList.add("hide-boring");
var buttons = document.createElement('div');
buttons.className = 'buttons';
buttons.innerHTML = "<button class=\"fa fa-eye\" title=\"Show hidden lines\" aria-label=\"Show hidden lines\"></button>";
// add expand button
var pre_block = block.parentNode;
pre_block.insertBefore(buttons, pre_block.firstChild);
pre_block.querySelector('.buttons').addEventListener('click', function (e) {
if (e.target.classList.contains('fa-eye')) {
e.target.classList.remove('fa-eye');
e.target.classList.add('fa-eye-slash');
e.target.title = 'Hide lines';
e.target.setAttribute('aria-label', e.target.title);
block.classList.remove('hide-boring');
} else if (e.target.classList.contains('fa-eye-slash')) {
e.target.classList.remove('fa-eye-slash');
e.target.classList.add('fa-eye');
e.target.title = 'Show hidden lines';
e.target.setAttribute('aria-label', e.target.title);
block.classList.add('hide-boring');
}
});
});
if (window.playground_copyable) {
Array.from(document.querySelectorAll('pre code')).forEach(function (block) {
var pre_block = block.parentNode;
if (!pre_block.classList.contains('playground')) {
var buttons = pre_block.querySelector(".buttons");
if (!buttons) {
buttons = document.createElement('div');
buttons.className = 'buttons';
pre_block.insertBefore(buttons, pre_block.firstChild);
}
var clipButton = document.createElement('button');
clipButton.className = 'fa fa-copy clip-button';
clipButton.title = 'Copy to clipboard';
clipButton.setAttribute('aria-label', clipButton.title);
clipButton.innerHTML = '<i class=\"tooltiptext\"></i>';
buttons.insertBefore(clipButton, buttons.firstChild);
}
});
}
// Process playground code blocks
Array.from(document.querySelectorAll(".playground")).forEach(function (pre_block) {
// Add play button
var buttons = pre_block.querySelector(".buttons");
if (!buttons) {
buttons = document.createElement('div');
buttons.className = 'buttons';
pre_block.insertBefore(buttons, pre_block.firstChild);
}
var runCodeButton = document.createElement('button');
runCodeButton.className = 'fa fa-play play-button';
runCodeButton.hidden = true;
runCodeButton.title = 'Run this code';
runCodeButton.setAttribute('aria-label', runCodeButton.title);
buttons.insertBefore(runCodeButton, buttons.firstChild);
runCodeButton.addEventListener('click', function (e) {
run_rust_code(pre_block);
});
if (window.playground_copyable) {
var copyCodeClipboardButton = document.createElement('button');
copyCodeClipboardButton.className = 'fa fa-copy clip-button';
copyCodeClipboardButton.innerHTML = '<i class="tooltiptext"></i>';
copyCodeClipboardButton.title = 'Copy to clipboard';
copyCodeClipboardButton.setAttribute('aria-label', copyCodeClipboardButton.title);
buttons.insertBefore(copyCodeClipboardButton, buttons.firstChild);
}
let code_block = pre_block.querySelector("code");
if (window.ace && code_block.classList.contains("editable")) {
var undoChangesButton = document.createElement('button');
undoChangesButton.className = 'fa fa-history reset-button';
undoChangesButton.title = 'Undo changes';
undoChangesButton.setAttribute('aria-label', undoChangesButton.title);
buttons.insertBefore(undoChangesButton, buttons.firstChild);
undoChangesButton.addEventListener('click', function () {
let editor = window.ace.edit(code_block);
editor.setValue(editor.originalCode);
editor.clearSelection();
});
}
});
})();
(function themes() {
var html = document.querySelector('html');
var themeToggleButton = document.getElementById('theme-toggle');
var themePopup = document.getElementById('theme-list');
var themeColorMetaTag = document.querySelector('meta[name="theme-color"]');
var stylesheets = {
ayuHighlight: document.querySelector("[href$='ayu-highlight.css']"),
tomorrowNight: document.querySelector("[href$='tomorrow-night.css']"),
highlight: document.querySelector("[href$='highlight.css']"),
};
function showThemes() {
themePopup.style.display = 'block';
themeToggleButton.setAttribute('aria-expanded', true);
themePopup.querySelector("button#" + get_theme()).focus();
}
function updateThemeSelected() {
themePopup.querySelectorAll('.theme-selected').forEach(function (el) {
el.classList.remove('theme-selected');
});
themePopup.querySelector("button#" + get_theme()).classList.add('theme-selected');
}
function hideThemes() {
themePopup.style.display = 'none';
themeToggleButton.setAttribute('aria-expanded', false);
themeToggleButton.focus();
}
function get_theme() {
var theme;
try { theme = localStorage.getItem('mdbook-theme'); } catch (e) { }
if (theme === null || theme === undefined) {
return default_theme;
} else {
return theme;
}
}
function set_theme(theme, store = true) {
let ace_theme;
if (theme == 'coal' || theme == 'navy') {
stylesheets.ayuHighlight.disabled = true;
stylesheets.tomorrowNight.disabled = false;
stylesheets.highlight.disabled = true;
ace_theme = "ace/theme/tomorrow_night";
} else if (theme == 'ayu') {
stylesheets.ayuHighlight.disabled = false;
stylesheets.tomorrowNight.disabled = true;
stylesheets.highlight.disabled = true;
ace_theme = "ace/theme/tomorrow_night";
} else {
stylesheets.ayuHighlight.disabled = true;
stylesheets.tomorrowNight.disabled = true;
stylesheets.highlight.disabled = false;
ace_theme = "ace/theme/dawn";
}
setTimeout(function () {
themeColorMetaTag.content = getComputedStyle(document.documentElement).backgroundColor;
}, 1);
if (window.ace && window.editors) {
window.editors.forEach(function (editor) {
editor.setTheme(ace_theme);
});
}
var previousTheme = get_theme();
if (store) {
try { localStorage.setItem('mdbook-theme', theme); } catch (e) { }
}
html.classList.remove(previousTheme);
html.classList.add(theme);
updateThemeSelected();
}
// Set theme
var theme = get_theme();
set_theme(theme, false);
themeToggleButton.addEventListener('click', function () {
if (themePopup.style.display === 'block') {
hideThemes();
} else {
showThemes();
}
});
themePopup.addEventListener('click', function (e) {
var theme;
if (e.target.className === "theme") {
theme = e.target.id;
} else if (e.target.parentElement.className === "theme") {
theme = e.target.parentElement.id;
} else {
return;
}
set_theme(theme);
});
themePopup.addEventListener('focusout', function(e) {
// e.relatedTarget is null in Safari and Firefox on macOS (see workaround below)
if (!!e.relatedTarget && !themeToggleButton.contains(e.relatedTarget) && !themePopup.contains(e.relatedTarget)) {
hideThemes();
}
});
// Should not be needed, but it works around an issue on macOS & iOS: https://github.com/rust-lang/mdBook/issues/628
document.addEventListener('click', function(e) {
if (themePopup.style.display === 'block' && !themeToggleButton.contains(e.target) && !themePopup.contains(e.target)) {
hideThemes();
}
});
document.addEventListener('keydown', function (e) {
if (e.altKey || e.ctrlKey || e.metaKey || e.shiftKey) { return; }
if (!themePopup.contains(e.target)) { return; }
switch (e.key) {
case 'Escape':
e.preventDefault();
hideThemes();
break;
case 'ArrowUp':
e.preventDefault();
var li = document.activeElement.parentElement;
if (li && li.previousElementSibling) {
li.previousElementSibling.querySelector('button').focus();
}
break;
case 'ArrowDown':
e.preventDefault();
var li = document.activeElement.parentElement;
if (li && li.nextElementSibling) {
li.nextElementSibling.querySelector('button').focus();
}
break;
case 'Home':
e.preventDefault();
themePopup.querySelector('li:first-child button').focus();
break;
case 'End':
e.preventDefault();
themePopup.querySelector('li:last-child button').focus();
break;
}
});
})();
(function sidebar() {
var html = document.querySelector("html");
var sidebar = document.getElementById("sidebar");
var sidebarLinks = document.querySelectorAll('#sidebar a');
var sidebarToggleButton = document.getElementById("sidebar-toggle");
var sidebarResizeHandle = document.getElementById("sidebar-resize-handle");
var firstContact = null;
function showSidebar() {
html.classList.remove('sidebar-hidden')
html.classList.add('sidebar-visible');
Array.from(sidebarLinks).forEach(function (link) {
link.setAttribute('tabIndex', 0);
});
sidebarToggleButton.setAttribute('aria-expanded', true);
sidebar.setAttribute('aria-hidden', false);
try { localStorage.setItem('mdbook-sidebar', 'visible'); } catch (e) { }
}
var sidebarAnchorToggles = document.querySelectorAll('#sidebar a.toggle');
function toggleSection(ev) {
ev.currentTarget.parentElement.classList.toggle('expanded');
}
Array.from(sidebarAnchorToggles).forEach(function (el) {
el.addEventListener('click', toggleSection);
});
function hideSidebar() {
html.classList.remove('sidebar-visible')
html.classList.add('sidebar-hidden');
Array.from(sidebarLinks).forEach(function (link) {
link.setAttribute('tabIndex', -1);
});
sidebarToggleButton.setAttribute('aria-expanded', false);
sidebar.setAttribute('aria-hidden', true);
try { localStorage.setItem('mdbook-sidebar', 'hidden'); } catch (e) { }
}
// Toggle sidebar
sidebarToggleButton.addEventListener('click', function sidebarToggle() {
if (html.classList.contains("sidebar-hidden")) {
var current_width = parseInt(
document.documentElement.style.getPropertyValue('--sidebar-width'), 10);
if (current_width < 150) {
document.documentElement.style.setProperty('--sidebar-width', '150px');
}
showSidebar();
} else if (html.classList.contains("sidebar-visible")) {
hideSidebar();
} else {
if (getComputedStyle(sidebar)['transform'] === 'none') {
hideSidebar();
} else {
showSidebar();
}
}
});
sidebarResizeHandle.addEventListener('mousedown', initResize, false);
function initResize(e) {
window.addEventListener('mousemove', resize, false);
window.addEventListener('mouseup', stopResize, false);
html.classList.add('sidebar-resizing');
}
function resize(e) {
var pos = (e.clientX - sidebar.offsetLeft);
if (pos < 20) {
hideSidebar();
} else {
if (html.classList.contains("sidebar-hidden")) {
showSidebar();
}
pos = Math.min(pos, window.innerWidth - 100);
document.documentElement.style.setProperty('--sidebar-width', pos + 'px');
}
}
//on mouseup remove windows functions mousemove & mouseup
function stopResize(e) {
html.classList.remove('sidebar-resizing');
window.removeEventListener('mousemove', resize, false);
window.removeEventListener('mouseup', stopResize, false);
}
document.addEventListener('touchstart', function (e) {
firstContact = {
x: e.touches[0].clientX,
time: Date.now()
};
}, { passive: true });
document.addEventListener('touchmove', function (e) {
if (!firstContact)
return;
var curX = e.touches[0].clientX;
var xDiff = curX - firstContact.x,
tDiff = Date.now() - firstContact.time;
if (tDiff < 250 && Math.abs(xDiff) >= 150) {
if (xDiff >= 0 && firstContact.x < Math.min(document.body.clientWidth * 0.25, 300))
showSidebar();
else if (xDiff < 0 && curX < 300)
hideSidebar();
firstContact = null;
}
}, { passive: true });
})();
(function chapterNavigation() {
document.addEventListener('keydown', function (e) {
if (e.altKey || e.ctrlKey || e.metaKey || e.shiftKey) { return; }
if (window.search && window.search.hasFocus()) { return; }
switch (e.key) {
case 'ArrowRight':
e.preventDefault();
var nextButton = document.querySelector('.nav-chapters.next');
if (nextButton) {
window.location.href = nextButton.href;
}
break;
case 'ArrowLeft':
e.preventDefault();
var previousButton = document.querySelector('.nav-chapters.previous');
if (previousButton) {
window.location.href = previousButton.href;
}
break;
}
});
})();
(function clipboard() {
var clipButtons = document.querySelectorAll('.clip-button');
function hideTooltip(elem) {
elem.firstChild.innerText = "";
elem.className = 'fa fa-copy clip-button';
}
function showTooltip(elem, msg) {
elem.firstChild.innerText = msg;
elem.className = 'fa fa-copy tooltipped';
}
var clipboardSnippets = new ClipboardJS('.clip-button', {
text: function (trigger) {
hideTooltip(trigger);
let playground = trigger.closest("pre");
return playground_text(playground, false);
}
});
Array.from(clipButtons).forEach(function (clipButton) {
clipButton.addEventListener('mouseout', function (e) {
hideTooltip(e.currentTarget);
});
});
clipboardSnippets.on('success', function (e) {
e.clearSelection();
showTooltip(e.trigger, "Copied!");
});
clipboardSnippets.on('error', function (e) {
showTooltip(e.trigger, "Clipboard error!");
});
})();
(function scrollToTop () {
var menuTitle = document.querySelector('.menu-title');
menuTitle.addEventListener('click', function () {
document.scrollingElement.scrollTo({ top: 0, behavior: 'smooth' });
});
})();
(function controllMenu() {
var menu = document.getElementById('menu-bar');
(function controllPosition() {
var scrollTop = document.scrollingElement.scrollTop;
var prevScrollTop = scrollTop;
var minMenuY = -menu.clientHeight - 50;
// When the script loads, the page can be at any scroll (e.g. if you reforesh it).
menu.style.top = scrollTop + 'px';
// Same as parseInt(menu.style.top.slice(0, -2), but faster
var topCache = menu.style.top.slice(0, -2);
menu.classList.remove('sticky');
var stickyCache = false; // Same as menu.classList.contains('sticky'), but faster
document.addEventListener('scroll', function () {
scrollTop = Math.max(document.scrollingElement.scrollTop, 0);
// `null` means that it doesn't need to be updated
var nextSticky = null;
var nextTop = null;
var scrollDown = scrollTop > prevScrollTop;
var menuPosAbsoluteY = topCache - scrollTop;
if (scrollDown) {
nextSticky = false;
if (menuPosAbsoluteY > 0) {
nextTop = prevScrollTop;
}
} else {
if (menuPosAbsoluteY > 0) {
nextSticky = true;
} else if (menuPosAbsoluteY < minMenuY) {
nextTop = prevScrollTop + minMenuY;
}
}
if (nextSticky === true && stickyCache === false) {
menu.classList.add('sticky');
stickyCache = true;
} else if (nextSticky === false && stickyCache === true) {
menu.classList.remove('sticky');
stickyCache = false;
}
if (nextTop !== null) {
menu.style.top = nextTop + 'px';
topCache = nextTop;
}
prevScrollTop = scrollTop;
}, { passive: true });
})();
(function controllBorder() {
function updateBorder() {
if (menu.offsetTop === 0) {
menu.classList.remove('bordered');
} else {
menu.classList.add('bordered');
}
}
updateBorder();
document.addEventListener('scroll', updateBorder, { passive: true });
})();
})();

7
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/* CSS for UI elements (a.k.a. chrome) */
@import 'variables.css';
html {
scrollbar-color: var(--scrollbar) var(--bg);
}
#searchresults a,
.content a:link,
a:visited,
a > .hljs {
color: var(--links);
}
/*
body-container is necessary because mobile browsers don't seem to like
overflow-x on the body tag when there is a <meta name="viewport"> tag.
*/
#body-container {
/*
This is used when the sidebar pushes the body content off the side of
the screen on small screens. Without it, dragging on mobile Safari
will want to reposition the viewport in a weird way.
*/
overflow-x: clip;
}
/* Menu Bar */
#menu-bar,
#menu-bar-hover-placeholder {
z-index: 101;
margin: auto calc(0px - var(--page-padding));
}
#menu-bar {
position: relative;
display: flex;
flex-wrap: wrap;
background-color: var(--bg);
border-bottom-color: var(--bg);
border-bottom-width: 1px;
border-bottom-style: solid;
}
#menu-bar.sticky,
.js #menu-bar-hover-placeholder:hover + #menu-bar,
.js #menu-bar:hover,
.js.sidebar-visible #menu-bar {
position: -webkit-sticky;
position: sticky;
top: 0 !important;
}
#menu-bar-hover-placeholder {
position: sticky;
position: -webkit-sticky;
top: 0;
height: var(--menu-bar-height);
}
#menu-bar.bordered {
border-bottom-color: var(--table-border-color);
}
#menu-bar i, #menu-bar .icon-button {
position: relative;
padding: 0 8px;
z-index: 10;
line-height: var(--menu-bar-height);
cursor: pointer;
transition: color 0.5s;
}
@media only screen and (max-width: 420px) {
#menu-bar i, #menu-bar .icon-button {
padding: 0 5px;
}
}
.icon-button {
border: none;
background: none;
padding: 0;
color: inherit;
}
.icon-button i {
margin: 0;
}
.right-buttons {
margin: 0 15px;
}
.right-buttons a {
text-decoration: none;
}
.left-buttons {
display: flex;
margin: 0 5px;
}
.no-js .left-buttons {
display: none;
}
.menu-title {
display: inline-block;
font-weight: 200;
font-size: 2.4rem;
line-height: var(--menu-bar-height);
text-align: center;
margin: 0;
flex: 1;
white-space: nowrap;
overflow: hidden;
text-overflow: ellipsis;
}
.js .menu-title {
cursor: pointer;
}
.menu-bar,
.menu-bar:visited,
.nav-chapters,
.nav-chapters:visited,
.mobile-nav-chapters,
.mobile-nav-chapters:visited,
.menu-bar .icon-button,
.menu-bar a i {
color: var(--icons);
}
.menu-bar i:hover,
.menu-bar .icon-button:hover,
.nav-chapters:hover,
.mobile-nav-chapters i:hover {
color: var(--icons-hover);
}
/* Nav Icons */
.nav-chapters {
font-size: 2.5em;
text-align: center;
text-decoration: none;
position: fixed;
top: 0;
bottom: 0;
margin: 0;
max-width: 150px;
min-width: 90px;
display: flex;
justify-content: center;
align-content: center;
flex-direction: column;
transition: color 0.5s, background-color 0.5s;
}
.nav-chapters:hover {
text-decoration: none;
background-color: var(--theme-hover);
transition: background-color 0.15s, color 0.15s;
}
.nav-wrapper {
margin-top: 50px;
display: none;
}
.mobile-nav-chapters {
font-size: 2.5em;
text-align: center;
text-decoration: none;
width: 90px;
border-radius: 5px;
background-color: var(--sidebar-bg);
}
.previous {
float: left;
}
.next {
float: right;
right: var(--page-padding);
}
@media only screen and (max-width: 1080px) {
.nav-wide-wrapper { display: none; }
.nav-wrapper { display: block; }
}
@media only screen and (max-width: 1380px) {
.sidebar-visible .nav-wide-wrapper { display: none; }
.sidebar-visible .nav-wrapper { display: block; }
}
/* Inline code */
:not(pre) > .hljs {
display: inline;
padding: 0.1em 0.3em;
border-radius: 3px;
}
:not(pre):not(a) > .hljs {
color: var(--inline-code-color);
overflow-x: initial;
}
a:hover > .hljs {
text-decoration: underline;
}
pre {
position: relative;
}
pre > .buttons {
position: absolute;
z-index: 100;
right: 0px;
top: 2px;
margin: 0px;
padding: 2px 0px;
color: var(--sidebar-fg);
cursor: pointer;
visibility: hidden;
opacity: 0;
transition: visibility 0.1s linear, opacity 0.1s linear;
}
pre:hover > .buttons {
visibility: visible;
opacity: 1
}
pre > .buttons :hover {
color: var(--sidebar-active);
border-color: var(--icons-hover);
background-color: var(--theme-hover);
}
pre > .buttons i {
margin-left: 8px;
}
pre > .buttons button {
cursor: inherit;
margin: 0px 5px;
padding: 3px 5px;
font-size: 14px;
border-style: solid;
border-width: 1px;
border-radius: 4px;
border-color: var(--icons);
background-color: var(--theme-popup-bg);
transition: 100ms;
transition-property: color,border-color,background-color;
color: var(--icons);
}
@media (pointer: coarse) {
pre > .buttons button {
/* On mobile, make it easier to tap buttons. */
padding: 0.3rem 1rem;
}
}
pre > code {
padding: 1rem;
}
/* FIXME: ACE editors overlap their buttons because ACE does absolute
positioning within the code block which breaks padding. The only solution I
can think of is to move the padding to the outer pre tag (or insert a div
wrapper), but that would require fixing a whole bunch of CSS rules.
*/
.hljs.ace_editor {
padding: 0rem 0rem;
}
pre > .result {
margin-top: 10px;
}
/* Search */
#searchresults a {
text-decoration: none;
}
mark {
border-radius: 2px;
padding: 0 3px 1px 3px;
margin: 0 -3px -1px -3px;
background-color: var(--search-mark-bg);
transition: background-color 300ms linear;
cursor: pointer;
}
mark.fade-out {
background-color: rgba(0,0,0,0) !important;
cursor: auto;
}
.searchbar-outer {
margin-left: auto;
margin-right: auto;
max-width: var(--content-max-width);
}
#searchbar {
width: 100%;
margin: 5px auto 0px auto;
padding: 10px 16px;
transition: box-shadow 300ms ease-in-out;
border: 1px solid var(--searchbar-border-color);
border-radius: 3px;
background-color: var(--searchbar-bg);
color: var(--searchbar-fg);
}
#searchbar:focus,
#searchbar.active {
box-shadow: 0 0 3px var(--searchbar-shadow-color);
}
.searchresults-header {
font-weight: bold;
font-size: 1em;
padding: 18px 0 0 5px;
color: var(--searchresults-header-fg);
}
.searchresults-outer {
margin-left: auto;
margin-right: auto;
max-width: var(--content-max-width);
border-bottom: 1px dashed var(--searchresults-border-color);
}
ul#searchresults {
list-style: none;
padding-left: 20px;
}
ul#searchresults li {
margin: 10px 0px;
padding: 2px;
border-radius: 2px;
}
ul#searchresults li.focus {
background-color: var(--searchresults-li-bg);
}
ul#searchresults span.teaser {
display: block;
clear: both;
margin: 5px 0 0 20px;
font-size: 0.8em;
}
ul#searchresults span.teaser em {
font-weight: bold;
font-style: normal;
}
/* Sidebar */
.sidebar {
position: fixed;
left: 0;
top: 0;
bottom: 0;
width: var(--sidebar-width);
font-size: 0.875em;
box-sizing: border-box;
-webkit-overflow-scrolling: touch;
overscroll-behavior-y: contain;
background-color: var(--sidebar-bg);
color: var(--sidebar-fg);
}
.sidebar-resizing {
-moz-user-select: none;
-webkit-user-select: none;
-ms-user-select: none;
user-select: none;
}
.js:not(.sidebar-resizing) .sidebar {
transition: transform 0.3s; /* Animation: slide away */
}
.sidebar code {
line-height: 2em;
}
.sidebar .sidebar-scrollbox {
overflow-y: auto;
position: absolute;
top: 0;
bottom: 0;
left: 0;
right: 0;
padding: 10px 10px;
}
.sidebar .sidebar-resize-handle {
position: absolute;
cursor: col-resize;
width: 0;
right: 0;
top: 0;
bottom: 0;
}
.js .sidebar .sidebar-resize-handle {
cursor: col-resize;
width: 5px;
}
.sidebar-hidden .sidebar {
transform: translateX(calc(0px - var(--sidebar-width)));
}
.sidebar::-webkit-scrollbar {
background: var(--sidebar-bg);
}
.sidebar::-webkit-scrollbar-thumb {
background: var(--scrollbar);
}
.sidebar-visible .page-wrapper {
transform: translateX(var(--sidebar-width));
}
@media only screen and (min-width: 620px) {
.sidebar-visible .page-wrapper {
transform: none;
margin-left: var(--sidebar-width);
}
}
.chapter {
list-style: none outside none;
padding-left: 0;
line-height: 2.2em;
}
.chapter ol {
width: 100%;
}
.chapter li {
display: flex;
color: var(--sidebar-non-existant);
}
.chapter li a {
display: block;
padding: 0;
text-decoration: none;
color: var(--sidebar-fg);
}
.chapter li a:hover {
color: var(--sidebar-active);
}
.chapter li a.active {
color: var(--sidebar-active);
}
.chapter li > a.toggle {
cursor: pointer;
display: block;
margin-left: auto;
padding: 0 10px;
user-select: none;
opacity: 0.68;
}
.chapter li > a.toggle div {
transition: transform 0.5s;
}
/* collapse the section */
.chapter li:not(.expanded) + li > ol {
display: none;
}
.chapter li.chapter-item {
line-height: 1.5em;
margin-top: 0.6em;
}
.chapter li.expanded > a.toggle div {
transform: rotate(90deg);
}
.spacer {
width: 100%;
height: 3px;
margin: 5px 0px;
}
.chapter .spacer {
background-color: var(--sidebar-spacer);
}
@media (-moz-touch-enabled: 1), (pointer: coarse) {
.chapter li a { padding: 5px 0; }
.spacer { margin: 10px 0; }
}
.section {
list-style: none outside none;
padding-left: 20px;
line-height: 1.9em;
}
/* Theme Menu Popup */
.theme-popup {
position: absolute;
left: 10px;
top: var(--menu-bar-height);
z-index: 1000;
border-radius: 4px;
font-size: 0.7em;
color: var(--fg);
background: var(--theme-popup-bg);
border: 1px solid var(--theme-popup-border);
margin: 0;
padding: 0;
list-style: none;
display: none;
/* Don't let the children's background extend past the rounded corners. */
overflow: hidden;
}
.theme-popup .default {
color: var(--icons);
}
.theme-popup .theme {
width: 100%;
border: 0;
margin: 0;
padding: 2px 20px;
line-height: 25px;
white-space: nowrap;
text-align: left;
cursor: pointer;
color: inherit;
background: inherit;
font-size: inherit;
}
.theme-popup .theme:hover {
background-color: var(--theme-hover);
}
.theme-selected::before {
display: inline-block;
content: "✓";
margin-left: -14px;
width: 14px;
}

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/* Base styles and content styles */
@import 'variables.css';
:root {
/* Browser default font-size is 16px, this way 1 rem = 10px */
font-size: 62.5%;
}
html {
font-family: "Open Sans", sans-serif;
color: var(--fg);
background-color: var(--bg);
text-size-adjust: none;
-webkit-text-size-adjust: none;
}
body {
margin: 0;
font-size: 1.6rem;
overflow-x: hidden;
}
code {
font-family: var(--mono-font) !important;
font-size: var(--code-font-size);
}
/* make long words/inline code not x overflow */
main {
overflow-wrap: break-word;
}
/* make wide tables scroll if they overflow */
.table-wrapper {
overflow-x: auto;
}
/* Don't change font size in headers. */
h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
font-size: unset;
}
.left { float: left; }
.right { float: right; }
.boring { opacity: 0.6; }
.hide-boring .boring { display: none; }
.hidden { display: none !important; }
h2, h3 { margin-top: 2.5em; }
h4, h5 { margin-top: 2em; }
.header + .header h3,
.header + .header h4,
.header + .header h5 {
margin-top: 1em;
}
h1:target::before,
h2:target::before,
h3:target::before,
h4:target::before,
h5:target::before,
h6:target::before {
display: inline-block;
content: "»";
margin-left: -30px;
width: 30px;
}
/* This is broken on Safari as of version 14, but is fixed
in Safari Technology Preview 117 which I think will be Safari 14.2.
https://bugs.webkit.org/show_bug.cgi?id=218076
*/
:target {
scroll-margin-top: calc(var(--menu-bar-height) + 0.5em);
}
.page {
outline: 0;
padding: 0 var(--page-padding);
margin-top: calc(0px - var(--menu-bar-height)); /* Compensate for the #menu-bar-hover-placeholder */
}
.page-wrapper {
box-sizing: border-box;
}
.js:not(.sidebar-resizing) .page-wrapper {
transition: margin-left 0.3s ease, transform 0.3s ease; /* Animation: slide away */
}
.content {
overflow-y: auto;
padding: 0 5px 50px 5px;
}
.content main {
margin-left: auto;
margin-right: auto;
max-width: var(--content-max-width);
}
.content p { line-height: 1.45em; }
.content ol { line-height: 1.45em; }
.content ul { line-height: 1.45em; }
.content a { text-decoration: none; }
.content a:hover { text-decoration: underline; }
.content img, .content video { max-width: 100%; }
.content .header:link,
.content .header:visited {
color: var(--fg);
}
.content .header:link,
.content .header:visited:hover {
text-decoration: none;
}
table {
margin: 0 auto;
border-collapse: collapse;
}
table td {
padding: 3px 20px;
border: 1px var(--table-border-color) solid;
}
table thead {
background: var(--table-header-bg);
}
table thead td {
font-weight: 700;
border: none;
}
table thead th {
padding: 3px 20px;
}
table thead tr {
border: 1px var(--table-header-bg) solid;
}
/* Alternate background colors for rows */
table tbody tr:nth-child(2n) {
background: var(--table-alternate-bg);
}
blockquote {
margin: 20px 0;
padding: 0 20px;
color: var(--fg);
background-color: var(--quote-bg);
border-top: .1em solid var(--quote-border);
border-bottom: .1em solid var(--quote-border);
}
kbd {
background-color: var(--table-border-color);
border-radius: 4px;
border: solid 1px var(--theme-popup-border);
box-shadow: inset 0 -1px 0 var(--theme-hover);
display: inline-block;
font-size: var(--code-font-size);
font-family: var(--mono-font);
line-height: 10px;
padding: 4px 5px;
vertical-align: middle;
}
:not(.footnote-definition) + .footnote-definition,
.footnote-definition + :not(.footnote-definition) {
margin-top: 2em;
}
.footnote-definition {
font-size: 0.9em;
margin: 0.5em 0;
}
.footnote-definition p {
display: inline;
}
.tooltiptext {
position: absolute;
visibility: hidden;
color: #fff;
background-color: #333;
transform: translateX(-50%); /* Center by moving tooltip 50% of its width left */
left: -8px; /* Half of the width of the icon */
top: -35px;
font-size: 0.8em;
text-align: center;
border-radius: 6px;
padding: 5px 8px;
margin: 5px;
z-index: 1000;
}
.tooltipped .tooltiptext {
visibility: visible;
}
.chapter li.part-title {
color: var(--sidebar-fg);
margin: 5px 0px;
font-weight: bold;
}
.result-no-output {
font-style: italic;
}

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css/global.css Normal file
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:root {
--content-max-width: 1000px;
}

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css/katex.css Normal file
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.katex {
font-size: 1em !important;
}

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css/print.css Normal file
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#sidebar,
#menu-bar,
.nav-chapters,
.mobile-nav-chapters {
display: none;
}
#page-wrapper.page-wrapper {
transform: none;
margin-left: 0px;
overflow-y: initial;
}
#content {
max-width: none;
margin: 0;
padding: 0;
}
.page {
overflow-y: initial;
}
code {
background-color: #666666;
border-radius: 5px;
/* Force background to be printed in Chrome */
-webkit-print-color-adjust: exact;
}
pre > .buttons {
z-index: 2;
}
a, a:visited, a:active, a:hover {
color: #4183c4;
text-decoration: none;
}
h1, h2, h3, h4, h5, h6 {
page-break-inside: avoid;
page-break-after: avoid;
}
pre, code {
page-break-inside: avoid;
white-space: pre-wrap;
}
.fa {
display: none !important;
}

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/* Globals */
:root {
--sidebar-width: 300px;
--page-padding: 15px;
--content-max-width: 750px;
--menu-bar-height: 50px;
--mono-font: "Source Code Pro", Consolas, "Ubuntu Mono", Menlo, "DejaVu Sans Mono", monospace, monospace;
--code-font-size: 0.875em /* please adjust the ace font size accordingly in editor.js */
}
/* Themes */
.ayu {
--bg: hsl(210, 25%, 8%);
--fg: #c5c5c5;
--sidebar-bg: #14191f;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #5c6773;
--sidebar-active: #ffb454;
--sidebar-spacer: #2d334f;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #b7b9cc;
--links: #0096cf;
--inline-code-color: #ffb454;
--theme-popup-bg: #14191f;
--theme-popup-border: #5c6773;
--theme-hover: #191f26;
--quote-bg: hsl(226, 15%, 17%);
--quote-border: hsl(226, 15%, 22%);
--table-border-color: hsl(210, 25%, 13%);
--table-header-bg: hsl(210, 25%, 28%);
--table-alternate-bg: hsl(210, 25%, 11%);
--searchbar-border-color: #848484;
--searchbar-bg: #424242;
--searchbar-fg: #fff;
--searchbar-shadow-color: #d4c89f;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #252932;
--search-mark-bg: #e3b171;
}
.coal {
--bg: hsl(200, 7%, 8%);
--fg: #98a3ad;
--sidebar-bg: #292c2f;
--sidebar-fg: #a1adb8;
--sidebar-non-existant: #505254;
--sidebar-active: #3473ad;
--sidebar-spacer: #393939;
--scrollbar: var(--sidebar-fg);
--icons: #43484d;
--icons-hover: #b3c0cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #141617;
--theme-popup-border: #43484d;
--theme-hover: #1f2124;
--quote-bg: hsl(234, 21%, 18%);
--quote-border: hsl(234, 21%, 23%);
--table-border-color: hsl(200, 7%, 13%);
--table-header-bg: hsl(200, 7%, 28%);
--table-alternate-bg: hsl(200, 7%, 11%);
--searchbar-border-color: #aaa;
--searchbar-bg: #b7b7b7;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #98a3ad;
--searchresults-li-bg: #2b2b2f;
--search-mark-bg: #355c7d;
}
.light {
--bg: hsl(0, 0%, 100%);
--fg: hsl(0, 0%, 0%);
--sidebar-bg: #fafafa;
--sidebar-fg: hsl(0, 0%, 0%);
--sidebar-non-existant: #aaaaaa;
--sidebar-active: #1f1fff;
--sidebar-spacer: #f4f4f4;
--scrollbar: #8F8F8F;
--icons: #747474;
--icons-hover: #000000;
--links: #20609f;
--inline-code-color: #301900;
--theme-popup-bg: #fafafa;
--theme-popup-border: #cccccc;
--theme-hover: #e6e6e6;
--quote-bg: hsl(197, 37%, 96%);
--quote-border: hsl(197, 37%, 91%);
--table-border-color: hsl(0, 0%, 95%);
--table-header-bg: hsl(0, 0%, 80%);
--table-alternate-bg: hsl(0, 0%, 97%);
--searchbar-border-color: #aaa;
--searchbar-bg: #fafafa;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #e4f2fe;
--search-mark-bg: #a2cff5;
}
.navy {
--bg: hsl(226, 23%, 11%);
--fg: #bcbdd0;
--sidebar-bg: #282d3f;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #505274;
--sidebar-active: #2b79a2;
--sidebar-spacer: #2d334f;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #b7b9cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #161923;
--theme-popup-border: #737480;
--theme-hover: #282e40;
--quote-bg: hsl(226, 15%, 17%);
--quote-border: hsl(226, 15%, 22%);
--table-border-color: hsl(226, 23%, 16%);
--table-header-bg: hsl(226, 23%, 31%);
--table-alternate-bg: hsl(226, 23%, 14%);
--searchbar-border-color: #aaa;
--searchbar-bg: #aeaec6;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #5f5f71;
--searchresults-border-color: #5c5c68;
--searchresults-li-bg: #242430;
--search-mark-bg: #a2cff5;
}
.rust {
--bg: hsl(60, 9%, 87%);
--fg: #262625;
--sidebar-bg: #3b2e2a;
--sidebar-fg: #c8c9db;
--sidebar-non-existant: #505254;
--sidebar-active: #e69f67;
--sidebar-spacer: #45373a;
--scrollbar: var(--sidebar-fg);
--icons: #737480;
--icons-hover: #262625;
--links: #2b79a2;
--inline-code-color: #6e6b5e;
--theme-popup-bg: #e1e1db;
--theme-popup-border: #b38f6b;
--theme-hover: #99908a;
--quote-bg: hsl(60, 5%, 75%);
--quote-border: hsl(60, 5%, 70%);
--table-border-color: hsl(60, 9%, 82%);
--table-header-bg: #b3a497;
--table-alternate-bg: hsl(60, 9%, 84%);
--searchbar-border-color: #aaa;
--searchbar-bg: #fafafa;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #888;
--searchresults-li-bg: #dec2a2;
--search-mark-bg: #e69f67;
}
@media (prefers-color-scheme: dark) {
.light.no-js {
--bg: hsl(200, 7%, 8%);
--fg: #98a3ad;
--sidebar-bg: #292c2f;
--sidebar-fg: #a1adb8;
--sidebar-non-existant: #505254;
--sidebar-active: #3473ad;
--sidebar-spacer: #393939;
--scrollbar: var(--sidebar-fg);
--icons: #43484d;
--icons-hover: #b3c0cc;
--links: #2b79a2;
--inline-code-color: #c5c8c6;
--theme-popup-bg: #141617;
--theme-popup-border: #43484d;
--theme-hover: #1f2124;
--quote-bg: hsl(234, 21%, 18%);
--quote-border: hsl(234, 21%, 23%);
--table-border-color: hsl(200, 7%, 13%);
--table-header-bg: hsl(200, 7%, 28%);
--table-alternate-bg: hsl(200, 7%, 11%);
--searchbar-border-color: #aaa;
--searchbar-bg: #b7b7b7;
--searchbar-fg: #000;
--searchbar-shadow-color: #aaa;
--searchresults-header-fg: #666;
--searchresults-border-color: #98a3ad;
--searchresults-li-bg: #2b2b2f;
--search-mark-bg: #355c7d;
}
}

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<style>
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svg { fill: white; }
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Apache License
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Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name 'Source'. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at:
http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font creation
efforts of academic and linguistic communities, and to provide a free and
open framework in which fonts may be shared and improved in partnership
with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any reserved
names are not used by derivative works. The fonts and derivatives,
however, cannot be released under any other type of license. The
requirement for fonts to remain under this license does not apply
to any document created using the fonts or their derivatives.
DEFINITIONS
"Font Software" refers to the set of files released by the Copyright
Holder(s) under this license and clearly marked as such. This may
include source files, build scripts and documentation.
"Reserved Font Name" refers to any names specified as such after the
copyright statement(s).
"Original Version" refers to the collection of Font Software components as
distributed by the Copyright Holder(s).
"Modified Version" refers to any derivative made by adding to, deleting,
or substituting -- in part or in whole -- any of the components of the
Original Version, by changing formats or by porting the Font Software to a
new environment.
"Author" refers to any designer, engineer, programmer, technical
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PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person obtaining
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Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
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3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the corresponding
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4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
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Copyright Holder(s) and the Author(s) or with their explicit written
permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions are
not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
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INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
OTHER DEALINGS IN THE FONT SOFTWARE.

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<h1 id="introduction"><a class="header" href="#introduction">Introduction</a></h1>
<p>TLSNotary is a protocol which allows users to export data from any website in a
credible way. This way they can verify the authenticity of parts of a
TLS-encrypted web session without compromising on privacy.</p>
<p>It works by adding a third party, the Notary, to the usual TLS connection
between the User and a web server. The User forwards the encrypted TLS traffic
to the Notary which checks that it has not been tampered with and notarizes the
whole TLS session by signing a transcript of it.</p>
<p>The User can now use this transcript and disclose parts of it to another
party, which we call the Verifier. The Verifier only needs to trust the Notary
in order to accept proofs from many different users. This way, TLSNotary
can be used for a variety of purposes. For example you can use TLSNotary to
prove that</p>
<ul>
<li>you have received a money transfer using your online banking account, without
revealing your login credentials or sensitive financial information.</li>
<li>you have access to an account on a web platform.</li>
<li>a website showed some specific content on a certain date.</li>
</ul>
<p>Overall, the TLSNotary protocol can be used in any scenario where you need to
prove to a third party facts about the content of a TLS connection.</p>
<p>Some interesting aspects of TLSNotary are:</p>
<ul>
<li>The protocol is transparent to the web server, because it is not aware of the
notarization process. For the server it just looks like normal browsing.</li>
<li>Data is kept private from the Notary. The Notary only sees the ciphertext and
never has access to the plaintext.</li>
<li>No modifications to the TLS protocol are needed. You can use it without any
changes to web servers.</li>
<li>The Notary and the Verifier can be the same entity. That means if you as a
Verifier do not want to trust some Notary server, you can run one yourself.</li>
</ul>
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<h1 id="introduction"><a class="header" href="#introduction">Introduction</a></h1>
<p>TLSNotary is a protocol which allows users to export data from any website in a
credible way. This way they can verify the authenticity of parts of a
TLS-encrypted web session without compromising on privacy.</p>
<p>It works by adding a third party, the Notary, to the usual TLS connection
between the User and a web server. The User forwards the encrypted TLS traffic
to the Notary which checks that it has not been tampered with and notarizes the
whole TLS session by signing a transcript of it.</p>
<p>The User can now use this transcript and disclose parts of it to another
party, which we call the Verifier. The Verifier only needs to trust the Notary
in order to accept proofs from many different users. This way, TLSNotary
can be used for a variety of purposes. For example you can use TLSNotary to
prove that</p>
<ul>
<li>you have received a money transfer using your online banking account, without
revealing your login credentials or sensitive financial information.</li>
<li>you have access to an account on a web platform.</li>
<li>a website showed some specific content on a certain date.</li>
</ul>
<p>Overall, the TLSNotary protocol can be used in any scenario where you need to
prove to a third party facts about the content of a TLS connection.</p>
<p>Some interesting aspects of TLSNotary are:</p>
<ul>
<li>The protocol is transparent to the web server, because it is not aware of the
notarization process. For the server it just looks like normal browsing.</li>
<li>Data is kept private from the Notary. The Notary only sees the ciphertext and
never has access to the plaintext.</li>
<li>No modifications to the TLS protocol are needed. You can use it without any
changes to web servers.</li>
<li>The Notary and the Verifier can be the same entity. That means if you as a
Verifier do not want to trust some Notary server, you can run one yourself.</li>
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<h1 id="overview"><a class="header" href="#overview">Overview</a></h1>
<p>The following diagram is a high-level protocol overview introducing the main components of
TLSNotary.</p>
<p><img src="tlsnotary_overview.png" alt="TLSNotary Overview" /></p>
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<h1 id="finite-field-arithmetic"><a class="header" href="#finite-field-arithmetic">Finite-Field Arithmetic</a></h1>
<p>Some protocols used in TLSNotary need to convert two-party sharings of products
or sums of some field elements into each other. For this purpose we use share
conversion protocols which use oblivious transfer (OT) as a sub-protocol. Here
we want to have a closer look at the security guarantees these protocols offer.</p>
<h3 id="adding-covert-security"><a class="header" href="#adding-covert-security">Adding covert security</a></h3>
<p>Our goal is to add covert security to our share conversion protocols. This
means that we want an honest party to be able to detect a malicious adversary,
who is then able to abort the protocol. Our main concern is that the adversary
might be able to leak private inputs of the honest party without being noticed.
For this reason we require that the adversary cannot do anything which would
give him a better chance than guessing the private input at random, which is<br />
guessing <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> bits with a probability of <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></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:0.8491em;"><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"></span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span></span> for not being detected.</p>
<p>In the following we want to have a closer look at how the sender and receiver can
deviate from the protocol.</p>
<h4 id="malicious-receiver"><a class="header" href="#malicious-receiver">Malicious receiver</a></h4>
<p>Note that in our protocol a malicious receiver cannot forge the protocol output,
since he does not send anything to the sender during protocol execution. Even
when this protocol is embedded into an outer protocol, where at some point the
receiver has to open his output or a computation involving it, then all he can
do is to open an output <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9463em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span></span></span></span> with <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9463em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>, which is just equivalent to
changing his input from <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</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:0.7519em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span></span></span></span>. </p>
<h4 id="malicious-sender"><a class="header" href="#malicious-sender">Malicious sender</a></h4>
<p>In the case of a malicious sender the following things can happen:</p>
<ol>
<li>The sender can impose an arbitrary field element <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7519em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span></span></span></span> as input onto the
receiver without him noticing. To do this he simply sends <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1078em;vertical-align:-0.2587em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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 mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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 mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> in
every OT, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> is i-th bit of <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7519em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span></span></span></span>.</li>
<li>The sender can execute a selective-failure attack, which allows him to learn
any predicate about the receiver's input. For each OT round <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span>, the sender
alters one of the OT values to be <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1078em;vertical-align:-0.2587em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4413em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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 mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></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:1.1078em;vertical-align:-0.2587em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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 mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></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:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span>, where <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6891em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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="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:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</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:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mclose">}</span></span></span></span>. This will cause that in the end the equation
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4445em;"></span><span class="mord mathnormal">a</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:0.6944em;"></span><span class="mord mathnormal">b</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:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">x</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:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span> no longer holds but only if the forged OT value has
actually been picked by the receiver.</li>
<li>The sender does not use a random number generator with a seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> to sample
the masks <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span>, instead he simply chooses them at will.</li>
</ol>
<h3 id="m2a-protocol-review"><a class="header" href="#m2a-protocol-review">M2A Protocol Review</a></h3>
<p>Without loss of generality let us recall the Multiplication-To-Addition (M2A)
protocol, but our observations also apply to the Addition-To-Multiplication
(A2M) protocol, which is very similar. We start with a short review of the M2A
protocol.</p>
<p>Let there be a sender with some field element <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> and some receiver with another
field element <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>. After protocol execution the sender ends up with <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span></span></span></span> and the
receiver ends up with <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>, so that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4445em;"></span><span class="mord mathnormal">a</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:0.6944em;"></span><span class="mord mathnormal">b</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:0.6667em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">x</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:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>.</p>
<ul>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</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:0.6833em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span></span></span></span></li>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> - rng seed</li>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">m</span></span></span></span> - bit-length of elements in <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span></span></span></span></li>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> - bit-length of rng seed</li>
</ul>
<h4 id="ot-sender"><a class="header" href="#ot-sender">OT Sender</a></h4>
<p>with input <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</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:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</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:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mclose"><span class="mclose">}</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6644em;"><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 mathnormal mtight">n</span></span></span></span></span></span></span></span></span></span></span></p>
<ol>
<li>Sample some random masks: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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="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:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">0</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:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">m</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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="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:0.6833em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span></span></span></span></li>
<li>For every <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span> compute:
<ul>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0728em;vertical-align:-0.2587em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></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:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span></li>
<li><span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0728em;vertical-align:-0.2587em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></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:0.4445em;"></span><span class="mord mathnormal">a</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:0.908em;vertical-align:-0.0833em;"></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:0.8247em;"><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 mathnormal mtight">i</span></span></span></span></span></span></span></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:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span></li>
</ul>
</li>
<li>Compute new share: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</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:1em;vertical-align:-0.25em;"></span><span class="mord"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</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></span></span></li>
<li>Send <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">i</span></span></span></span> OTs to receiver: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0728em;vertical-align:-0.2587em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4413em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><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">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2587em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></li>
</ol>
<h4 id="ot-receiver"><a class="header" href="#ot-receiver">OT Receiver</a></h4>
<p>with input <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">b</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:0.6833em;"></span><span class="mord mathcal" style="margin-right:0.09931em;">F</span></span></span></span></p>
<ol>
<li>Set <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><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">i</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="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:1.2079em;vertical-align:-0.2769em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.931em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1449em;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"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span></span> (from OT)</li>
<li>Compute new share: <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</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:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><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">i</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></span></span></li>
</ol>
<h3 id="replay-protocol"><a class="header" href="#replay-protocol">Replay protocol</a></h3>
<p>In order to mitigate the mentioned protocol deviations in the case of a malicious
sender we will introduce a replay protocol.</p>
<p>In this section we will use capital letters for values sent in the replay
protocol, which in the case of an honest sender are equal to their lowercase
counterparts.</p>
<p>The idea for the replay protocol is that at some point after the conversion
protocol, the sender has to reveal the rng seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> and his input <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span> to the
receiver. In order to do this, he will send <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span> to the receiver after
the conversion protocol has been executed. If the sender is honest then of
course <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</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:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</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:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span>. The receiver can then check if the value he picked
during protocol execution does match what he can now reconstruct from <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span>, i.e. that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2079em;vertical-align:-0.2769em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.931em;"><span style="top:-2.4231em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1449em;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"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></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:1.2079em;vertical-align:-0.2769em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.931em;"><span style="top:-2.4231em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span><span style="top:-3.1449em;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"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2769em;"><span></span></span></span></span></span></span></span></span></span>.</p>
<p><strong>Using this replay protocol the sender at some point reveals all his secrets
because he sends his rng seed and protocol input to the receiver. This means
that we can only use covertly secure share conversion with replay as a
sub-protocol if it is acceptable for the outer protocol, that the input to
share-conversion becomes public at some later point.</strong></p>
<p>Now in practice we often want to execute several rounds of share-conversion, as we
need to convert several field elements. Because of this we let the sender use
the same rng seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> to seed his rng once and then he uses this rng instance
for all protocol rounds. This means we have <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span></span></span></span> protocol executions <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5945em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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="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:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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="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:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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="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:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><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">n</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></span></span>, and all masks <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;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 mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span> produced from this rng seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span>.
So the sender will write his seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and all the <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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></span></span> to some tape, which in
the end is sent to the receiver. As a security precaution we also let the sender
commit to his rng seed before the first protocol execution. In detail:</p>
<h5 id="sender"><a class="header" href="#sender">Sender</a></h5>
<ol>
<li>Sender has some inputs <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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></span></span> and picks some rng seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span>.</li>
<li>Sender commits to his rng seed and sends the commitment to the receiver.</li>
<li>Sender sends all his OTs for <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span> protocol executions.</li>
<li>Sender sends tape which contains the rng seed <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and all the <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</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></span></span>.</li>
</ol>
<h5 id="receiver"><a class="header" href="#receiver">Receiver</a></h5>
<ol>
<li>Receiver checks that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> is indeed the committed rng seed.</li>
<li>For every protocol execution <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span></span></span></span> the receiver checks that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4412em;vertical-align:-0.413em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0282em;"><span style="top:-2.4231em;margin-left:-0.1389em;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 mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">i</span></span></span></span><span style="top:-3.2421em;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"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2819em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.413em;"><span></span></span></span></span></span></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:1.4412em;vertical-align:-0.413em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0282em;"><span style="top:-2.4231em;margin-left:0em;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 mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">i</span></span></span></span><span style="top:-3.2421em;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"><span class="mord mathnormal mtight">b</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">i</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2819em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.413em;"><span></span></span></span></span></span></span></span></span></span>.</li>
</ol>
<p>Having a look at the ways a malicious sender could cheat from earlier, we
notice:</p>
<ol>
<li>The sender can no longer impose an arbitrary field element <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7519em;"></span><span class="mord"><span class="mord mathnormal">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7519em;"><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"></span></span></span></span></span></span></span></span></span></span></span></span> onto the
receiver, because the receiver would notice that <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span> during the replay.</li>
<li>The sender can still carry out a selective-failure attack, but this is
equivalent to guessing <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span></span> bits of <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span> at random with a probability of
<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></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:0.8491em;"><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"></span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span></span></span></span></span> for being undetected.</li>
<li>The sender is now forced to use an rng seed to produce the masks, because
during the replay, these masks are reproduced from <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span></span> and indirectly checked
via <span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</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:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span>.</li>
</ol>
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<h1 id="commitment"><a class="header" href="#commitment">Commitment</a></h1>
<p>At the end of the TLSNotary protocol, the User has the authenticated AES ciphertext which can be thought of as a commitment to the plaintext. This form of commitment is not amenable to use cases when the User wants to make part of the plaintext public while keeping another part private. Naively, the User's option is to prove the decryption of the ciphertext in zero-knowledge which is computationally expensive.</p>
<p>We describe two less computationally heavy approaches for converting the AES ciphertext commitments. </p>
<p>The first approach is useful for commitments to the data which the User intends to make public. It is based on decrypting the ciphertext with Garbled Circuits and producing a hash commitment to the wire labels.</p>
<p>The second approach is useful for commitments to the private data which the User later intends to prove statements about in zero-knowledge. This approach produces a Poseidon hash over the private data. </p>
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<h1 id="notarization-phase"><a class="header" href="#notarization-phase">Notarization Phase</a></h1>
<p>During the Notarization Phase the <code>Requester</code>, otherwise referred to as the <code>User</code>, and the <code>Notary</code> work together to generate an authenticated <code>Transcript</code> of a TLS session with a <code>Server</code>.</p>
<p>Listed below are some key points regarding this process:</p>
<ul>
<li>The identity of the <code>Server</code> is not revealed to the <code>Notary</code>, but the <code>Requester</code> is capable of proving the <code>Server</code> identity to a <code>Verifier</code> later.</li>
<li>The <code>Notary</code> only ever sees the <em>encrypted</em> application data of the TLS session.</li>
<li>The protocol guarantees that the <code>Requester</code> is not solely capable of constructing requests, nor can they forge responses from the <code>Server</code>.</li>
</ul>
<h2 id="requester"><a class="header" href="#requester">Requester</a></h2>
<p>The <code>Requester</code> is the party which runs the TLS connection with the <code>Server</code>. The <code>Requester</code> constructs application payloads, eg. HTTP requests, and coordinates with the <code>Notary</code> to encrypt them with the TLS session keys prior to sending them. Subsequently, the <code>Requester</code> works with the <code>Notary</code> to decrypt responses from the <code>Server</code>. The plaintext of the application data is only ever revealed to the <code>Requester</code>.</p>
<h2 id="notary"><a class="header" href="#notary">Notary</a></h2>
<p>The <code>Notary</code> is the party of which the authenticity of the <code>Transcript</code> relies on. During the session the <code>Notary</code> withholds its' shares of the TLS keys and participates in a series of secure 2-party computation protocols with the <code>Requester</code> to operate the TLS connection.</p>
<h2 id="server"><a class="header" href="#server">Server</a></h2>
<p>The <code>Server</code> can be any server which supports TLS. The TLSNotary protocol is entirely transparent to the <code>Server</code>, thus it can not be censored nor does it have to support any additional functionality.</p>
<img src="https://raw.githubusercontent.com/tlsnotary/docs-assets/main/diagrams/tls12-multiround.png">
<h2 id="transcript"><a class="header" href="#transcript">Transcript</a></h2>
<p>The primary artifact generated from this phase is called the <code>Transcript</code>. It contains session meta-data, handshake data, and commitments to all the requests and responses. Typically the <code>Transcript</code> is signed by the <code>Notary</code>, however that is not necessary in the case where the <code>Notary</code> will also act as the <code>Verifier</code> in the selective disclosure phase.</p>
<blockquote>
<p>Note that the server ephemeral key does not reveal the identity of the server to the <code>Notary</code>.</p>
</blockquote>
<img src="https://raw.githubusercontent.com/tlsnotary/docs-assets/main/diagrams/transcript.png">
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<h3 id="overview"><a class="header" href="#overview">Overview</a></h3>
<p>The pre-master secret (<code>PMS</code>) must be put through a <code>PRF</code> (pseudo-random function) defined by the TLS spec in order to compute the symmetric TLS keys and also to compute the <code>verify_data</code> for the <code>Client_Finished</code> and the <code>Server_Finished</code> messages.</p>
<p>Below we describe how the parties (<code>N</code> stands for <code>Notary</code> and <code>U</code> stands for <code>User</code>) who have their shares of <code>PMS</code> can use 2PC to compute the <code>PRF</code>. </p>
<blockquote>
<p>Since the TLSNotary protocol already uses Garbled Circuits and Oblivious Transfer which give 128-bit computational security for the parties against each other, we argue that it is acceptable to perform some PRF computations outside of 2PC as long as it is done with at least 128-bit security.
Performing some PRF computations outside of 2PC allows to save on computation and bandwidth.</p>
</blockquote>
<blockquote>
<p>Note that the User's TLS connection retains the standard TLS security guarantees against any third-party adversary. </p>
</blockquote>
<p>To elaborate, recall how <a href="https://en.wikipedia.org/wiki/HMAC">HMAC</a> is computed (assuming |k| &lt;= block size):</p>
<pre><code>HMAC(k, m) = H((k ⊕ opad) | H((k ⊕ ipad) | m))
</code></pre>
<p>Notice that both H(k ⊕ opad) and H(k ⊕ ipad) can be computed separately prior to finalization. In this
document we name these units as such:</p>
<ul>
<li><code>outer hash state</code>: H(k ⊕ opad)</li>
<li><code>inner hash state</code>: H(k ⊕ ipad)</li>
<li><code>inner hash</code>: H((k ⊕ ipad) | m)</li>
</ul>
<p>In TLS, the master secret is computed like so:</p>
<pre><code class="language-python">seed = &quot;master secret&quot; | client_random | server_random
a0 = seed
a1 = HMAC(pms, a0)
a2 = HMAC(pms, a1)
p1 = HMAC(pms, a1 | seed)
p2 = HMAC(pms, a2 | seed)
ms = (p1 | p2)[:48]
</code></pre>
<p>Notice that in each step the key, in this case <code>PMS</code>, is constant. Thus both the <code>outer</code> and <code>inner hash state</code> can be reused for each step.</p>
<p>Below is the description of the all the steps to compute the <code>PRF</code> both inside and outside the 2PC circuit.</p>
<h2 id="computing-the-master-secret"><a class="header" href="#computing-the-master-secret">Computing the master secret</a></h2>
<h3 id="inside-the-circuit"><a class="header" href="#inside-the-circuit">Inside the circuit</a></h3>
<ol>
<li>To evaluate the circuit, the parties input their <code>PMS</code> shares. The circuit outputs:</li>
</ol>
<ul>
<li>H(PMS ⊕ opad) called <code>PMS</code> <code>outer hash state</code> to <code>N</code> and</li>
<li>H(PMS ⊕ ipad) called <code>PMS</code> <code>inner hash state</code> to <code>U</code></li>
</ul>
<h3 id="outside-the-circuit"><a class="header" href="#outside-the-circuit">Outside the circuit</a></h3>
<ol start="2">
<li>
<p><code>U</code> computes H((PMS ⊕ ipad) || a0) called <code>inner hash</code> of <code>a1</code> and passes it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>a1</code> and passes it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes the <code>inner hash</code> of <code>a2</code> and passes it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>a2</code> and passes it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes the <code>inner hash</code> of p2 and passes it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>p2</code> and passes it to <code>U</code>.
&gt;Note that now both parties know <code>p2</code> which is the last 16 bytes of the master secret. They still don't know the other 32 bytes of the master secret, which ensures adequate security.</p>
</li>
<li>
<p><code>U</code> computes the <code>inner hash</code> of <code>p1</code>.</p>
</li>
</ol>
<h3 id="inside-the-circuit-1"><a class="header" href="#inside-the-circuit-1">Inside the circuit</a></h3>
<ol start="9">
<li>To evaluate the circuit, <code>N</code> inputs the <code>PMS outer hash state</code> and <code>U</code> inputs <code>p2</code> and the <code>inner hash</code> of <code>p1</code>. The circuit computes the master secret (<code>MS</code>).</li>
</ol>
<h2 id="computing-the-expanded-keys"><a class="header" href="#computing-the-expanded-keys">Computing the expanded keys</a></h2>
<p>The parties proceed to compute the <code>expanded keys</code>. The corresponding python code is:</p>
<pre><code class="language-python">seed = str.encode(&quot;key expansion&quot;) + server_random + client_random
a0 = seed
a1 = hmac.new(ms , a0, hashlib.sha256).digest()
a2 = hmac.new(ms , a1, hashlib.sha256).digest()
p1 = hmac.new(ms, a1+seed, hashlib.sha256).digest()
p2 = hmac.new(ms, a2+seed, hashlib.sha256).digest()
ek = (p1 + p2)[:40]
client_write_key = ek[:16]
server_write_key = ek[16:32]
client_write_IV = ek[32:36]
server_write_IV = ek[36:40]
</code></pre>
<h3 id="inside-the-circuit-2"><a class="header" href="#inside-the-circuit-2">Inside the circuit</a></h3>
<ol start="10">
<li>Having computed <code>MS</code>, the circuit outputs:</li>
</ol>
<ul>
<li>H(MS ⊕ opad) called the <code>MS outer hash state</code> to <code>N</code> and</li>
<li>H(MS ⊕ ipad) called the <code>MS inner hash state</code> to <code>U</code></li>
</ul>
<h3 id="outside-the-circuit-1"><a class="header" href="#outside-the-circuit-1">Outside the circuit</a></h3>
<ol start="11">
<li>
<p><code>U</code> computes the <code>inner hash</code> of <code>a1</code> and sends it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>a1</code> and sends it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes the <code>inner hash</code> of <code>a2</code> and sends it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>a2</code> and sends it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes the <code>inner hash state</code> of <code>p1</code> and the <code>inner hash state</code> of <code>p2</code>.</p>
</li>
</ol>
<h3 id="inside-the-circuit-3"><a class="header" href="#inside-the-circuit-3">Inside the circuit</a></h3>
<ol start="16">
<li>To evaluate the circuit, <code>N</code> inputs <code>MS outer hash state</code> (from Step 10) and <code>U</code> inputs <code>inner hash state</code> of <code>p1</code> and <code>inner hash state</code> of <code>p2</code>. The circuit computes <code>p1</code> and <code>p2</code>. The circuit outputs xor shares of the <code>expanded keys</code> to each party.</li>
</ol>
<h2 id="computing-the-encrypted-client_finished"><a class="header" href="#computing-the-encrypted-client_finished">Computing the encrypted Client_Finished</a></h2>
<h3 id="inside-the-circuit-4"><a class="header" href="#inside-the-circuit-4">Inside the circuit</a></h3>
<ol start="17">
<li>To evaluate the circuit, the parties input their shares of the <code>expanded keys</code>. The circuit outputs data needed to encrypt and authenticate the <code>Client_Finished</code> (<code>CF</code>) message.</li>
</ol>
<h3 id="outside-the-circuit-2"><a class="header" href="#outside-the-circuit-2">Outside the circuit</a></h3>
<p>The parties proceed to compute <code>verify_data</code> for the <code>CF</code> message. The corresponding python code is:</p>
<pre><code class="language-python"># (handshake_hash) is a sha256 hash of all TLS handshake message up to this point
seed = str.encode('client finished') + handshake_hash
a0 = seed
a1 = hmac.new(ms, a0, hashlib.sha256).digest()
p1 = hmac.new(ms, a1+seed, hashlib.sha256).digest()
verify_data = p1[:12]
</code></pre>
<ol start="18">
<li>
<p><code>U</code> computes <code>inner hash</code> of <code>a1</code> and sends it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> (who has <code>MS</code> <code>outer hash state</code> from Step 10) computes <code>a1</code> and sends it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes <code>inner hash</code> of <code>p1</code> and sends it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> computes <code>p1</code> and gets <code>verify_data</code> and sends it to <code>U</code>.</p>
</li>
</ol>
<blockquote>
<p>Note that it is safe for <code>N</code> to know <code>verify_data</code> for <code>CF</code>. </p>
</blockquote>
<p>Using the data from Step 17, <code>U</code> proceeds to encrypt and authenticate <code>CF</code> and sends it to the webserver.</p>
<h2 id="verifying-the-server_finished"><a class="header" href="#verifying-the-server_finished">Verifying the Server_Finished</a></h2>
<p>Upon <code>U</code>'s receiving the encrypted <code>Server_Finished</code> (<code>SF</code>) from the webserver, the parties proceed to compute <code>verify_data</code> for <code>SF</code>, to enable <code>U</code> to check that the received <code>SF</code> is correct. The corresponding python code is:</p>
<pre><code class="language-python"># (handshake_hash) is a sha256 hash of all TLS handshake message up to this point
seed = str.encode('server finished') + handshake_hash
a0 = seed
a1 = hmac.new(ms, a0, hashlib.sha256).digest()
p1 = hmac.new(ms, a1+seed, hashlib.sha256).digest()
verify_data = p1[:12]
</code></pre>
<h3 id="outside-the-circuit-3"><a class="header" href="#outside-the-circuit-3">Outside the circuit</a></h3>
<ol start="22">
<li>
<p><code>U</code> computes <code>inner hash</code> of <code>a1</code> and sends it to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> (who has <code>MS</code> <code>outer hash state</code> from Step 10) computes <code>a1</code> and sends it to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> computes <code>inner hash</code> of <code>p1</code>.</p>
</li>
</ol>
<h3 id="inside-the-circuit-5"><a class="header" href="#inside-the-circuit-5">Inside the circuit</a></h3>
<ol start="25">
<li>To evaluate the circuit, <code>N</code> inputs <code>MS</code> <code>outer hash state</code> (from Step 10) and <code>U</code> inputs <code>inner hash</code> of <code>p1</code>. The circuit outputs <code>verify_data</code> for <code>SF</code> to <code>U</code>.</li>
</ol>
<p>The parties proceed to decrypt and authenticate the <code>SF</code> in 2PC. <code>U</code> checks that <code>verify_data</code> from <code>SF</code> matches <code>verify_data</code> from Step 25.</p>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../../intro.html">Introduction</a></li><li class="chapter-item expanded affix "><a href="../../protocol/index.html">Protocol</a></li><li class="chapter-item expanded "><a href="../../overview.html"><strong aria-hidden="true">1.</strong> Overview</a></li><li class="chapter-item expanded "><a href="../../protocol/notarization/index.html"><strong aria-hidden="true">2.</strong> Notarization</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">2.1.</strong> TLS Handshake</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../../protocol/notarization/key_exchange.html"><strong aria-hidden="true">2.1.1.</strong> Key Exchange</a></li><li class="chapter-item expanded "><a href="../../protocol/notarization/prf.html"><strong aria-hidden="true">2.1.2.</strong> Symmetric key derivation</a></li></ol></li><li class="chapter-item expanded "><a href="../../protocol/notarization/encryption.html"><strong aria-hidden="true">2.2.</strong> Encryption</a></li><li class="chapter-item expanded "><a href="../../protocol/notarization/commitment.html"><strong aria-hidden="true">2.3.</strong> Commitment</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../../protocol/notarization/public_data_commitment.html" class="active"><strong aria-hidden="true">2.3.1.</strong> Commitment to public data</a></li></ol></li></ol></li><li class="chapter-item expanded "><div><strong aria-hidden="true">3.</strong> Selective Disclosure</div></li><li class="chapter-item expanded "><a href="../../protocol/2pc/garbled_circuits.html"><strong aria-hidden="true">4.</strong> Secure 2-Party Computation</a></li><li><ol class="section"><li class="chapter-item expanded "><div><strong aria-hidden="true">4.1.</strong> Garbled Circuits</div></li><li><ol class="section"><li class="chapter-item expanded "><a href="../../protocol/2pc/deap.html"><strong aria-hidden="true">4.1.1.</strong> Dual Execution with Asymmetric Privacy</a></li></ol></li><li class="chapter-item expanded "><div><strong aria-hidden="true">4.2.</strong> Oblivious Transfer</div></li><li class="chapter-item expanded "><div><strong aria-hidden="true">4.3.</strong> Paillier</div></li><li class="chapter-item expanded "><a href="../../protocol/2pc/mac.html"><strong aria-hidden="true">4.4.</strong> MAC</a></li><li class="chapter-item expanded "><a href="../../protocol/2pc/ff-arithmetic.html"><strong aria-hidden="true">4.5.</strong> Finite-Field Arithmetic</a></li></ol></li></ol>
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<h1 id="commitment-to-public-data"><a class="header" href="#commitment-to-public-data">Commitment to public data</a></h1>
<p>We describe an interactive protocol between the User <code>U</code> and the Notary <code>N</code>, whereby <code>U</code> can convert the authenticated AES ciphertext into a hash commitment to Garbled Circuits wire labels.</p>
<h2 id="creating-the-new-commitment"><a class="header" href="#creating-the-new-commitment">Creating the new commitment</a></h2>
<ol start="0">
<li>
<p>At the end of the TLSNotary session, both <code>U</code> and <code>N</code> know the authenticated AES <code>ciphertext</code>. </p>
</li>
<li>
<p><code>N</code> reveals his TLS session key shares to <code>U</code>.</p>
</li>
<li>
<p><code>U</code> decrypts the <code>ciphertext</code> in the clear and learns the plaintext <code>p</code>.</p>
</li>
<li>
<p><code>N</code> picks a <code>seed</code> and uses it as the source of randomness to generate (in the semi-honest model) a privacy-free garbled circuit whose functionality is to accept the plaintext input, encrypt it, and output the ciphertext. </p>
</li>
<li>
<p>With <code>p</code> as her circuit input, <code>U</code> receives input wire labels <code>IWLs</code> via Oblivious Transfer and then evaluates the circuit on those <code>IWLs</code>. The result of the evaluation are output wire labels <code>OWLs</code> which <code>U</code> does not know the decoding for.</p>
</li>
<li>
<p><code>U</code> sends two commitments: <code>commitment to IWLs</code> and <code>commitment to OWLs</code> to <code>N</code>.</p>
</li>
<li>
<p><code>N</code> reveals the <code>seed</code> and <code>U</code> checks that the circuit (including its <code>IWLs</code> and <code>OWLs</code>) was generated correctly and, if successful, reveals her <code>OWLs</code>.</p>
</li>
<li>
<p><code>N</code> verifies <code>commitment to OWLs</code> and then checks that decoded <code>OWLs</code> match the <code>ciphertext</code> (from Step 0) and, if successful, signs (<code>seed</code> + <code>commitment to IWLs</code>). </p>
</li>
</ol>
<blockquote>
<p>Now, (<code>seed</code> + <code>commitment to IWLs</code>) become <code>U</code>'s new commitment to <code>p</code>.</p>
</blockquote>
<h2 id="verifying-the-commitment"><a class="header" href="#verifying-the-commitment">Verifying the commitment</a></h2>
<p>Verifier performs the following steps:</p>
<ol>
<li>
<p>Receives the following from <code>U</code>: plaintext <code>p</code>, <code>signature</code> for (<code>seed</code> + <code>commitment to IWLs</code>), <code>seed</code>, <code>commitment to IWLs</code>.</p>
</li>
<li>
<p>(using a trusted <code>N</code>s pubkey) Verifies the <code>signature</code>.</p>
</li>
<li>
<p>Re-generates the <code>IWLs</code> from the <code>seed</code>.</p>
</li>
<li>
<p>Picks only those <code>IWLs</code> which correspond to <code>p</code> and checks that the commitment to those <code>IWLs</code> matches <code>commitment to IWLs</code>.</p>
</li>
<li>
<p>Accepts <code>p</code> as authentic.</p>
</li>
</ol>
<h2 id="dynamic-commitment-using-a-merkle-tree"><a class="header" href="#dynamic-commitment-using-a-merkle-tree">Dynamic commitment using a Merkle tree</a></h2>
<p>In situations where <code>U</code> does not know in advance which subset of the public data she will be revealing later to the Verifier, <code>U</code> can commit to the Merkle tree of all her input wire labels (from Step 4 above).
Later, <code>U</code> can reveal only those Merkle leaves which she wants to make public to the Verifier. </p>
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<script>
window.playground_copyable = true;
</script>
<script src="../../elasticlunr.min.js"></script>
<script src="../../mark.min.js"></script>
<script src="../../searcher.js"></script>
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searcher.js Normal file
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"use strict";
window.search = window.search || {};
(function search(search) {
// Search functionality
//
// You can use !hasFocus() to prevent keyhandling in your key
// event handlers while the user is typing their search.
if (!Mark || !elasticlunr) {
return;
}
//IE 11 Compatibility from https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/String/startsWith
if (!String.prototype.startsWith) {
String.prototype.startsWith = function(search, pos) {
return this.substr(!pos || pos < 0 ? 0 : +pos, search.length) === search;
};
}
var search_wrap = document.getElementById('search-wrapper'),
searchbar = document.getElementById('searchbar'),
searchbar_outer = document.getElementById('searchbar-outer'),
searchresults = document.getElementById('searchresults'),
searchresults_outer = document.getElementById('searchresults-outer'),
searchresults_header = document.getElementById('searchresults-header'),
searchicon = document.getElementById('search-toggle'),
content = document.getElementById('content'),
searchindex = null,
doc_urls = [],
results_options = {
teaser_word_count: 30,
limit_results: 30,
},
search_options = {
bool: "AND",
expand: true,
fields: {
title: {boost: 1},
body: {boost: 1},
breadcrumbs: {boost: 0}
}
},
mark_exclude = [],
marker = new Mark(content),
current_searchterm = "",
URL_SEARCH_PARAM = 'search',
URL_MARK_PARAM = 'highlight',
teaser_count = 0,
SEARCH_HOTKEY_KEYCODE = 83,
ESCAPE_KEYCODE = 27,
DOWN_KEYCODE = 40,
UP_KEYCODE = 38,
SELECT_KEYCODE = 13;
function hasFocus() {
return searchbar === document.activeElement;
}
function removeChildren(elem) {
while (elem.firstChild) {
elem.removeChild(elem.firstChild);
}
}
// Helper to parse a url into its building blocks.
function parseURL(url) {
var a = document.createElement('a');
a.href = url;
return {
source: url,
protocol: a.protocol.replace(':',''),
host: a.hostname,
port: a.port,
params: (function(){
var ret = {};
var seg = a.search.replace(/^\?/,'').split('&');
var len = seg.length, i = 0, s;
for (;i<len;i++) {
if (!seg[i]) { continue; }
s = seg[i].split('=');
ret[s[0]] = s[1];
}
return ret;
})(),
file: (a.pathname.match(/\/([^/?#]+)$/i) || [,''])[1],
hash: a.hash.replace('#',''),
path: a.pathname.replace(/^([^/])/,'/$1')
};
}
// Helper to recreate a url string from its building blocks.
function renderURL(urlobject) {
var url = urlobject.protocol + "://" + urlobject.host;
if (urlobject.port != "") {
url += ":" + urlobject.port;
}
url += urlobject.path;
var joiner = "?";
for(var prop in urlobject.params) {
if(urlobject.params.hasOwnProperty(prop)) {
url += joiner + prop + "=" + urlobject.params[prop];
joiner = "&";
}
}
if (urlobject.hash != "") {
url += "#" + urlobject.hash;
}
return url;
}
// Helper to escape html special chars for displaying the teasers
var escapeHTML = (function() {
var MAP = {
'&': '&amp;',
'<': '&lt;',
'>': '&gt;',
'"': '&#34;',
"'": '&#39;'
};
var repl = function(c) { return MAP[c]; };
return function(s) {
return s.replace(/[&<>'"]/g, repl);
};
})();
function formatSearchMetric(count, searchterm) {
if (count == 1) {
return count + " search result for '" + searchterm + "':";
} else if (count == 0) {
return "No search results for '" + searchterm + "'.";
} else {
return count + " search results for '" + searchterm + "':";
}
}
function formatSearchResult(result, searchterms) {
var teaser = makeTeaser(escapeHTML(result.doc.body), searchterms);
teaser_count++;
// The ?URL_MARK_PARAM= parameter belongs inbetween the page and the #heading-anchor
var url = doc_urls[result.ref].split("#");
if (url.length == 1) { // no anchor found
url.push("");
}
// encodeURIComponent escapes all chars that could allow an XSS except
// for '. Due to that we also manually replace ' with its url-encoded
// representation (%27).
var searchterms = encodeURIComponent(searchterms.join(" ")).replace(/\'/g, "%27");
return '<a href="' + path_to_root + url[0] + '?' + URL_MARK_PARAM + '=' + searchterms + '#' + url[1]
+ '" aria-details="teaser_' + teaser_count + '">' + result.doc.breadcrumbs + '</a>'
+ '<span class="teaser" id="teaser_' + teaser_count + '" aria-label="Search Result Teaser">'
+ teaser + '</span>';
}
function makeTeaser(body, searchterms) {
// The strategy is as follows:
// First, assign a value to each word in the document:
// Words that correspond to search terms (stemmer aware): 40
// Normal words: 2
// First word in a sentence: 8
// Then use a sliding window with a constant number of words and count the
// sum of the values of the words within the window. Then use the window that got the
// maximum sum. If there are multiple maximas, then get the last one.
// Enclose the terms in <em>.
var stemmed_searchterms = searchterms.map(function(w) {
return elasticlunr.stemmer(w.toLowerCase());
});
var searchterm_weight = 40;
var weighted = []; // contains elements of ["word", weight, index_in_document]
// split in sentences, then words
var sentences = body.toLowerCase().split('. ');
var index = 0;
var value = 0;
var searchterm_found = false;
for (var sentenceindex in sentences) {
var words = sentences[sentenceindex].split(' ');
value = 8;
for (var wordindex in words) {
var word = words[wordindex];
if (word.length > 0) {
for (var searchtermindex in stemmed_searchterms) {
if (elasticlunr.stemmer(word).startsWith(stemmed_searchterms[searchtermindex])) {
value = searchterm_weight;
searchterm_found = true;
}
};
weighted.push([word, value, index]);
value = 2;
}
index += word.length;
index += 1; // ' ' or '.' if last word in sentence
};
index += 1; // because we split at a two-char boundary '. '
};
if (weighted.length == 0) {
return body;
}
var window_weight = [];
var window_size = Math.min(weighted.length, results_options.teaser_word_count);
var cur_sum = 0;
for (var wordindex = 0; wordindex < window_size; wordindex++) {
cur_sum += weighted[wordindex][1];
};
window_weight.push(cur_sum);
for (var wordindex = 0; wordindex < weighted.length - window_size; wordindex++) {
cur_sum -= weighted[wordindex][1];
cur_sum += weighted[wordindex + window_size][1];
window_weight.push(cur_sum);
};
if (searchterm_found) {
var max_sum = 0;
var max_sum_window_index = 0;
// backwards
for (var i = window_weight.length - 1; i >= 0; i--) {
if (window_weight[i] > max_sum) {
max_sum = window_weight[i];
max_sum_window_index = i;
}
};
} else {
max_sum_window_index = 0;
}
// add <em/> around searchterms
var teaser_split = [];
var index = weighted[max_sum_window_index][2];
for (var i = max_sum_window_index; i < max_sum_window_index+window_size; i++) {
var word = weighted[i];
if (index < word[2]) {
// missing text from index to start of `word`
teaser_split.push(body.substring(index, word[2]));
index = word[2];
}
if (word[1] == searchterm_weight) {
teaser_split.push("<em>")
}
index = word[2] + word[0].length;
teaser_split.push(body.substring(word[2], index));
if (word[1] == searchterm_weight) {
teaser_split.push("</em>")
}
};
return teaser_split.join('');
}
function init(config) {
results_options = config.results_options;
search_options = config.search_options;
searchbar_outer = config.searchbar_outer;
doc_urls = config.doc_urls;
searchindex = elasticlunr.Index.load(config.index);
// Set up events
searchicon.addEventListener('click', function(e) { searchIconClickHandler(); }, false);
searchbar.addEventListener('keyup', function(e) { searchbarKeyUpHandler(); }, false);
document.addEventListener('keydown', function(e) { globalKeyHandler(e); }, false);
// If the user uses the browser buttons, do the same as if a reload happened
window.onpopstate = function(e) { doSearchOrMarkFromUrl(); };
// Suppress "submit" events so the page doesn't reload when the user presses Enter
document.addEventListener('submit', function(e) { e.preventDefault(); }, false);
// If reloaded, do the search or mark again, depending on the current url parameters
doSearchOrMarkFromUrl();
}
function unfocusSearchbar() {
// hacky, but just focusing a div only works once
var tmp = document.createElement('input');
tmp.setAttribute('style', 'position: absolute; opacity: 0;');
searchicon.appendChild(tmp);
tmp.focus();
tmp.remove();
}
// On reload or browser history backwards/forwards events, parse the url and do search or mark
function doSearchOrMarkFromUrl() {
// Check current URL for search request
var url = parseURL(window.location.href);
if (url.params.hasOwnProperty(URL_SEARCH_PARAM)
&& url.params[URL_SEARCH_PARAM] != "") {
showSearch(true);
searchbar.value = decodeURIComponent(
(url.params[URL_SEARCH_PARAM]+'').replace(/\+/g, '%20'));
searchbarKeyUpHandler(); // -> doSearch()
} else {
showSearch(false);
}
if (url.params.hasOwnProperty(URL_MARK_PARAM)) {
var words = decodeURIComponent(url.params[URL_MARK_PARAM]).split(' ');
marker.mark(words, {
exclude: mark_exclude
});
var markers = document.querySelectorAll("mark");
function hide() {
for (var i = 0; i < markers.length; i++) {
markers[i].classList.add("fade-out");
window.setTimeout(function(e) { marker.unmark(); }, 300);
}
}
for (var i = 0; i < markers.length; i++) {
markers[i].addEventListener('click', hide);
}
}
}
// Eventhandler for keyevents on `document`
function globalKeyHandler(e) {
if (e.altKey || e.ctrlKey || e.metaKey || e.shiftKey || e.target.type === 'textarea' || e.target.type === 'text') { return; }
if (e.keyCode === ESCAPE_KEYCODE) {
e.preventDefault();
searchbar.classList.remove("active");
setSearchUrlParameters("",
(searchbar.value.trim() !== "") ? "push" : "replace");
if (hasFocus()) {
unfocusSearchbar();
}
showSearch(false);
marker.unmark();
} else if (!hasFocus() && e.keyCode === SEARCH_HOTKEY_KEYCODE) {
e.preventDefault();
showSearch(true);
window.scrollTo(0, 0);
searchbar.select();
} else if (hasFocus() && e.keyCode === DOWN_KEYCODE) {
e.preventDefault();
unfocusSearchbar();
searchresults.firstElementChild.classList.add("focus");
} else if (!hasFocus() && (e.keyCode === DOWN_KEYCODE
|| e.keyCode === UP_KEYCODE
|| e.keyCode === SELECT_KEYCODE)) {
// not `:focus` because browser does annoying scrolling
var focused = searchresults.querySelector("li.focus");
if (!focused) return;
e.preventDefault();
if (e.keyCode === DOWN_KEYCODE) {
var next = focused.nextElementSibling;
if (next) {
focused.classList.remove("focus");
next.classList.add("focus");
}
} else if (e.keyCode === UP_KEYCODE) {
focused.classList.remove("focus");
var prev = focused.previousElementSibling;
if (prev) {
prev.classList.add("focus");
} else {
searchbar.select();
}
} else { // SELECT_KEYCODE
window.location.assign(focused.querySelector('a'));
}
}
}
function showSearch(yes) {
if (yes) {
search_wrap.classList.remove('hidden');
searchicon.setAttribute('aria-expanded', 'true');
} else {
search_wrap.classList.add('hidden');
searchicon.setAttribute('aria-expanded', 'false');
var results = searchresults.children;
for (var i = 0; i < results.length; i++) {
results[i].classList.remove("focus");
}
}
}
function showResults(yes) {
if (yes) {
searchresults_outer.classList.remove('hidden');
} else {
searchresults_outer.classList.add('hidden');
}
}
// Eventhandler for search icon
function searchIconClickHandler() {
if (search_wrap.classList.contains('hidden')) {
showSearch(true);
window.scrollTo(0, 0);
searchbar.select();
} else {
showSearch(false);
}
}
// Eventhandler for keyevents while the searchbar is focused
function searchbarKeyUpHandler() {
var searchterm = searchbar.value.trim();
if (searchterm != "") {
searchbar.classList.add("active");
doSearch(searchterm);
} else {
searchbar.classList.remove("active");
showResults(false);
removeChildren(searchresults);
}
setSearchUrlParameters(searchterm, "push_if_new_search_else_replace");
// Remove marks
marker.unmark();
}
// Update current url with ?URL_SEARCH_PARAM= parameter, remove ?URL_MARK_PARAM and #heading-anchor .
// `action` can be one of "push", "replace", "push_if_new_search_else_replace"
// and replaces or pushes a new browser history item.
// "push_if_new_search_else_replace" pushes if there is no `?URL_SEARCH_PARAM=abc` yet.
function setSearchUrlParameters(searchterm, action) {
var url = parseURL(window.location.href);
var first_search = ! url.params.hasOwnProperty(URL_SEARCH_PARAM);
if (searchterm != "" || action == "push_if_new_search_else_replace") {
url.params[URL_SEARCH_PARAM] = searchterm;
delete url.params[URL_MARK_PARAM];
url.hash = "";
} else {
delete url.params[URL_MARK_PARAM];
delete url.params[URL_SEARCH_PARAM];
}
// A new search will also add a new history item, so the user can go back
// to the page prior to searching. A updated search term will only replace
// the url.
if (action == "push" || (action == "push_if_new_search_else_replace" && first_search) ) {
history.pushState({}, document.title, renderURL(url));
} else if (action == "replace" || (action == "push_if_new_search_else_replace" && !first_search) ) {
history.replaceState({}, document.title, renderURL(url));
}
}
function doSearch(searchterm) {
// Don't search the same twice
if (current_searchterm == searchterm) { return; }
else { current_searchterm = searchterm; }
if (searchindex == null) { return; }
// Do the actual search
var results = searchindex.search(searchterm, search_options);
var resultcount = Math.min(results.length, results_options.limit_results);
// Display search metrics
searchresults_header.innerText = formatSearchMetric(resultcount, searchterm);
// Clear and insert results
var searchterms = searchterm.split(' ');
removeChildren(searchresults);
for(var i = 0; i < resultcount ; i++){
var resultElem = document.createElement('li');
resultElem.innerHTML = formatSearchResult(results[i], searchterms);
searchresults.appendChild(resultElem);
}
// Display results
showResults(true);
}
fetch(path_to_root + 'searchindex.json')
.then(response => response.json())
.then(json => init(json))
.catch(error => { // Try to load searchindex.js if fetch failed
var script = document.createElement('script');
script.src = path_to_root + 'searchindex.js';
script.onload = () => init(window.search);
document.head.appendChild(script);
});
// Exported functions
search.hasFocus = hasFocus;
})(window.search);

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:root {
--content-max-width: 1000px;
}

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.katex {
font-size: 1em !important;
}

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/* Tomorrow Night Theme */
/* https://github.com/jmblog/color-themes-for-highlightjs */
/* Original theme - https://github.com/chriskempson/tomorrow-theme */
/* https://github.com/jmblog/color-themes-for-highlightjs */
/* Tomorrow Comment */
.hljs-comment {
color: #969896;
}
/* Tomorrow Red */
.hljs-variable,
.hljs-attribute,
.hljs-tag,
.hljs-regexp,
.ruby .hljs-constant,
.xml .hljs-tag .hljs-title,
.xml .hljs-pi,
.xml .hljs-doctype,
.html .hljs-doctype,
.css .hljs-id,
.css .hljs-class,
.css .hljs-pseudo {
color: #cc6666;
}
/* Tomorrow Orange */
.hljs-number,
.hljs-preprocessor,
.hljs-pragma,
.hljs-built_in,
.hljs-literal,
.hljs-params,
.hljs-constant {
color: #de935f;
}
/* Tomorrow Yellow */
.ruby .hljs-class .hljs-title,
.css .hljs-rule .hljs-attribute {
color: #f0c674;
}
/* Tomorrow Green */
.hljs-string,
.hljs-value,
.hljs-inheritance,
.hljs-header,
.hljs-name,
.ruby .hljs-symbol,
.xml .hljs-cdata {
color: #b5bd68;
}
/* Tomorrow Aqua */
.hljs-title,
.css .hljs-hexcolor {
color: #8abeb7;
}
/* Tomorrow Blue */
.hljs-function,
.python .hljs-decorator,
.python .hljs-title,
.ruby .hljs-function .hljs-title,
.ruby .hljs-title .hljs-keyword,
.perl .hljs-sub,
.javascript .hljs-title,
.coffeescript .hljs-title {
color: #81a2be;
}
/* Tomorrow Purple */
.hljs-keyword,
.javascript .hljs-function {
color: #b294bb;
}
.hljs {
display: block;
overflow-x: auto;
background: #1d1f21;
color: #c5c8c6;
}
.coffeescript .javascript,
.javascript .xml,
.tex .hljs-formula,
.xml .javascript,
.xml .vbscript,
.xml .css,
.xml .hljs-cdata {
opacity: 0.5;
}
.hljs-addition {
color: #718c00;
}
.hljs-deletion {
color: #c82829;
}