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curryrasul
2023-02-06 14:15:26 +00:00
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window.onunload = function () { };
// Global variable, shared between modules
function playground_text(playground) {
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();
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return code_block.textContent;
} else {
return code_block.innerText;
}
@@ -166,7 +168,6 @@ function playground_text(playground) {
.filter(function (node) {return node.classList.contains("editable"); })
.forEach(function (block) { block.classList.remove('language-rust'); });
Array
code_nodes
.filter(function (node) {return !node.classList.contains("editable"); })
.forEach(function (block) { hljs.highlightBlock(block); });
@@ -600,7 +601,7 @@ function playground_text(playground) {
text: function (trigger) {
hideTooltip(trigger);
let playground = trigger.closest("pre");
return playground_text(playground);
return playground_text(playground, false);
}
});

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<title>Circuits - Rate-Limiting Nullifier</title>
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document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
@@ -340,9 +348,11 @@ component main { public [x, epoch, rln_identifier] } = RLN(15);
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@@ -352,6 +362,7 @@ component main { public [x, epoch, rln_identifier] } = RLN(15);
<a rel="prev" href="protocol_spec.html" class="nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
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@@ -359,12 +370,18 @@ component main { public [x, epoch, rln_identifier] } = RLN(15);
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@@ -372,5 +389,7 @@ component main { public [x, epoch, rln_identifier] } = RLN(15);
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@@ -84,7 +90,7 @@
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<i id="print-button" class="fa fa-print"></i>
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@@ -124,6 +131,7 @@
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<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
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@@ -168,12 +179,18 @@
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@@ -84,7 +90,7 @@
<div id="page-wrapper" class="page-wrapper">
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<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar" class="menu-bar sticky bordered">
<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">
@@ -111,6 +117,7 @@
<a href="print.html" title="Print this book" aria-label="Print this book">
<i id="print-button" class="fa fa-print"></i>
</a>
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@@ -124,6 +131,7 @@
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<!-- Apply ARIA attributes after the sidebar and the sidebar toggle button are added to the DOM -->
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document.getElementById('sidebar-toggle').setAttribute('aria-expanded', sidebar === 'visible');
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</script>
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<script src="searcher.js"></script>
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21
overview.html
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<link rel="stylesheet" href="css/print.css" media="print">
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@@ -84,7 +90,7 @@
<div id="page-wrapper" class="page-wrapper">
<div class="page">
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar" class="menu-bar sticky bordered">
<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">
@@ -111,6 +117,7 @@
<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>
@@ -124,6 +131,7 @@
</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');
@@ -151,9 +159,11 @@
<a rel="prev" href="rln.html" class="mobile-nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
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</a>
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<div style="clear: both"></div>
</nav>
</div>
@@ -163,6 +173,7 @@
<a rel="prev" href="rln.html" class="nav-chapters previous" title="Previous chapter" aria-label="Previous chapter" aria-keyshortcuts="Left">
<i class="fa fa-angle-left"></i>
</a>
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<i class="fa fa-angle-right"></i>
</a>
@@ -170,12 +181,18 @@
</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>
@@ -183,5 +200,7 @@
<!-- Custom JS scripts -->
<script src="mermaid.min.js"></script>
<script src="mermaid-init.js"></script>
</body>
</html>

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print.html
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@@ -5,7 +5,10 @@
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<title>Rate-Limiting Nullifier</title>
<meta name="robots" content="noindex" />
<!-- Custom HTML head -->
<meta name="description" content="">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="theme-color" content="#ffffff" />
@@ -16,15 +19,18 @@
<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">
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<script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head>
@@ -85,7 +91,7 @@
<div id="page-wrapper" class="page-wrapper">
<div class="page">
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar-hover-placeholder"></div>
<div id="menu-bar" class="menu-bar sticky bordered">
<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">
@@ -112,6 +118,7 @@
<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>
@@ -125,6 +132,7 @@
</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');
@@ -459,7 +467,7 @@ component main { public [x, epoch, rln_identifier] } = RLN(15);
<img src="./images/line.png" width="500" height="400">
</p>
<p>We also can &quot;restore&quot; the function analytically. For that let's denote: \[f(x) = y_1 * \frac{x - x_2}{x_1 - x_2} + y_2 * \frac{x - x_1}{x_2 - x_1}\]
where \(x_1 = 5, x_2 = 10, y_1 = 5, y_2 = 32\). If we make substitution we got: \[f(x) = 3x + 2 \]
where \(x_1 = 1, x_2 = 10, y_1 = 5, y_2 = 32\). If we make substitution we got: \[f(x) = 3x + 2 \]
which is the same polynomial.</p>
<p>The same technique can be made with every polynomial. Main thing to remember is that we need \(n + 1\) points to interpolate \(n\)-degree polynomial.</p>
<p>Now that we know how interpolation works, we can learn how it is used in SSS.</p>
@@ -537,22 +545,31 @@ So, the shares are: \((5, 55), (8, 70), (16, 110)\)</li>
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<p>We also can &quot;restore&quot; the function analytically. For that let's denote: \[f(x) = y_1 * \frac{x - x_2}{x_1 - x_2} + y_2 * \frac{x - x_1}{x_2 - x_1}\]
where \(x_1 = 5, x_2 = 10, y_1 = 5, y_2 = 32\). If we make substitution we got: \[f(x) = 3x + 2 \]
where \(x_1 = 1, x_2 = 10, y_1 = 5, y_2 = 32\). If we make substitution we got: \[f(x) = 3x + 2 \]
which is the same polynomial.</p>
<p>The same technique can be made with every polynomial. Main thing to remember is that we need \(n + 1\) points to interpolate \(n\)-degree polynomial.</p>
<p>Now that we know how interpolation works, we can learn how it is used in SSS.</p>
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