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arnaucube
2021-08-25 22:40:13 +02:00
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@@ -4,16 +4,16 @@
<head>
<meta name="description" content="In the following notes I've tried to summarize the KZG Commitment scheme with the concepts that helped me to follow the reasoning." />
<meta charset="utf-8">
<title> Notes on KZG polynomial commitments - arnaucube</title>
<meta name="title" content=" Notes on KZG polynomial commitments - arnaucube">
<title> Notes on KZG polynomial commitments - arnaucube - blog</title>
<meta name="title" content=" Notes on KZG polynomial commitments - arnaucube - blog">
<meta name="description" content="In the following notes I've tried to summarize the KZG Commitment scheme with the concepts that helped me to follow the reasoning.">
<meta property="og:title" content=" Notes on KZG polynomial commitments - arnaucube" />
<meta property="og:title" content=" Notes on KZG polynomial commitments - arnaucube - blog" />
<meta property="og:description" content="In the following notes I've tried to summarize the KZG Commitment scheme with the concepts that helped me to follow the reasoning." />
<meta property="og:url" content="https://arnaucube.com/blog/kzg-commitments.html" />
<meta property="og:type" content="article" />
<meta property="og:image" content="https://arnaucube.com/blog/" />
<meta name="twitter:title" content=" Notes on KZG polynomial commitments - arnaucube">
<meta name="twitter:title" content=" Notes on KZG polynomial commitments - arnaucube - blog">
<meta name="twitter:description" content="In the following notes I've tried to summarize the KZG Commitment scheme with the concepts that helped me to follow the reasoning.">
<meta name="twitter:image" content="https://arnaucube.com/blog/">
<meta name="twitter:card" content="summary_large_image">
@@ -40,7 +40,14 @@
style="height:50px;font-size:130%;">
<div class="container">
<a href="/blog" style="color:#000;">Blog index</a>
<a href="/" style="color:#000;float:right;">arnaucube.com</a>
<div style="float:right;">
<a href="/" style="color:#000;display:inline-block;">arnaucube.com</a>
<div class="onoffswitch" style="margin:10px;display:inline-block;" title="change theme">
<input onclick="switchTheme()" type="checkbox" name="onoffswitch" class="onoffswitch-checkbox"
id="themeSwitcher">
<label class="onoffswitch-label" for="themeSwitcher"></label>
</div>
</div>
</div>
<img style="height:5px; width:100%; margin-top:8px;" src="img/gradient-line.jpg" />
</nav>
@@ -136,7 +143,7 @@ $$</p>
<h3>Conclusions</h3>
<p>The content covered in this notes is just a quick overview, but allows us to see the potential of the scheme. One next iteration from what we&rsquo;ve seen is the approach to do batch proofs, which allows us to evaluate at multiple points with a single evaluation proof. This scheme can be used as a <em>vector commitment</em>, using a polynomial where the $p(i) = x_i$ for all values of $x_i$ of the vector, which can be obtained from the $x_i$ values and computing the <a href="https://en.wikipedia.org/wiki/Lagrange_polynomial">Lagrange interpolation</a>. This is quite useful combined with the mentioned batch proofs.</p>
<p>The content covered in this notes is just a quick overview, but allows us to see the potential of the scheme. One next iteration from what we&rsquo;ve seen is the approach to do batch proofs, which allows us to evaluate at multiple points with a single evaluation proof. This scheme can be used as a <em>vector commitment</em>, using a polynomial where the $p(i) = x_i$ for all values of $x_i$ of the vector, which can be obtained from the $x_i$ values and computing the <a href="https://en.wikipedia.org/wiki/Lagrange_polynomial">Lagrange interpolation</a>. This is quite useful combined with the mentioned batch proofs. The <em>batch proofs</em> logic can be found at the <a href="https://arnaucube.com/blog/kzg-batch-proof.html">blog/kzg-batch-proof</a> notes (kind of the continuation of the current notes).</p>
<p>As a final note, in order to try to digest the notes, I&rsquo;ve did a <em>toy implementation</em> of this scheme at <a href="https://github.com/arnaucube/kzg-commitments-study">https://github.com/arnaucube/kzg-commitments-study</a>. It&rsquo;s quite simple, but contains the logic overviewed in this notes.</p>
@@ -183,6 +190,33 @@ $$</p>
throwOnError : true
});
});
///
let theme = localStorage.getItem("theme");
if ((theme === "light-theme")||(theme==null)) {
theme = "light-theme";
document.getElementById("themeSwitcher").checked = false;
} else if (theme === "dark-theme") {
theme = "dark-theme";
document.getElementById("themeSwitcher").checked = true;
}
document.body.className = theme;
localStorage.setItem("theme", theme);
function switchTheme() {
theme = localStorage.getItem("theme");
if (theme === "light-theme") {
theme = "dark-theme";
document.getElementById("themeSwitcher").checked = true;
} else {
theme = "light-theme";
document.getElementById("themeSwitcher").checked = false;
}
document.body.className = theme;
localStorage.setItem("theme", theme);
console.log(theme);
}
</script>
<script src="https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js"></script>