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      <a href='/blog/protogalaxy.html'><div class="row postThumb">
        <h3>Notes on ProtoGalaxy</h3>

<p>The idea of these notes is to provide some extra intuition and explainations on ProtoGalaxy&rsquo;s paper.
ProtoGalaxy is a <em>folding scheme</em> which iterates on ideas from ProtoStar paper.</p>

<p><em>2023-08-20</em></p>

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</a><a href='https://raw.githubusercontent.com/arnaucube/math/master/notes_hypernova.pdf'><div class="row postThumb">
        <h3>Notes on HyperNova (pdf)</h3>

<p>This document contains notes on HyperNova and CCS.</p>

<p><em>2023-05-16</em></p>

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</a><a href='/blog/ipa.html'><div class="row postThumb">
        <h3>IPA polynomial commitment by hand</h3>

<p>This post overviews the IPA polynomial commitment described in the Halo paper, first by providing an overview on the protocol, then by doing a step-by-step example with small values, following the style done in the &ldquo;Plonk by hand series&rdquo; from Joshua Fitzgerald, and later by providing a Sage implementation of the protocol.</p>

<p><em>2023-04-06</em></p>

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</a><a href='https://raw.githubusercontent.com/arnaucube/math/master/notes_fri.pdf'><div class="row postThumb">
        <h3>Notes on FRI (pdf)</h3>

<p>This document contains notes on FRI low degree testing and the trick to convert it to a polynomial commitment scheme.</p>

<p><em>2023-02-26</em></p>

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</a><a href='/blog/powersoftau.html'><div class="row postThumb">
        <h3>Implementing the powers of tau contributor</h3>

<p>In the following notes we go over the ideas behind the <em>Powers of Tau</em> ceremony, how participants contribute and how the contributions are verified (logic &amp; code). We focus on the Ethereum&rsquo;s upcoming KZG-Ceremony.</p>

<p><em>2023-01-02</em></p>

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</a><a href='/blog/ringsig.html'><div class="row postThumb">
        <h3>bLSAG ring signatures overview</h3>

<p>Notes on bLSAG: Back&rsquo;s Linkable Spontaneous Anonymous Group signatures</p>

<p><em>2022-07-20</em></p>

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</a><a href='/blog/shamir-secret-sharing.html'><div class="row postThumb">
        <h3>Lagrange Polynomial Interpolation and Shamir secret sharing</h3>

<p>Overview of Langrange Polynomial interpolation and Shamir&rsquo;s secret sharing.</p>

<p><em>2021-10-10</em></p>

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</a><a href='/blog/kzg-batch-proof.html'><div class="row postThumb">
        <h3>Batch proof in KZG Commitments</h3>

<p>The benefit of <em>batch proof</em> is that allows us to proof multiple points while the proof size remains constant to one <span class="math inline">\(\mathbb{G}_1\)</span> point.</p>

<p><em>2021-08-14</em></p>

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</a><a href='/blog/kzg-commitments.html'><div class="row postThumb">
        <h3>Notes on KZG polynomial commitments</h3>

<p>In the following notes I&rsquo;ve tried to summarize the KZG Commitments scheme with the concepts that helped me to follow the reasoning.</p>

<p><em>2021-08-05</em></p>

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</a><a href='/blog/blind-signatures-ec.html'><div class="row postThumb">
        <h3>Notes on blind signatures over elliptic curves</h3>

<p>In this notes, we will cover the scheme proposed at <em>&ldquo;New Blind Signature Schemes Based on the (Elliptic Curve) Discrete Logarithm Problem&rdquo;</em> paper by Hamid Mala &amp; Nafiseh Nezhadansari.</p>

<p><em>2021-07-30</em></p>

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</a><a href='/blog/coffeeminer-hacking-wifi-cryptocurrency-miner.html'><div class="row postThumb">
        <h3>CoffeeMiner: Hacking WiFi to inject cryptocurrency miner to HTML requests</h3>

<p>The goal of this post, is to explain how can be done the attack of MITM (Machine-In-The-Middle) to inject some javascript in the html pages, to force all the machines connected to a WiFi network to be mining a cryptocurrency for the attacker.</p>

<p><em>2018-01-04</em></p>

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</a><a href='/blog/flock-botnet.html'><div class="row postThumb">
        <h3>Auto generated tweets from Markov chains</h3>

<p>Developing a twitter botnet with autonomous bots replying tweets with text generated based on probabilities in Markov chains</p>

<p><em>2017-12-29</em></p>

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</a><a href='/blog/blogo.html'><div class="row postThumb">
        <h3>Static blog template engine implementation in Go</h3>

<p>How has this blog been made? In this post we will see how to develop a minimalistic static blog template engine with Go.</p>

<p><em>2017-12-26</em></p>

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