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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta name="generator" content="HTML Tidy for Linux (vers 25 March 2009), see www.w3.org">
<title>Chapter 2. Tutorial - PBC</title>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<div class="toc">
<ul>
<li><a href="">Crypto Notes</a></li>
<li>
<span class="chapter"><a href="">1. Elliptic Curves in Cryptography</a></span>
<ul>
<li><span class="section"><a id="ec-af" href="javascript:void(0);">Addition Formulae</a></span></li>
<li><span class="section"><a id="ec-ecdlp" href="javascript:void(0);">ECDLP</a></span></li>
</ul>
</li>
</ul>
</div>
<div class="content">
<div id="myDiv" class="chapter" title="Applied crypto notes">
<div class="titlepage">
<div>
<div>
<h2 class="title"><a name="_tutorial"></a>A few notes on applied crypto</h2>
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</div>
<p>In this page i will keep track of crypto notes that i have selected thoughout stydying various sources of applied crypto.
These notes corresponds to practical elliptic curves that are being widely used in protocols such as SSL,TLS,hardware platforms and does not include '$exotic$' curves. The following is a simplification of an elliptic curve equation:
$$Y^2=X^3+ax+b$$
The fields that are being used for elliptic curve cryptography are:
<ul>
<li><b>Characteristic p: $\mathbb{F}_p$</li>
<li>Characteristic 2: $\mathbb{F}_{2^n}$</li>
<li></b>$\mathbb{F}_{p^n}$, for small $n$ (used for pairing based cryptography)</li>
</ul>
The number of solution for an elliptic curve is given by:
$E(K)\{points (x,y) \in K^2\}\cup \{\mathcal{O}_E\}$
</p>
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