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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
<head>
<title>Zenroom LUA</title>
<link rel="stylesheet" href="" type="text/css" />
</head>
<body>
<div id="container">
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<div id="product_logo"></div>
<div id="product_name"><big><b></b></big></div>
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<!-- Menu -->
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<br/>
<h1>Zenroom</h1>
<ul>
<li><a href="../index.html">Index</a></li>
</ul>
<h2>Contents</h2>
<ul>
<li><a href="#Functions">Functions</a></li>
<li><a href="#Class_ecp">Class ecp </a></li>
</ul>
<h2>Modules</h2>
<ul class="nowrap">
<li><a href="../modules/OCTET.html">OCTET</a></li>
<li><a href="../modules/HASH.html">HASH</a></li>
<li><a href="../modules/ECDH.html">ECDH</a></li>
<li><strong>ECP</strong></li>
<li><a href="../modules/String.html">String</a></li>
<li><a href="../modules/Table.html">Table</a></li>
<li><a href="../modules/INSPECT.html">INSPECT</a></li>
<li><a href="../modules/ZEN.html">ZEN</a></li>
<li><a href="../modules/BIG.html">BIG</a></li>
</ul>
<h2>Examples</h2>
<ul class="nowrap">
<li><a href="../examples/keygen.lua.html">keygen.lua</a></li>
<li><a href="../examples/crypt-to-multi.lua.html">crypt-to-multi.lua</a></li>
</ul>
</div>
<div id="content">
<h1>Module <code>ECP</code></h1>
<p>
<h1>Elliptic Curve Point Arithmetic (ECP)</h1>
<p> Base arithmetical operations on elliptic curve point coordinates.</p>
</p>
<p> ECP arithmetic operations are provided to implement existing and
new encryption schemes: they are elliptic curve cryptographic
primitives and work the same across different curves.</p>
<p> It is possible to create ECP points instances using the <a href="../modules/ECP.html#new">new</a>
method. The values of each coordinate can be imported using <a href="../modules/BIG.html#">BIG</a>
methods <code>BIG.hex()</code> or <code>BIG.base64()</code>.</p>
<p> Once ECP numbers are created this way, the arithmetic operations
of addition, subtraction and multiplication can be executed
normally using overloaded operators (+ - *).</p>
<h3>Info:</h3>
<ul>
<li><strong>Copyright</strong>: Dyne.org foundation 2017-2019</li>
<li><strong>License</strong>: AGPLv3</li>
<li><strong>Author</strong>: Denis "Jaromil" Roio</li>
</ul>
<h2><a href="#Functions">Functions</a></h2>
<table class="function_list">
<tr>
<td class="name" nowrap><a href="#new">new (coordinates)</a></td>
<td class="summary">Create a new ECP point from an <a href="../modules/OCTET.html#">OCTET</a> argument containing its coordinates.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#generator">generator ()</a></td>
<td class="summary">Returns the generator of the curve: an ECP point that is multiplied by any <a href="../modules/BIG.html#">BIG</a> number to obtain a correspondent point on the curve.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#infinity">infinity ()</a></td>
<td class="summary">Returns a new ECP infinity point that is definitely not on the curve.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#order">order ()</a></td>
<td class="summary">Gives the order of the curve, a <a href="../modules/BIG.html#">BIG</a> number contained in an octet.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#mapit">mapit (OCTET)</a></td>
<td class="summary">Map an <a href="../modules/OCTET.html#">OCTET</a> of exactly 64 bytes length to a point on the curve: the OCTET should be the output of an hash function.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#validate">validate (OCTET)</a></td>
<td class="summary">Verify that an <a href="../modules/OCTET.html#">OCTET</a> really corresponds to an ECP point on the curve.</td>
</tr>
</table>
<h2><a href="#Class_ecp">Class ecp </a></h2>
<table class="function_list">
<tr>
<td class="name" nowrap><a href="#ecp:affine">ecp:affine ()</a></td>
<td class="summary">Make an existing ECP point affine with its curve</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:isinf">ecp:isinf ()</a></td>
<td class="summary">Returns true if an ECP coordinate points to infinity (out of the curve) and false otherwise.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:add">ecp:add (first, second)</a></td>
<td class="summary">Add two ECP points to each other (commutative and associative operation).</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:sub">ecp:sub (first, second)</a></td>
<td class="summary">Subtract an ECP point from another (commutative and associative operation).</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:negative">ecp:negative ()</a></td>
<td class="summary">Transforms an ECP point into its equivalent negative point on the elliptic curve.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:double">ecp:double ()</a></td>
<td class="summary">Transforms an ECP pointo into the double of its value, multiplying it by two.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:mul">ecp:mul (ecp, number)</a></td>
<td class="summary">Multiply an ECP point by a <a href="../modules/BIG.html#">BIG</a> number.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:eq">ecp:eq (first, second)</a></td>
<td class="summary">Compares two ECP objects and returns true if they indicate the same point on the curve (they are equal) or false otherwise.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:octet">ecp:octet ()</a></td>
<td class="summary">Returns an octet containing the coordinate of an ECP point on the curve.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:x">ecp:x ()</a></td>
<td class="summary">Gives the X coordinate of the ECP point as a single <a href="../modules/BIG.html#">BIG</a> number.</td>
</tr>
<tr>
<td class="name" nowrap><a href="#ecp:y">ecp:y ()</a></td>
<td class="summary">Gives the Y coordinate of the ECP point as a single <a href="../modules/BIG.html#">BIG</a> number.</td>
</tr>
</table>
<br/>
<br/>
<h2 class="section-header "><a name="Functions"></a>Functions</h2>
<dl class="function">
<dt>
<a name = "new"></a>
<strong>new (coordinates)</strong>
</dt>
<dd>
Create a new ECP point from an <a href="../modules/OCTET.html#">OCTET</a> argument containing its coordinates. (octet)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">coordinates</span>
of the point on the elliptic curve
</li>
</ul>
<h3>Returns:</h3>
<ol>
a new ECP point on the curve
</ol>
<h3>See also:</h3>
<ul>
<a href="../modules/ECP.html#ecp:octet">ECP:octet</a>
</ul>
</dd>
<dt>
<a name = "generator"></a>
<strong>generator ()</strong>
</dt>
<dd>
Returns the generator of the curve: an ECP point that is multiplied by any <a href="../modules/BIG.html#">BIG</a> number to obtain a correspondent point on the curve. ()
<h3>Returns:</h3>
<ol>
ECP point of the curve's generator.
</ol>
</dd>
<dt>
<a name = "infinity"></a>
<strong>infinity ()</strong>
</dt>
<dd>
Returns a new ECP infinity point that is definitely not on the curve. ()
<h3>Returns:</h3>
<ol>
ECP pointing to infinity (out of the curve).
</ol>
</dd>
<dt>
<a name = "order"></a>
<strong>order ()</strong>
</dt>
<dd>
Gives the order of the curve, a <a href="../modules/BIG.html#">BIG</a> number contained in an octet. ()
<h3>Returns:</h3>
<ol>
a <a href="../modules/BIG.html#">BIG</a> number containing the curve's order
</ol>
</dd>
<dt>
<a name = "mapit"></a>
<strong>mapit (OCTET)</strong>
</dt>
<dd>
Map an <a href="../modules/OCTET.html#">OCTET</a> of exactly 64 bytes length to a point on the curve: the OCTET should be the output of an hash function. (OCTET)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">OCTET</span>
resulting from an hash function
</li>
</ul>
<h3>Returns:</h3>
<ol>
an ECP that is univocally linked to the input OCTET
</ol>
</dd>
<dt>
<a name = "validate"></a>
<strong>validate (OCTET)</strong>
</dt>
<dd>
Verify that an <a href="../modules/OCTET.html#">OCTET</a> really corresponds to an ECP point on the curve. (OCTET)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">OCTET</span>
point to be validated
</li>
</ul>
<h3>Returns:</h3>
<ol>
bool value: true if valid, false if not valid
</ol>
</dd>
</dl>
<h2 class="section-header has-description"><a name="Class_ecp"></a>Class ecp </h2>
<div class="section-description">
Instance Methods
</div>
<dl class="function">
<dt>
<a name = "ecp:affine"></a>
<strong>ecp:affine ()</strong>
</dt>
<dd>
Make an existing ECP point affine with its curve ()
<h3>Returns:</h3>
<ol>
ECP point made affine
</ol>
</dd>
<dt>
<a name = "ecp:isinf"></a>
<strong>ecp:isinf ()</strong>
</dt>
<dd>
Returns true if an ECP coordinate points to infinity (out of the curve) and false otherwise. ()
<h3>Returns:</h3>
<ol>
false if point is on curve, true if its off curve into infinity.
</ol>
</dd>
<dt>
<a name = "ecp:add"></a>
<strong>ecp:add (first, second)</strong>
</dt>
<dd>
Add two ECP points to each other (commutative and associative operation). Can be made using the overloaded operator <code>+</code> between two ECP objects just like the would be numbers.
(first,second)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">first</span>
number to be summed
</li>
<li><span class="parameter">second</span>
number to be summed
</li>
</ul>
<h3>Returns:</h3>
<ol>
sum resulting from the addition
</ol>
</dd>
<dt>
<a name = "ecp:sub"></a>
<strong>ecp:sub (first, second)</strong>
</dt>
<dd>
Subtract an ECP point from another (commutative and associative operation). Can be made using the overloaded operator <code>-</code> between two ECP objects just like the would be numbers.
(first,second)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">first</span>
number from which the second should be subtracted
</li>
<li><span class="parameter">second</span>
number to use in the subtraction
</li>
</ul>
<h3>Returns:</h3>
<ol>
new ECP point resulting from the subtraction
</ol>
</dd>
<dt>
<a name = "ecp:negative"></a>
<strong>ecp:negative ()</strong>
</dt>
<dd>
Transforms an ECP point into its equivalent negative point on the elliptic curve. ()
</dd>
<dt>
<a name = "ecp:double"></a>
<strong>ecp:double ()</strong>
</dt>
<dd>
Transforms an ECP pointo into the double of its value, multiplying it by two. This works faster than multiplying it an arbitrary number of times.
()
</dd>
<dt>
<a name = "ecp:mul"></a>
<strong>ecp:mul (ecp, number)</strong>
</dt>
<dd>
Multiply an ECP point by a <a href="../modules/BIG.html#">BIG</a> number. Can be made using the overloaded operator <code>*</code>
(ecp,num)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">ecp</span>
point on the elliptic curve to be multiplied
</li>
<li><span class="parameter">number</span>
indicating how many times it should be multiplied
</li>
</ul>
<h3>Returns:</h3>
<ol>
new ecp point resulting from the multiplication
</ol>
</dd>
<dt>
<a name = "ecp:eq"></a>
<strong>ecp:eq (first, second)</strong>
</dt>
<dd>
Compares two ECP objects and returns true if they indicate the same point on the curve (they are equal) or false otherwise. It can also be executed by using the <code>==</code> overloaded operator.
(first,second)
<h3>Parameters:</h3>
<ul>
<li><span class="parameter">first</span>
ecp point to be compared
</li>
<li><span class="parameter">second</span>
ecp point to be compared
</li>
</ul>
<h3>Returns:</h3>
<ol>
bool value: true if equal, false if not equal
</ol>
</dd>
<dt>
<a name = "ecp:octet"></a>
<strong>ecp:octet ()</strong>
</dt>
<dd>
Returns an octet containing the coordinate of an ECP point on the curve. It can be used to export the value of an ECP point into a string, using <a href="../modules/OCTET.html#octet:hex">OCTET:hex</a> or <a href="../modules/OCTET.html#octet:base64">OCTET:base64</a> encapsulation. It can be decoded back to an ECP point using <a href="../modules/ECP.html#new">ECP:new</a>.
()
<h3>Returns:</h3>
<ol>
the ECP point as an OCTET sequence
</ol>
</dd>
<dt>
<a name = "ecp:x"></a>
<strong>ecp:x ()</strong>
</dt>
<dd>
Gives the X coordinate of the ECP point as a single <a href="../modules/BIG.html#">BIG</a> number. ()
<h3>Returns:</h3>
<ol>
a BIG number indicating the X coordinate of the point on curve.
</ol>
</dd>
<dt>
<a name = "ecp:y"></a>
<strong>ecp:y ()</strong>
</dt>
<dd>
Gives the Y coordinate of the ECP point as a single <a href="../modules/BIG.html#">BIG</a> number. ()
<h3>Returns:</h3>
<ol>
a BIG number indicating the Y coordinate of the point on curve.
</ol>
</dd>
</dl>
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