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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="EccPointsAdd"></a>
EccPointsAdd
</h2>

Returns the sum of two points on an elliptic curve over a finite
field.

<p><p>

<h3>
Syntax:
</h3>
<pre>sum := EccPointsAdd(K,ec,P1,P2);</pre>

<p>

<table>
<tr>
<td>finite field </td>
<td><pre>  K  </pre></td>
<td></td>
</tr>
<tr>
<td>list </td>
<td><pre>  E  </pre></td>
<td></td>
</tr>
<tr>
<td>list </td>
<td><pre>  P1  </pre></td>
<td></td>
</tr>
<tr>
<td>list </td>
<td><pre>  P2  </pre></td>
<td></td>
</tr>
<tr>
<td>list </td>
<td><pre>  sum  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#EccIntPointMult">EccIntPointMult</a>, <a href="kashref.html#EccPointIsOnCurve">EccPointIsOnCurve</a>, <a href="kashref.html#EccEncryptEccDecrypt">EccEncryptEccDecrypt</a>, <a href="kashref.html#FF">FF</a>

<p>

<h3>
Description:
</h3>
Using the group law on an elliptic curve E over a finite field K
two points P_1=[x_1,y_1] and P_2=[x_2,y_2] are added. E is
either given by a list of two or five elements of K or integers. If
the equation of E is y^2=x^3+a_4 x+a_6 the curve is represented
by [a_4,a_6], if the equation of E is
y^2+a_1 xy+a_3y=x^3+a_2x^2+a_4 x+a_6 then the representation is
[a_1,a_2,a_3,a_4,a_6]. Points on the curve are given by a pair of
elements of K or integers; the point at infinity is represented by
the empty list [\;].

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> K := FF(11);
Finite field of size 11
kash> E := [0,0,0,1,6];
[ 0, 0, 0, 1, 6 ]
kash> EccPointsAdd(K,E,[2,7],[5,9]);
[ 2, 4 ]
kash> EccPointsAdd(K,E,[2,7],[]);
> [ 2, 7 ]

</pre>

<p>


<hr>

<p>
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