.. _sphx_glr_api_gallery_crypto_curves:

Elliptic curves
---------------

The group law on a small curve and scalar multiplication.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Replace modular exponentiation with repeated addition of curve points. The public key Q=xG is easy to compute; recovering x is the discrete-log problem. Our 19-element example is small enough to solve exhaustively.">

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  .. image:: /api/gallery/crypto/curves/images/thumb/sphx_glr_plot_01_elliptic_curves_thumb.png
    :alt:

  :doc:`/api/gallery/crypto/curves/plot_01_elliptic_curves`

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      <div class="sphx-glr-thumbnail-title">Elliptic-curve cryptography: a finite group you can draw (Miller and Koblitz 1985)</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/crypto/curves/plot_01_elliptic_curves