.. _sphx_glr_api_gallery_crypto_sharing:

Secret sharing
--------------

Shamir's threshold scheme and Feldman's verifiable variant.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="The secret is the constant coefficient of a random polynomial. Any threshold number of evaluations determines it; fewer evaluations leave it undetermined. Arithmetic takes place in a prime field, not over floating-point reals.">

.. only:: html

  .. image:: /api/gallery/crypto/sharing/images/thumb/sphx_glr_plot_01_secret_sharing_thumb.png
    :alt:

  :doc:`/api/gallery/crypto/sharing/plot_01_secret_sharing`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Shamir's secret sharing: reconstruct a secret without storing it whole (1979)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In Shamir&#x27;s scheme every share holder must trust the dealer: nothing stops a dealer from handing out shares that do not lie on one polynomial. Feldman had the dealer publish ga_j for each coefficient a_j. Each holder checks gy == product of C_j(xj), which holds only for points on the committed polynomial.">

.. only:: html

  .. image:: /api/gallery/crypto/sharing/images/thumb/sphx_glr_plot_02_feldman_vss_thumb.png
    :alt:

  :doc:`/api/gallery/crypto/sharing/plot_02_feldman_vss`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Feldman's verifiable secret sharing (1987)</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/crypto/sharing/plot_01_secret_sharing
   /api/gallery/crypto/sharing/plot_02_feldman_vss