.. _sphx_glr_api_gallery_crypto_commitments:

Commitments
-----------

Sealed envelopes made of hashes and group elements.


.. 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="Alice and Bob, on the phone, want a fair coin toss. If Alice calls first, Bob can lie. Blum&#x27;s fix: Alice commits to her call, Bob announces the coin, then Alice opens the commitment. A commitment must be binding (Alice cannot change her call) and hiding (Bob cannot read it early).">

.. only:: html

  .. image:: /api/gallery/crypto/commitments/images/thumb/sphx_glr_plot_01_coin_flipping_thumb.png
    :alt:

  :doc:`/api/gallery/crypto/commitments/plot_01_coin_flipping`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coin flipping by telephone: hash commitments (Blum 1981)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Pedersen committed to a value v as C = gv  h*r, with a random blinding factor r and a second generator h whose logarithm nobody knows. For any other value there is a blinding factor giving the same C, so the commitment hides v perfectly; opening it to a different value would reveal log_g(h). And commitments multiply to a commitment of the sum.">

.. only:: html

  .. image:: /api/gallery/crypto/commitments/images/thumb/sphx_glr_plot_02_pedersen_thumb.png
    :alt:

  :doc:`/api/gallery/crypto/commitments/plot_02_pedersen`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pedersen commitments: perfectly hiding and additive (1991)</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/crypto/commitments/plot_01_coin_flipping
   /api/gallery/crypto/commitments/plot_02_pedersen