.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/privacy/mixing/plot_02_tumblebit.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_privacy_mixing_plot_02_tumblebit.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_privacy_mixing_plot_02_tumblebit.py:


TumbleBit: an untrusted tumbler that cannot link payments (2017)
================================================================

A mixing service, a *tumbler*, takes coins from payers and pays payees.
Heilman, Alshenibr, Baldimtsi, Scafuro and Goldberg made one that can
neither steal nor tell who paid whom. The tumbler promises each payee a
token locked under an RSA *puzzle* :math:`z = \epsilon^e \bmod N`, which
only it can solve. The payee blinds the puzzle with a random :math:`\rho`,

.. math::

   z' = z \rho^{e} \bmod N, \qquad (z')^{d} = \epsilon \rho ,

and a payer pays the tumbler to solve :math:`z'`. Dividing the solution by
:math:`\rho` gives :math:`\epsilon`, which opens the token. The tumbler
saw :math:`z` with the payee and :math:`z'` with the payer: unrelated
numbers, as in Chaum's blind signatures.

.. GENERATED FROM PYTHON SOURCE LINES 22-26

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk








.. GENERATED FROM PYTHON SOURCE LINES 27-29

Twenty payments through one tumbler
-----------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 29-38

.. code-block:: Python


    pairs = [(f"payer{i}", f"payee{i}") for i in range(20)]
    blinded = bk.privacy.run_tumbler(pairs, seed=1)
    plain = bk.privacy.run_tumbler(pairs, blind=False, seed=1)
    assert all(blinded.paid) and all(plain.paid)
    print("links without blinding:", len(bk.privacy.tumbler_links(plain)))
    print("links with blinding:   ", len(bk.privacy.tumbler_links(blinded)))
    assert bk.privacy.tumbler_links(blinded) == ()





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    links without blinding: 20
    links with blinding:    0




.. GENERATED FROM PYTHON SOURCE LINES 39-42

The tumbler's two logs
----------------------
Without blinding the same puzzle appears in both; with blinding, never.

.. GENERATED FROM PYTHON SOURCE LINES 42-58

.. code-block:: Python


    n = bk.privacy.TUMBLER_KEY.n
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4), sharey=True)
    for ax, run, title in ((ax1, plain, "unblinded"), (ax2, blinded, "blinded")):
        ax.scatter(
            [z / n for _, z in run.promised],
            [z / n for _, z in run.solved],
            color="#2563eb",
        )
        ax.plot([0, 1], [0, 1], color="#64748b", linestyle=":")
        ax.set(xlabel="puzzle promised to payee i / N", title=f"{title} puzzles")
    ax1.set_ylabel("puzzle solved for payer i / N")
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/privacy/mixing/images/sphx_glr_plot_02_tumblebit_001.png
   :alt: unblinded puzzles, blinded puzzles
   :srcset: /api/gallery/privacy/mixing/images/sphx_glr_plot_02_tumblebit_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 59-65

Exercise
--------
Every payment in a TumbleBit epoch has the same size, and all are made
in the same window. Why do both matter for unlinkability, even though
the puzzles are blinded?
A worked solution is in :doc:`/exercises/privacy`.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.085 seconds)


.. _sphx_glr_download_api_gallery_privacy_mixing_plot_02_tumblebit.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/privacy/mixing/plot_02_tumblebit.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_tumblebit.ipynb <plot_02_tumblebit.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_tumblebit.py <plot_02_tumblebit.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_tumblebit.zip <plot_02_tumblebit.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_