.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/privacy/mixing/plot_01_coinjoin.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_01_coinjoin.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_01_coinjoin.py:


CoinJoin: many payers, one transaction (2013)
=============================================

Gregory Maxwell observed that the inputs of a Bitcoin transaction need
not belong to one person. In a CoinJoin, several users each contribute an
input and name an output; each checks the joint transaction and signs only
its own input. If the mixed outputs all have one *denomination* :math:`d`,
an observer cannot tell whose is whose, and the common-input heuristic now
merges strangers.

Change is the weak point. Each change output is an input minus :math:`d`,

.. math::

   \text{change}_i = a_i - d ,

which usually points straight back at its input. Only the equal outputs
are anonymous: :math:`n` of them hide each participant among :math:`n`.

.. GENERATED FROM PYTHON SOURCE LINES 23-29

.. code-block:: Python

    from random import Random

    import matplotlib.pyplot as plt

    import blockchainkit as bk








.. GENERATED FROM PYTHON SOURCE LINES 30-32

One round
---------

.. GENERATED FROM PYTHON SOURCE LINES 32-47

.. code-block:: Python


    participants = [("ann", "a1", 10), ("bob", "b1", 13), ("cat", "c1", 17), ("dan", "d1", 10)]
    round_ = bk.privacy.coinjoin(participants, 10, seed=1)
    for address, amount in round_.transaction.outputs:
        print(f"{address}  {amount:>3}")
    print("anonymity set of the 10-coin outputs:", round_.anonymity_set)
    links = bk.privacy.link_change(round_.transaction, 10)
    assert all(round_.owners[c] == round_.owners[i] for c, i in links.items())
    print("change linked to its input:", {round_.owners[c] for c in links})

    clusters = bk.privacy.cluster_addresses([round_.transaction])
    score = bk.privacy.score_clusters(clusters, round_.owners)
    assert score.false_merges == 1
    print("the input heuristic merges", len(clusters[0]), "addresses of 4 users into one cluster")





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

 .. code-block:: none

    b42728bfaea822ae    3
    5007614821705756   10
    84a78c39bf93a468   10
    a9a04e1352d51aff   10
    17663be6439ae9c6    7
    9f853c0b158c51b3   10
    anonymity set of the 10-coin outputs: 4
    change linked to its input: {'bob', 'cat'}
    the input heuristic merges 4 addresses of 4 users into one cluster




.. GENERATED FROM PYTHON SOURCE LINES 48-51

Larger rounds
-------------
Inputs between 10 and 30 coins, denomination 10.

.. GENERATED FROM PYTHON SOURCE LINES 51-71

.. code-block:: Python


    rng = Random(4)
    sizes = [2, 5, 10, 20, 50]
    anonymous, linked = [], []
    for n in sizes:
        people = [(f"u{i}", f"in{i}", rng.randrange(10, 31)) for i in range(n)]
        r = bk.privacy.coinjoin(people, 10, seed=n)
        anonymous.append(r.anonymity_set)
        linked.append(len(bk.privacy.link_change(r.transaction, 10)) / n)
    # A change output that happens to equal the denomination joins the set too.
    assert all(a >= n for a, n in zip(anonymous, sizes, strict=True))

    fig, ax = plt.subplots(figsize=(6, 4))
    ax.plot(sizes, linked, marker="o", color="#dc2626")
    ax.set(xlabel="participants", ylabel="fraction of change outputs linked", ylim=(0, 1.05))
    ax.set_title("Equal outputs hide among n; change points back to its input")
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/privacy/mixing/images/sphx_glr_plot_01_coinjoin_001.png
   :alt: Equal outputs hide among n; change points back to its input
   :srcset: /api/gallery/privacy/mixing/images/sphx_glr_plot_01_coinjoin_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 72-78

Exercise
--------
In a round of three with inputs 15, 15 and 25 and denomination 10, which
change outputs can :func:`~blockchainkit.privacy.systems.coinjoin.link_change`
link? What does that suggest about choosing inputs?
A worked solution is in :doc:`/exercises/privacy`.


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

   **Total running time of the script:** (0 minutes 0.055 seconds)


.. _sphx_glr_download_api_gallery_privacy_mixing_plot_01_coinjoin.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_01_coinjoin.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_coinjoin.ipynb <plot_01_coinjoin.ipynb>`

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

      :download:`Download Python source code: plot_01_coinjoin.py <plot_01_coinjoin.py>`

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

      :download:`Download zipped: plot_01_coinjoin.zip <plot_01_coinjoin.zip>`


.. only:: html

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

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