.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/privacy/analysis/plot_01_k_anonymity_anonymity_sets.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_analysis_plot_01_k_anonymity_anonymity_sets.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_analysis_plot_01_k_anonymity_anonymity_sets.py:


k-anonymity and anonymity sets: hiding among k (2002)
=====================================================

Latanya Sweeney showed that a ZIP code, a birth date and a sex single out
most Americans. A table is *k-anonymous* if every combination of these
*quasi-identifiers* appears at least :math:`k` times, so each person hides
among :math:`k`. Generalising values, a ZIP to its first three digits or a
date to a year, merges rows until :math:`k` is reached.

The same year, anonymity on networks was measured the same way: by the
*anonymity set* of possible senders. An attacker who finds some senders
likelier than others has less uncertainty than the set's size suggests,
so Serjantov and Danezis, and Díaz et al., counted

.. math::

   |S|_{\text{eff}} = 2^{H}, \qquad H = -\sum_i p_i \log_2 p_i ,

the number of equally likely senders that leave the same uncertainty.

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python

    from random import Random

    import matplotlib.pyplot as plt

    import blockchainkit as bk








.. GENERATED FROM PYTHON SOURCE LINES 31-33

Generalising a table
--------------------

.. GENERATED FROM PYTHON SOURCE LINES 33-55

.. code-block:: Python


    rng = Random(1997)
    rows = [
        {
            "zip": f"021{rng.randrange(30, 40)}",
            "born": f"19{rng.randrange(50, 90)}-{rng.randrange(1, 13):02d}",
            "sex": rng.choice("FM"),
        }
        for _ in range(400)
    ]
    quasi = ["zip", "born", "sex"]
    steps = {
        "as released": rows,
        "ZIP to 4 digits": [{**r, "zip": r["zip"][:4]} for r in rows],
        "birth to year": [{**r, "zip": r["zip"][:4], "born": r["born"][:4]} for r in rows],
        "birth to decade": [{**r, "zip": r["zip"][:3], "born": r["born"][:3]} for r in rows],
    }
    ks = {name: bk.privacy.k_anonymity(table, quasi) for name, table in steps.items()}
    unique = sum(1 for n in bk.privacy.equivalence_classes(rows, quasi).values() if n == 1)
    print(f"{unique} of {len(rows)} rows are unique as released; k by step: {ks}")
    assert ks["as released"] == 1 and ks["birth to decade"] > 1





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

 .. code-block:: none

    386 of 400 rows are unique as released; k by step: {'as released': 1, 'ZIP to 4 digits': 1, 'birth to year': 1, 'birth to decade': 41}




.. GENERATED FROM PYTHON SOURCE LINES 56-59

Size is not the whole story
---------------------------
Ten possible senders, as the attacker's suspicion of one grows.

.. GENERATED FROM PYTHON SOURCE LINES 59-77

.. code-block:: Python


    suspicion = [i / 20 for i in range(1, 20)]
    effective = [bk.privacy.effective_anonymity_set([p] + [(1 - p) / 9] * 9) for p in suspicion]
    assert abs(effective[1] - 10) < 1e-9

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
    ax1.bar(list(ks), list(ks.values()), color="#2563eb")
    ax1.set(ylabel="k", title="Generalising raises k")
    ax1.tick_params(axis="x", labelrotation=20)
    ax2.plot(suspicion, effective, color="#dc2626")
    ax2.axhline(10, color="#64748b", linestyle="--", label="set size")
    ax2.set(xlabel="probability of the likeliest sender", ylabel="effective anonymity set")
    ax2.set_title("Ten senders, but not equally likely")
    ax2.legend()
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/privacy/analysis/images/sphx_glr_plot_01_k_anonymity_anonymity_sets_001.png
   :alt: Generalising raises k, Ten senders, but not equally likely
   :srcset: /api/gallery/privacy/analysis/images/sphx_glr_plot_01_k_anonymity_anonymity_sets_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 78-84

Exercise
--------
A table is 5-anonymous, but in one class of five rows every patient has
the same diagnosis. What does an attacker who knows a neighbour is in
that class learn, and what property did Machanavajjhala et al. add?
A worked solution is in :doc:`/exercises/privacy`.


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

   **Total running time of the script:** (0 minutes 0.096 seconds)


.. _sphx_glr_download_api_gallery_privacy_analysis_plot_01_k_anonymity_anonymity_sets.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/analysis/plot_01_k_anonymity_anonymity_sets.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_k_anonymity_anonymity_sets.ipynb <plot_01_k_anonymity_anonymity_sets.ipynb>`

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

      :download:`Download Python source code: plot_01_k_anonymity_anonymity_sets.py <plot_01_k_anonymity_anonymity_sets.py>`

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

      :download:`Download zipped: plot_01_k_anonymity_anonymity_sets.zip <plot_01_k_anonymity_anonymity_sets.zip>`


.. only:: html

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

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