.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/privacy/signatures/plot_03_cryptonote_stealth_addresses.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_signatures_plot_03_cryptonote_stealth_addresses.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_signatures_plot_03_cryptonote_stealth_addresses.py:


CryptoNote stealth addresses: a fresh key for every payment (2013)
==================================================================

A reused address links every payment it receives. CryptoNote let a payee
publish one address :math:`(A, B) = (g^a, g^b)` from which each payer
derives a fresh one-time key. The payer picks :math:`r`, publishes
:math:`R = g^r`, and pays to

.. math::

   P = g^{H(A^r)} B .

The payee recognises it by computing :math:`R^a = A^r`, and spends it with
:math:`x = H(R^a) + b`. The view key :math:`a` alone finds payments
without being able to spend them.

.. GENERATED FROM PYTHON SOURCE LINES 20-26

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    G = bk.crypto.TEACHING_GROUP








.. GENERATED FROM PYTHON SOURCE LINES 27-29

Payments to one address
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 29-46

.. code-block:: Python


    bob = bk.privacy.stealth_keys(view_secret=31_337, spend_secret=27_182)
    others = [bk.privacy.stealth_keys(1_000 + i, 2_000 + i) for i in range(4)]
    ledger = []
    for k in range(12):
        payee = bob if k % 3 == 0 else others[k % 4]
        output = bk.privacy.stealth_payment(payee.view_public, payee.spend_public, 5_000 + k)
        ledger.append((payee is bob, output))

    found = [o for _, o in ledger if bk.privacy.owns_output(o, bob.view_secret, bob.spend_public)]
    assert found == [o for mine, o in ledger if mine]
    print(f"bob's view key finds {len(found)} of {len(ledger)} outputs")
    for output in found:
        x = bk.privacy.one_time_secret(output, bob.view_secret, bob.spend_secret)
        assert G.public(x) == output.one_time_key
    assert len({o.one_time_key for o in found}) == len(found)





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

 .. code-block:: none

    bob's view key finds 4 of 12 outputs




.. GENERATED FROM PYTHON SOURCE LINES 47-50

What the ledger shows
---------------------
Bob's outputs are scattered among the rest.

.. GENERATED FROM PYTHON SOURCE LINES 50-63

.. code-block:: Python


    fig, ax = plt.subplots(figsize=(7, 3))
    for k, (mine, output) in enumerate(ledger):
        ax.scatter(k, output.one_time_key / G.p, color="#16a34a" if mine else "#64748b")
    ax.scatter([], [], color="#16a34a", label="paid to bob")
    ax.scatter([], [], color="#64748b", label="paid to others")
    ax.set(xlabel="output", ylabel="one-time key / p", ylim=(0, 1))
    ax.set_title("One published address, unlinkable outputs")
    ax.legend()
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/privacy/signatures/images/sphx_glr_plot_03_cryptonote_stealth_addresses_001.png
   :alt: One published address, unlinkable outputs
   :srcset: /api/gallery/privacy/signatures/images/sphx_glr_plot_03_cryptonote_stealth_addresses_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 64-69

Exercise
--------
Bob gives his view key to an auditor. What can the auditor learn about
Bob's incoming and outgoing payments, and what can it not do?
A worked solution is in :doc:`/exercises/privacy`.


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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_api_gallery_privacy_signatures_plot_03_cryptonote_stealth_addresses.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/signatures/plot_03_cryptonote_stealth_addresses.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_03_cryptonote_stealth_addresses.ipynb <plot_03_cryptonote_stealth_addresses.ipynb>`

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

      :download:`Download Python source code: plot_03_cryptonote_stealth_addresses.py <plot_03_cryptonote_stealth_addresses.py>`

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

      :download:`Download zipped: plot_03_cryptonote_stealth_addresses.zip <plot_03_cryptonote_stealth_addresses.zip>`


.. only:: html

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

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