.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/crypto/blind_signatures/plot_01_blind_signatures.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_crypto_blind_signatures_plot_01_blind_signatures.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_crypto_blind_signatures_plot_01_blind_signatures.py:


Chaum's blind signatures: authenticate a message the signer cannot see (1982)
=============================================================================

Chaum's construction separates authorization from knowledge of a message.
This experiment exposes RSA's multiplicative blinding identity with tiny
integers; a usable payment system needs encoding, issuance, and spent-token rules.

What to look for
----------------

Follow the original message, its hidden form, and the final signature. The final check
succeeds after removing the hiding factor; this is only the signing step of a payment
system.

Read cells in order. An ``assert`` that produces no output has passed.
The final exercise asks you to change an input and explain the result.

The history behind this experiment: :doc:`/history/crypto_breakthroughs`.
See :doc:`/exercises/crypto` for a worked solution to the exercise.

.. GENERATED FROM PYTHON SOURCE LINES 24-37

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    key = bk.crypto.rsa_keypair()
    message, factor = 42, 7
    blinded = bk.crypto.rsa_blind(message, factor, key)
    blind_signature = key.decrypt(blinded)  # Private exponentiation by the signer.
    signature = bk.crypto.rsa_unblind(blind_signature, factor, key)
    assert key.encrypt(signature) == message
    assert signature == key.decrypt(message)
    print(f"Message {message}; blinded request {blinded}; final signature {signature}")





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

 .. code-block:: none

    Message 42; blinded request 2508; final signature 3065




.. GENERATED FROM PYTHON SOURCE LINES 38-40

The signer sees the middle column, not the blinding factor
----------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-67

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(10, 3.8))
    ax.set(xlim=(0, 1), ylim=(0, 1))
    ax.axis("off")
    labels = [
        (0.15, 0.65, f"Holder\nm = {message}\nr = {factor}"),
        (0.5, 0.65, f"Signer receives\nm r^e mod n\n= {blinded}"),
        (0.85, 0.65, f"Signer returns\n(blinded)^d\n= {blind_signature}"),
        (0.5, 0.15, f"Holder removes r\ns = {signature}\ns^e mod n = {message}"),
    ]
    for x, y, label in labels:
        ax.text(
            x,
            y,
            label,
            ha="center",
            va="center",
            bbox={"boxstyle": "round,pad=0.6", "fc": "#eef2ff", "ec": "#6366f1"},
        )
    for start, end in [
        ((0.26, 0.65), (0.37, 0.65)),
        ((0.64, 0.65), (0.74, 0.65)),
        ((0.85, 0.44), (0.63, 0.22)),
    ]:
        ax.annotate("", xy=end, xytext=start, arrowprops={"arrowstyle": "->", "lw": 1.5})
    ax.set_title("Authorization and message visibility are different properties")
    fig.tight_layout()




.. image-sg:: /api/gallery/crypto/blind_signatures/images/sphx_glr_plot_01_blind_signatures_001.png
   :alt: Authorization and message visibility are different properties
   :srcset: /api/gallery/crypto/blind_signatures/images/sphx_glr_plot_01_blind_signatures_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 68-72

Exercise
--------
Try an r that shares a factor with n. Why can it not be removed? Explain
why blind signatures alone do not prevent spending the same token twice.


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

   **Total running time of the script:** (0 minutes 0.279 seconds)


.. _sphx_glr_download_api_gallery_crypto_blind_signatures_plot_01_blind_signatures.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/crypto/blind_signatures/plot_01_blind_signatures.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_blind_signatures.ipynb <plot_01_blind_signatures.ipynb>`

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

      :download:`Download Python source code: plot_01_blind_signatures.py <plot_01_blind_signatures.py>`

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

      :download:`Download zipped: plot_01_blind_signatures.zip <plot_01_blind_signatures.zip>`


.. only:: html

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

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