.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/structures/hash_chains/plot_01_lamport_hash_chain.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_structures_hash_chains_plot_01_lamport_hash_chain.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_structures_hash_chains_plot_01_lamport_hash_chain.py:


Hash chains and one-time passwords (Lamport 1981)
=================================================

Lamport proposed logging in without ever sending a reusable password. Hash a
secret seed n times and give the server only the last value. Each login
reveals the value before it: the server hashes it once and compares. A
captured password is useless, because the next one is its *preimage*.
This became S/KEY (1995), and hash chains reappear in blockchains as
commit-reveal randomness and in Lamport-style signatures.

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

Each password verifies against the previous anchor, and the anchor moves
back along the chain. Replaying a captured password fails, and the attacker
cannot step backwards without inverting SHA-256.

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

.. GENERATED FROM PYTHON SOURCE LINES 24-26

Log in five times
-----------------

.. GENERATED FROM PYTHON SOURCE LINES 26-40

.. code-block:: Python

    import matplotlib.pyplot as plt

    import blockchainkit as bk

    chain = bk.structures.hash_chain(b"Alice's secret seed", 100)
    anchor = chain[-1]  # Registered with the server once.
    used = []
    for login in range(5):
        password = chain[-2 - login]
        assert bk.structures.verify_one_time_password(password, anchor)
        used.append(password)
        anchor = password  # The server keeps the newest accepted value.
    print("5 logins accepted; the server now stores", anchor.hex()[:16], "...")





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

 .. code-block:: none

    5 logins accepted; the server now stores 0768bbf7b5a19e83 ...




.. GENERATED FROM PYTHON SOURCE LINES 41-43

A captured password cannot be replayed
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python

    eavesdropped = used[-1]
    assert not bk.structures.verify_one_time_password(eavesdropped, anchor)
    next_password = chain[-7]
    assert bk.crypto.sha256(next_password) == anchor  # Only the seed holder can produce this.








.. GENERATED FROM PYTHON SOURCE LINES 49-51

Remaining logins
----------------

.. GENERATED FROM PYTHON SOURCE LINES 51-58

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(7, 3))
    ax.barh(
        ["used", "remaining"], [len(used), len(chain) - 1 - len(used)], color=["#94a3b8", "#2563eb"]
    )
    ax.set(xlabel="passwords", title="A chain of 100 hashes gives 99 logins")
    fig.tight_layout()




.. image-sg:: /api/gallery/structures/hash_chains/images/sphx_glr_plot_01_lamport_hash_chain_001.png
   :alt: A chain of 100 hashes gives 99 logins
   :srcset: /api/gallery/structures/hash_chains/images/sphx_glr_plot_01_lamport_hash_chain_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 59-63

Exercise
--------
Why must passwords be revealed in reverse order of computation? What does
a server learn if it is breached, compared with storing a password hash?


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

   **Total running time of the script:** (0 minutes 0.066 seconds)


.. _sphx_glr_download_api_gallery_structures_hash_chains_plot_01_lamport_hash_chain.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/structures/hash_chains/plot_01_lamport_hash_chain.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_lamport_hash_chain.ipynb <plot_01_lamport_hash_chain.ipynb>`

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

      :download:`Download Python source code: plot_01_lamport_hash_chain.py <plot_01_lamport_hash_chain.py>`

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

      :download:`Download zipped: plot_01_lamport_hash_chain.zip <plot_01_lamport_hash_chain.zip>`


.. only:: html

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

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