.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/crypto/hashing/plot_04_sha256_avalanche.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_hashing_plot_04_sha256_avalanche.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_hashing_plot_04_sha256_avalanche.py:


SHA-256 and the avalanche effect (FIPS 180-2, 2002)
===================================================

SHA-256 became the standardized hash behind Bitcoin's block hashes,
addresses, and Merkle trees. A good hash behaves like a random function:
flipping one input bit flips each output bit with probability one half.

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

Flip every bit of a message in turn. The number of changed output bits
clusters around 128 of 256, following a Binomial(256, 1/2) distribution.
This is useful intuition, not a proof of collision or preimage resistance.

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 21-36

.. code-block:: Python

    import blockchainkit as bk
    from blockchainkit.crypto.visualizers import plot_hamming_distances

    message = b"blockchainkit: a reproducible experiment"
    digest = bk.crypto.sha256(message)
    assert digest.hex() == bk.crypto.merkle_damgard_sha256(message).hex()
    distances = []
    for bit in range(len(message) * 8):
        flipped = bytearray(message)
        flipped[bit // 8] ^= 1 << (bit % 8)
        distances.append(bk.crypto.hamming_distance(digest, bk.crypto.sha256(bytes(flipped))))
    mean = sum(distances) / len(distances)
    assert 120 < mean < 136
    print("Mean changed digest bits:", mean, "out of 256")





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

 .. code-block:: none

    Mean changed digest bits: 127.66875 out of 256




.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python

    ax = plot_hamming_distances(distances)
    ax.figure.tight_layout()




.. image-sg:: /api/gallery/crypto/hashing/images/sphx_glr_plot_04_sha256_avalanche_001.png
   :alt: Avalanche: about half the output bits change
   :srcset: /api/gallery/crypto/hashing/images/sphx_glr_plot_04_sha256_avalanche_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 41-46

Exercise
--------
Hash only the first byte of each digest and find collisions. Compare the
number of trials to the birthday estimate. Why is this not an attack on
the full SHA-256 output?


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

   **Total running time of the script:** (0 minutes 0.152 seconds)


.. _sphx_glr_download_api_gallery_crypto_hashing_plot_04_sha256_avalanche.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/hashing/plot_04_sha256_avalanche.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_sha256_avalanche.ipynb <plot_04_sha256_avalanche.ipynb>`

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

      :download:`Download Python source code: plot_04_sha256_avalanche.py <plot_04_sha256_avalanche.py>`

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

      :download:`Download zipped: plot_04_sha256_avalanche.zip <plot_04_sha256_avalanche.zip>`


.. only:: html

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

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