tinybid 0.2.0
Minimal pure-Python library that implements a basic single-item first-price auction via a secure multi-party computation (MPC) protocol.
License: MIT
Requires Python: >=3.7

=======
tinybid
=======

Minimal pure-Python library that implements a basic single-item first-price auction via a `secure multi-party computation protocol <https://eprint.iacr.org/2023/1740>`__.

|pypi| |readthedocs| |actions| |coveralls|

.. |pypi| image:: https://badge.fury.io/py/tinybid.svg
   :target: https://badge.fury.io/py/tinybid
   :alt: PyPI version and link.

.. |readthedocs| image:: https://readthedocs.org/projects/tinybid/badge/?version=latest
   :target: https://tinybid.readthedocs.io/en/latest/?badge=latest
   :alt: Read the Docs documentation status.

.. |actions| image:: https://github.com/nillion-oss/tinybid/workflows/lint-test-cover-docs/badge.svg
   :target: https://github.com/nillion-oss/tinybid/actions/workflows/lint-test-cover-docs.yml
   :alt: GitHub Actions status.

.. |coveralls| image:: https://coveralls.io/repos/github/nillion-oss/tinybid/badge.svg?branch=main
   :target: https://coveralls.io/github/nillion-oss/tinybid?branch=main
   :alt: Coveralls test coverage summary.

Purpose
-------

This library demonstrates how a functionality can be implemented using a `secure multi-party computation (MPC) protocol <https://eprint.iacr.org/2023/1740>`__ for evaluating arithmetic sum-of-products expressions (as implemented in `tinynmc <https://pypi.org/project/tinynmc>`__). The approach used in this library can serve as a template for any workflow that relies on multiple simultaneous instances of such a protocol.

Installation and Usage
----------------------

This library is available as a `package on PyPI <https://pypi.org/project/tinybid>`__:

.. code-block:: bash

    python -m pip install tinybid

The library can be imported in the usual way:

.. code-block:: python

    import tinybid
    from tinybid import *

Basic Example
^^^^^^^^^^^^^

.. |node| replace:: ``node``
.. _node: https://tinybid.readthedocs.io/en/0.2.0/_source/tinybid.html#tinybid.tinybid.node

Suppose that a workflow is supported by three nodes (parties performing a decentralized auction). The |node|_ objects would be instantiated locally by each of these three parties:

.. code-block:: python

    >>> nodes = [node(), node(), node()]

The preprocessing workflow that the nodes must execute can be simulated. The number of bids that a workflow requires must be known, and it is assumed that all permitted bid prices are integers greater than or equal to ``0`` and strictly less than a fixed maximum value. The number of bids and the number of distinct prices must be known during preprocessing:

.. code-block:: python

    >>> preprocess(nodes, bids=4, prices=16)

Each bidder must submit a request for the opportunity to submit a bid. Below, each of the four bidders creates such a request:

.. code-block:: python

    >>> request_zero = request(identifier=0)
    >>> request_one = request(identifier=1)
    >>> request_two = request(identifier=2)
    >>> request_three = request(identifier=3)

Each bidder can deliver a request to each node, and each node can then locally to generate masks that can be returned to the requesting bidder:

.. code-block:: python

    >>> masks_zero = [node.masks(request_zero) for node in nodes]
    >>> masks_one = [node.masks(request_one) for node in nodes]
    >>> masks_two = [node.masks(request_two) for node in nodes]
    >>> masks_three = [node.masks(request_three) for node in nodes]

.. |bid| replace:: ``bid``
.. _bid: https://tinybid.readthedocs.io/en/0.2.0/_source/tinybid.html#tinybid.tinybid.bid

Each bidder can then generate locally a |bid|_ instance (*i.e.*, a masked bid price):

.. code-block:: python

    >>> bid_zero = bid(masks_zero, 7)
    >>> bid_one = bid(masks_one, 11)
    >>> bid_two = bid(masks_two, 2)
    >>> bid_three = bid(masks_three, 11)

Every bidder can broadcast its masked bid to all the nodes. Each node can locally assemble these as they arrive. Once a node has received all masked bids, it can determine its share of each component of the overall outcome of the auction:

.. code-block:: python

    >>> shares = [
    ...     node.outcome([bid_zero, bid_one, bid_two, bid_three])
    ...     for node in nodes
    ... ]

.. |set| replace:: ``set``
.. _set: https://docs.python.org/3/library/functions.html#func-set

.. |int| replace:: ``int``
.. _int: https://docs.python.org/3/library/functions.html#int

The overall outcome can be reconstructed from the shares by the auction operator. The outcome is represented as a |set|_ containing the |int|_ identifiers of the winning bidders:

.. code-block:: python

    >>> list(sorted(reveal(shares)))
    [1, 3]

Implementation
--------------
The auction workflow relies on a data structure for representing an individual bid that is inspired by `one-hot <https://en.wikipedia.org/wiki/One-hot>`__ encodings. For example, suppose there are six possible prices and four bidders. Each bid can be represented as a list containing six `field <https://en.wikipedia.org/wiki/Field_(mathematics)>`__ elements, where each component corresponds to one of the six possible prices.Ensure

Each bidder assembles a list in which the component corresponding to their bid price encodes their unique identifier and in which all other entries are 1. The bidders' unique identifiers are encoded in such a way that the product of any combination of encodings can be decomposed. The table below represents four bids: 3, 4, 1, and 4 (going from top to bottom). In each row, the identifier encoding for bidder *i* is calculated using the formula 2^(2^(*i* + 1)).

+-------------------------+-------+-------+-------+-------+-------+-------+
| **possible bid prices** | **0** | **1** | **2** | **3** | **4** | **5** |
+-------------------------+-------+-------+-------+-------+-------+-------+
| **bid from bidder 0**   |   1   |   1   |   1   |  2^2  |   1   |   1   |
+-------------------------+-------+-------+-------+-------+-------+-------+
| **bid from bidder 1**   |   1   |   1   |   1   |   1   |  2^4  |   1   |
+-------------------------+-------+-------+-------+-------+-------+-------+
| **bid from bidder 2**   |   1   |  2^8  |   1   |   1   |   1   |   1   |
+-------------------------+-------+-------+-------+-------+-------+-------+
| **bid from bidder 3**   |   1   |   1   |   1   |   1   |  2^16 |   1   |
+-------------------------+-------+-------+-------+-------+-------+-------+

.. |int_bit_length| replace:: ``int.bit_length``
.. _int_bit_length: https://docs.python.org/3/library/stdtypes.html#int.bit_length

The overall outcome of the auction can be determined by (1) performing a componentwise multiplication of the lists and (2) determining which identifiers contributed to the non-1 value with the highest index. The table below presents the entries of the componentwise product of the bids above, the exponents of the entries (which can be computed using, for example, |int_bit_length|_), and the binary representations of the exponents. It is evident that the winning bidders can be inferred by examining the binary representation of the exponent of the non-1 component with the highest index.

+-------------------------+-------+-------+-------+-------+-------------+-------+
| **possible bid prices** | **0** | **1** | **2** | **3** | **4**       | **5** |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **product**             |   1   |  2^8  |   1   |  2^2  |  2^(4 + 16) |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **exponent**            |   0   |   8   |   0   |   2   |     4 + 16  |   0   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **exponent in binary**  | 00000 | 01000 | 00000 | 00010 |      10100  | 00000 |
+-------------------------+-------+-------+-------+-------+-------------+-------+

In order to keep things simple, assume that all bidders have an interest in ensuring that only the winning bids can be determined from the outcome. Under this assumption, the in-the-clear version of the workflow presented above can be modified in a straightforward way to reveal only the winning bidders. In particular, the 1 entries in every list that appear *before* the bid price component are instead replaced by random nonzero field elements (generated locally by the bidder assembling the bid). This ensures that the overall componentwise product hides all bid information other than the winning bid price and the identities of the winning bidders.

In the table below, *R* is a placeholder symbol representing various random field elements. Note that any field element multiplied by a random field element (represented by *R*) yields some other random field element (also represented by *R*). Thus, in the below product, the only components not masked via multiplication by a random field element are (1) the component encoding the identifiers of the winning bidders and (2) all components corresponding to prices above the highest bid(s).

+-------------------------+-------+-------+-------+-------+-------------+-------+
| **possible bid prices** | **0** | **1** | **2** | **3** | **4**       | **5** |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **bid from bidder 0**   |  *R*  |  *R*  |  *R*  |  2^2  |   1         |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **bid from bidder 1**   |  *R*  |  *R*  |  *R*  |  *R*  |  2^4        |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **bid from bidder 2**   |  *R*  |  2^8  |   1   |   1   |   1         |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **bid from bidder 3**   |  *R*  |  *R*  |  *R*  |  *R*  |  2^16       |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+
| **product**             |  *R*  |  *R*  |  *R*  |  *R*  |  2^(4 + 16) |   1   |
+-------------------------+-------+-------+-------+-------+-------------+-------+

.. |tinynmc_node| replace:: ``node``
.. _tinynmc_node: https://tinynmc.readthedocs.io/en/0.2.0/_source/tinynmc.html#tinynmc.tinynmc.node

.. |tinybid_node| replace:: ``node``
.. _tinybid_node: https://tinybid.readthedocs.io/en/0.2.0/_source/tinybid.html#tinybid.tinybid.node

Each component of the overall product is calculated using a distinct instance of the protocol implemented by `tinynmc <https://pypi.org/project/tinynmc>`__. This is accomplished by maintaining multiple distinct `tinynmc <https://pypi.org/project/tinynmc>`__ |tinynmc_node|_ objects (one for each possible bid price) inside each `tinybid <https://pypi.org/project/tinybid>`__ |tinybid_node|_ object. In this way, the bid information is protected both from the auction operator (thanks to the random field elements) and from the nodes (thanks to masking via the `MPC protocol <https://eprint.iacr.org/2023/1740>`__).

Development
-----------
All installation and development dependencies are fully specified in ``pyproject.toml``. The ``project.optional-dependencies`` object is used to `specify optional requirements <https://peps.python.org/pep-0621>`__ for various development tasks. This makes it possible to specify additional options (such as ``docs``, ``lint``, and so on) when performing installation using `pip <https://pypi.org/project/pip>`__:

.. code-block:: bash

    python -m pip install .[docs,lint]

Documentation
^^^^^^^^^^^^^
The documentation can be generated automatically from the source files using `Sphinx <https://www.sphinx-doc.org>`__:

.. code-block:: bash

    python -m pip install .[docs]
    cd docs
    sphinx-apidoc -f -E --templatedir=_templates -o _source .. && make html

Testing and Conventions
^^^^^^^^^^^^^^^^^^^^^^^
All unit tests are executed and their coverage is measured when using `pytest <https://docs.pytest.org>`__ (see the ``pyproject.toml`` file for configuration details):

.. code-block:: bash

    python -m pip install .[test]
    python -m pytest

Alternatively, all unit tests are included in the module itself and can be executed using `doctest <https://docs.python.org/3/library/doctest.html>`__:

.. code-block:: bash

    python src/tinybid/tinybid.py -v

Style conventions are enforced using `Pylint <https://pylint.readthedocs.io>`__:

.. code-block:: bash

    python -m pip install .[lint]
    python -m pylint src/tinybid

Contributions
^^^^^^^^^^^^^
In order to contribute to the source code, open an issue or submit a pull request on the `GitHub page <https://github.com/nillion-oss/tinybid>`__ for this library.

Versioning
^^^^^^^^^^
The version number format for this library and the changes to the library associated with version number increments conform with `Semantic Versioning 2.0.0 <https://semver.org/#semantic-versioning-200>`__.

Publishing
^^^^^^^^^^
This library can be published as a `package on PyPI <https://pypi.org/project/tinybid>`__ by a package maintainer. First, install the dependencies required for packaging and publishing:

.. code-block:: bash

    python -m pip install .[publish]

Ensure that the correct version number appears in ``pyproject.toml``, and that any links in this README document to the Read the Docs documentation of this package (or its dependencies) have appropriate version numbers. Also ensure that the Read the Docs project for this library has an `automation rule <https://docs.readthedocs.io/en/stable/automation-rules.html>`__ that activates and sets as the default all tagged versions. Create and push a tag for this version (replacing ``?.?.?`` with the version number):

.. code-block:: bash

    git tag ?.?.?
    git push origin ?.?.?

Remove any old build/distribution files. Then, package the source into a distribution archive:

.. code-block:: bash

    rm -rf build dist src/*.egg-info
    python -m build --sdist --wheel .

Finally, upload the package distribution archive to `PyPI <https://pypi.org>`__:

.. code-block:: bash

    python -m twine upload dist/*