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Data structure for representing additive secret shares of integers, designed for use within secure MPC protocol implementations.

Project description

Data structure for representing additive secret shares of integers, designed for use within secure multi-party computation (MPC) protocol implementations.

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This library provides a data structure and methods that make it possible work with n-out-of-n additive secret shares of integers within secure multi-party computation (MPC) protocol implementations. Secret shares of signed and unsigned integers can be represented using elements from finite fields, with support currently limited to fields having a power-of-two order.

Installation and Usage

This library is available as a package on PyPI:

python -m pip install additive

The library can be imported in the usual ways:

import additive
from additive import *


This library makes it possible to concisely construct multiple secret shares from an integer:

>>> from additive import shares
>>> (a, b) = shares(123)
>>> (c, d) = shares(456)
>>> ((a + c) + (b + d)).to_int()

It is possible to specify the exponent in the order of the finite field used to represent secret shares, as well as whether the encoding of the integer should support signed integers:

>>> (s, t) = shares(-123, exponent=8, signed=True)
>>> (s + t).to_int()

The number of shares can be specified explicitly (the default is two shares):

>>> (r, s, t) = shares(123, quantity=3)

The share data structure supports Python’s built-in addition operators, enabling both operations on shares and concise reconstruction of values from a collection of shares:

>>> (r + s + t).to_int()
>>> sum([r, s, t]).to_int()

In addition, conversion methods for Base64 strings and bytes-like objects are included to support encoding and decoding of share objects:

>>> from additive import share
>>> share.from_base64('HgEA').to_bytes().hex()
>>> [s.to_base64() for s in shares(123)]
['PvmKMG8=', 'PoJ1z5A=']


All installation and development dependencies are fully specified in pyproject.toml. The project.optional-dependencies object is used to specify optional requirements for various development tasks. This makes it possible to specify additional options (such as docs, lint, and so on) when performing installation using pip:

python -m pip install .[docs,lint]


The documentation can be generated automatically from the source files using Sphinx:

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 (see the pyproject.toml file for configuration details):

python -m pip install .[test]
python -m pytest

Alternatively, all unit tests are included in the module itself and can be executed using doctest:

python src/additive/ -v

Style conventions are enforced using Pylint:

python -m pip install .[lint]
python -m pylint src/additive


In order to contribute to the source code, open an issue or submit a pull request on the GitHub page for this library.


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.


This library can be published as a package on PyPI by a package maintainer. First, install the dependencies required for packaging and publishing:

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 that activates and sets as the default all tagged versions. Create and push a tag for this version (replacing ?.?.? with the version number):

git tag ?.?.?
git push origin ?.?.?

Remove any old build/distribution files. Then, package the source into a distribution archive:

rm -rf build dist src/*.egg-info
python -m build --sdist --wheel .

Finally, upload the package distribution archive to PyPI:

python -m twine upload dist/*

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