pailliers 0.3.1

Minimal pure-Python implementation of Paillier's additively homomorphic cryptosystem.

Minimal pure-Python implementation of Paillier’s additively homomorphic cryptosystem.

Installation and Usage

This library is available as a package on PyPI:

python -m pip install pailliers

The library can be imported in the usual manner:

from pailliers import *

Examples

This library supports the creation of secret keys, derivation of public keys from secret keys, encryption of integers into ciphertexts using public keys via encrypt, and decryption of ciphertexts into integers using secret keys via decrypt:

>>> secret_key = secret(2048)
>>> public_key = public(secret_key)
>>> c = encrypt(public_key, 123)
>>> int(decrypt(secret_key, c))
123

The encrypt function returns instances of the cipher class (which is derived from the built-in int type) that represent ciphertexts. Because the cipher class includes definitions of special methods (such as __add__ and __mul__) corresponding to Python’s built-in addition and multiplication operators, these operators can be used to add two ciphertexts and to multiply a ciphertext by an integer scalar:

>>> c = encrypt(public_key, 123)
>>> d = encrypt(public_key, 456)
>>> r = (c * 2) + d
>>> int(decrypt(secret_key, r))
702

Other special methods make it possible to use a single variable to accumulate iteratively (via __iadd__ and __imul__) and to use the built-in sum function (via __radd__):

>>> b = 0
>>> b += encrypt(public_key, 1)
>>> b += encrypt(public_key, 2)
>>> b += encrypt(public_key, 3)
>>> b *= 2
>>> b = sum([b, b, b])
>>> int(decrypt(secret_key, b))
36

Addition will only work on two or more instances of the cipher class. To facilitate the use of cipher instances that do not all maintain internal copies of the same public key (e.g., in cases where memory constraints are an issue or ciphertexts are stored/communicated separately from key information), the add and mul functions are also provided. The public key must be supplied explicitly to these functions:

>>> c = int(encrypt(public_key, 123))
>>> d = int(encrypt(public_key, 456))
>>> r = mul(public_key, cipher(c), 2)
>>> s = add(public_key, r, cipher(d))
>>> int(decrypt(secret_key, s))
702

An alternative to the above is to instantiate cipher instances using explicit ciphertext values and the public key used to encrypt them:

>>> c = int(encrypt(public_key, 123))
>>> d = int(encrypt(public_key, 456))
>>> c = cipher(c, public_key)
>>> d = cipher(d, public_key)
>>> s = (2 * c) + d
>>> int(decrypt(secret_key, s))
702

Development

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]"

Documentation

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/pailliers/pailliers.py -v

Style conventions are enforced using Pylint:

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

Contributions

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

Publishing

This library can be published as a package on PyPI via the GitHub Actions workflow found in .github/workflows/build-publish-sign-release.yml that follows the recommendations found in the Python Packaging User Guide.

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.

To publish the package, create and push a tag for the version being published (replacing ?.?.? with the version number):

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