sophiegermain

Pure-Python library that provides a selection of Sophie Germain primes that are organized by representation size.

Purpose

Some cryptographic protocols involve the use of Sophie Germain and safe primes. In such cases, it is often useful to choose a Sophie Germain or safe prime based on the range of values (i.e., congruence classes of integers or finite field elements) that an instantiation of a protocol must accommodate. This library provides immediate access to the smallest Sophie Germain prime for each possible binary representation length (up to and including 2049 bits).

Installation and Usage

This library is available as a package on PyPI:

python -m pip install sophiegermain

The library can be imported in the usual way:

import sophiegermain
from sophiegermain import sophiegermain

This library makes it possible to retrieve instantly the smallest Sophie Germain prime that is of a given bit length (up to and including 2049 bits):

>>> sophiegermain(2)
2
>>> sophiegermain(8)
131
>>> sophiegermain(16)
32771
>>> sophiegermain(32)
2147483693
>>> sophiegermain(257)
115792089237316195423570985008687907853269984665640564039457584007913129658411
>>> sophiegermain(1025).bit_length()
1025
>>> sophiegermain(2049).bit_length()
2049

Implementation

The function used to generate the collection of Sophie Germain primes made available by this library can be found in the source code. The entries were tested using the isprime function found in the SymPy library. This means that all values made available by this library that can be represented using 63 bits or fewer are definitively prime. For larger values, isprime relies on the Baillie-PSW primality test.

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/sophiegermain/sophiegermain.py -v

Style conventions are enforced using Pylint:

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

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 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/*

NillionNetwork/sophiegermain