SageMath Library for Cryptographic Functions

A SageMath library for cryptographic functions, focusing on quadratic APN (Almost Perfect Nonlinear) functions.

The library provides tools for:

• converting between different representations of a function
• generating known infinite families of quadratic APN polynomials in univariate form
• deciding whether a function belongs to these families

Features

• Conversion routines between univariate polynomial representation and other common representations of vectorial Boolean functions:
  • truth tables
  • quadratic matrices
  • sequences
  • bivariate forms
  • trivariate forms
• Implementations of known infinite families of quadratic APN functions in univariate form
• Membership testing for identifying whether a function belongs to a known family

Requirements

• SageMath 10.8 +
• Python 3.9 +

Installation

From PyPI (recommended)

In a Sage terminal write

pip install sagemath-cryptographic-functions-library

Or from a regular terminal write

sage --pip install sagemath-cryptographic-functions-library

From GitHub

In a Sage terminal write

pip install git+https://github.com/hoeeg/SageMath_library_for_cryptographic_functions.git

Or in regular terminal write

sage --pip install git+https://github.com/hoeeg/SageMath_library_for_cryptographic_functions.git

Usage

The package can either be imported by module

from sagemath_cryptographic_functions_library import conversions, families, membership
families.family_4(3)
...

or by importing functions directly

from sagemath_cryptographic_functions_library import family_4
family_4(3)
...

Using Sage Online

You can try Sage online without installing anything locally from any of

 

For a local install, the Sage Installation Guide walks through the available options.

More about Sage or how to download it, can be found in its Documentation.

Layout

├── sagemath_cryptographic_functions_library/
│   ├── __init__.py
│   ├── conversions.py    Conversions between representations
│   ├── families.py       Known APN family constructions
│   ├── helpers.py        Finite field utility functions
│   └── membership.py     Membership testing algorithms
├── README.md             This file
├── pyproject.toml        Build configuration
└── LICENCE               Copyright information