SboxU v1.3

Description

SAGE/Python functions useful for studying S-boxes and Boolean functions such as computing the DDT, computing the Walsh spectrum, affine equivalence testing... Some of them are implemented in C++ and/or in parallel to improve their performances.

Dependencies

Most functions in sboxU only depend on a recent version of SAGE (it was tested with version 9.0). Some use openmp for multithreading, and you may need to install it in order to successfully compile.

UPDATE (v1.2): fftw is no longer required. It was replaced with pocketfft, which is contained entirely within pocketfft_hdronly.h.

Installing openmp can be done with:

sudo apt-get install libomp-dev

or, on macOS:

brew install libomp

Usage

To retrieve this module, use the following command:

git clone https://github.com/lpp-crypto/sboxU/

Then, you need to compile the content of the sboxU/sboxU_cython folder. This process only relies on SAGE To compile it:

cd sboxU/sboxU_cython
sage setup.py build_ext --inplace

This compiles the C++ part of sboxU and allows it to be called from a SAGE script. To use it in your project, simply move the sboxU folder to your project's directory. You can then import sboxU like any other python module. As an example of the functions provided by sboxU, the SAGE script example.py stored alongside the folder sboxU generates random permutations and tests their affine equivalence.

Then, in order to use the functions provided by sboxU, simply paste/make a link to the folder sboxU from the directory in which you are working. For example, if you have a script called test.py in which you want to call the functions in sboxU then your directory should look like this:

$ ls
test.py
README.md
sboxu/

and the file test.py should contain from sboxU import *. You can also import sboxU in a sage notebook session provided that you started sage from the folder containing it.

Troubleshooting

• undefined symbol: _Py_ZeroStruct If you get such an error, there are probably mismatches between the python versions used. This typically happens if you have 2 versions of SAGE installed, used the most recent one to compile sboxU, but then use an older one in your scripts.

Authors (in alphabetic order)

Jules Baudrin

Aurélien Boeuf

Xavier Bonnetain

Alain Couvreur

Mathias Joly

Léo Perrin

Acknowledgements

When operating over fields of odd characteristic, we use the [pocketfft] (https://gitlab.mpcdf.mpg.de/mtr/pocketfft) library (pocketfft_hdronly.h was taken from the cpp branch) and we would like to thank their authors.