Integral cryptanalysis in characteristic p

This is supplementary material to the work Integral cryptanalysis in characteristic $p$.

Newton Polytope based analysis

SPN.ipynb, Feistel.ipynb, HadesMiMC-Rf.ipynb and HadesMiMC-Rp.ipynb contain the code used for the analysis in sections 6.2 and 7.2 based on newton polytopes. These notebooks should be run with a sagemath kernel. For the density estimations in Feistel.ipynb the sage package latte_int is required.

Installation instruction for latte_int can be found here. This code has most recently been tested with sagemath 10.7 and latte_int version 1.7.6

Constrained optimisation based analysis

AESprime.ipynb, small-psquare.ipynb and mid-psquare.ipynb contain the code used for the analsysis in section 7.1. These notebooks should be run with a normal python kernel with ortools and galois installed.

The python packages can be installed with pip install ortools galois. This code has most recently been tested with python version 3.13.7, ortool version 9.14.6206 and galois version 0.4.7.