/efficient_milp_modelings

Code for the paper "Efficient MILP modelings for Sboxes and Linear Layers of SPN ciphers", ToSC 2020.

Primary LanguagePython

README

This repository contains the code used to obtain some of our results in the paper "Efficient MILP modelings for Sboxes and Linear Layers of SPN ciphers."

  • sbox contains python (or SageMath) files that are useful for modeling 4-bit Sboxes.
  • impossible_differentials contains python files that build Gurobi models for searching for impossible differentials for Skinny and the AES.

We have not published the code for 8-bit Sboxes yet but the models of the DDTs used in impossible differential search are given as pickle files.

Overview of the sbox directory

  • arbitrary_sbox_gen.py generates a pickle file for an arbitrary Sbox DDT (only transitions zero -> non zero are impossible).
  • check_model.sage checks the correctness of a model of a DDT given by a pickle file.
  • convex_hull.sage generates a big set of inequalities with the convex hull technique. Uses the SageMath Sboxes and Polyhedra tools.
  • identity_sbox_gen.py generates a pickle file for the identity Sbox DDT.
  • minimize.py performs step 2 given a big set of inequalities with greedy or minimization techniques.
  • utilities.py defines some small useful functions for the other files.

Overview of the impossible_differentials directory

  • aes_equiv_sbox.pkl is the model of the DDT of an affine equivalent AES Sbox.
  • aes.py builds and tests the Gurobi model for the AES.
  • arbitrary_sbox_8_8.pkl is the model of the DDT of an arbitrary 8-bit Sbox (for testing purposes).
  • identity_sbox_8.pkl is the model of the DDT of the identity 8-bit Sbox (testing).
  • main_aes.py launches the search for impossible differentials for the AES.
  • main_skinny.py is the same for Skinny.
  • primitive.py contains classes and functions common to aes.py and skinny.py.
  • skinny.py builds and tests the Gurobi model for Skinny.
  • skinny_sbox.pkl is the model of the DDT of the Skinny 8-bit Sbox.
  • utilities.py defines small useful functions.