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.