Exact Formula for RX-Differential Probability through Modular Addition for All Rotations

This repository contains supporting code for the paper

"Exact Formula for RX-Differential Probability through Modular Addition for All Rotations"

from ToSC 2025 (1), by Alex Biryukov, Baptiste Lambin and Aleksei Udovenko.

See also slides from the presentation.

Setup

Requirements:

• python3 (tested on v3.9), pypy3 is recommended for good performance
• gcc/g++ compiler
• Gurobi C++ library installed (and license), for the Alzette part only

Contents

verifyTheory contains code related to verifying our theory (Sections 2-3 from the paper):

• verifying main lemmas/theorems (Section 2, Section 2.7);
• verifying constant addition theorem (Section 2.6);
• verifying claims regarding previous formula from TOSC 2016 (Section 3).

Alzette contains main code and data related to the MILP-based search of Alzette and its verification (Section 5, Section 5.1):

• MILP search for trails (heuristic + full precise) (Section 5);
• search logs and trails (Appendix D);
• experimental verification of trails/distinguishers with logs.

Malzette contains code and data related to the Malzette permutation (Section 6):

• generation of Malzette instances (Section 6.1);
• experimental verification of trails/distinguishers with logs (Section 6.2).

More Contents

impossibleDiff contains code related to experiments with impossible RX-differentials (Appendix G in the paper).

otherTrails contains code and some logs related to RX-trail searches for Speck and Salsa and other primitives.