Open problems of proving security of ARX-based ciphers to differential cryptanalysis

There are many ARX-based symmetric primitives that form the core of modern lightweight cryptography. The paper considers the known methods of proving differential properties of ARX-based ciphers based on application of partial difference distribution tables, probabilistic neutral bits and SAT solvers. The known long trail strategy that allows designing provable secure ARX-based block ciphers is also considered. The open problems of proving ARX-ciphers security to differential attacks are formulated. It is underlined that there is no universal theory that allows evaluating security of any ARX-based primitive to differential cryptanalysis.