Improved Neural Distinguishers with (Related-key) Differentials: Applications in SIMON and SIMECK

In CRYPTO 2019, Gohr made a pioneering attempt, and successfully applied deep learning to the differential cryptanalysis against NSA block cipher Speck32/64, achieving higher accuracy than the pure differential distinguishers. By its very nature, mining effective features in data plays a crucial role in data-driven deep learning. In this paper, in addition to considering the integrity of the information from the training data of the ciphertext pair, domain knowledge about the structure of differential cryptanalysis is also considered into the training process of deep learning to improve the performance. Besides, based on the SAT/SMT solvers, we find other high probability compatible differential characteristics which effectively improve the performance compared with previous work. We build neural distinguishers (NDs) and related-key neural distinguishers (RKNDs) against Simon and Simeck. The ND and RKND for Simon32/64 reach 11-, 11-round with an accuracy of 59.55% and 97.90%, respectively. For Simon64/128, the ND achieve an accuracy of 60.32% in 13-round, while it is 95.49% for the RKND. For Simeck32/64, ND and RKND of 11-, 14-round are obtained, reaching an accuracy of 63.32% and 87.06%, respectively. And we build 17-round ND and 21-round RKND for Simeck64/128 with an accuracy of 64.24% and 62.96%, respectively. Currently, these are the longest (related-key) neural distinguishers with higher accuracy for Simon32/64, Simon64/128, Simeck32/64 and Simeck64/128.