  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. Meanwhile, taking the performance of the differential-neural
distinguisher of SIMON32/64 as an entry point, we investigate the impact of
input difference on the performance of the hybrid distinguishers to choose the
proper input difference. Eventually, we improve the accuracy of the neural
distinguishers of SIMON32/64, SIMON64/128, SIMECK32/64, and SIMECK64/128. We
also obtain related-key differential-based neural distinguishers on
round-reduced versions of SIMON32/64, SIMON64/128, SIMECK32/64, and
SIMECK64/128 for the first time.
