At Crypto 2019, Gohr first adopted the neural distinguisher for differential cryptanalysis, and since then, this work received increasing attention. However, most of the existing work focuses on improving and applying the neural distinguisher, the studies delving into the intrinsic principles of neural distinguishers are finite. At Eurocrypt 2021, Benamira et al. conducted a study on Gohr’s neural distinguisher. But for the neural distinguishers proposed later, such as the r-round neural distinguishers trained with k ciphertext pairs or ciphertext differences, denoted as NDcpk_r (Gohr’s neural distinguisher is the special NDcpk_r with K = 1) and NDcdk_r , such research is lacking. In this work, we devote ourselves to study the intrinsic principles and relationship between NDcdk_r and NDcpk_r. Firstly, we explore the working principle of NDcd1_r through a series of experiments and find that it strongly relies on the probability distribution of ciphertext differences. Its operational mechanism bears a strong resemblance to that of NDcp1_r given by Benamira et al.. Therefore, we further compare them from the perspective of differential cryptanalysis and sample features, demonstrating the superior performance of NDcp1_r can be attributed to the relationships between certain ciphertext bits, especially the significant bits. We then extend our investigation to NDcpk_r, and show that its ability to recognize samples heavily relies on the average differential probability of k ciphertext pairs and some relationships in the ciphertext itself, but the reliance between k ciphertext pairs is very weak. Finally, in light of the findings of our research, we introduce a strategy to enhance the accuracy of the neural distinguisher by using a fixed difference to generate the negative samples instead of the random one. Through the implementation of this approach, we manage to improve the accuracy of the neural distinguishers by approximately 2% to 8% for 7-round Speck32/64 and 9-round Simon32/64.

In CRYPTO 2019, Gohr first introduced the deep learning method to cryptanalysis for SPECK32/64. A differential-neural distinguisher was obtained using ResNet neural network. Zhang et al. used multiple parallel convolutional layers with different kernel sizes to capture information from multiple dimensions, thus improving the accuracy or obtaining a more round of distinguisher for SPECK32/64 and SIMON32/64. Inspired by Zhang's work, we apply the network structure to other ciphers. We not only improve the accuracy of the distinguisher, but also increase the number of rounds of the distinguisher, that is, distinguish more rounds of ciphertext and random number for DES, Chaskey and PRESENT.