Investigating and Enhancing the Neural Distinguisher for Differential Cryptanalysis

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 NDᶜᵖ_kᵣ (Gohr's neural distinguisher is the special NDᶜᵖ_kᵣ with k=1) and NDᶜᵈ_kᵣ , such research is lacking. In this work, we devote ourselves to study the intrinsic principles and relationship between NDᶜᵈ_kᵣ and NDᶜᵖ_kᵣ. Firstly, we explore the working principle of NDᶜᵈ_1ᵣ 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 NDᶜᵖ_1ᵣ given by Benamira et al.. Therefore, we further compare them from the perspective of differential cryptanalysis and sample features, demonstrating the superior performance of NDᶜᵖ_1ᵣ can be attributed to the relationships between certain ciphertext bits, especially the significant bits. We then extend our investigation to NDᶜᵖ_kᵣ, 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.