Cryptanalysis based on deep learning has become a hotspot in the international cryptography community since it was proposed. The key point of differential cryptanalysis based on deep learning is to find a neural differential distinguisher with longer rounds or higher probability. Therefore it is important to research how to improve the accuracy and the rounds of neural differential distinguisher. In this paper, we design SAT-based algorithms to find a good input difference so that the accuracy of the neural distinguisher can be improved as high as possible. As applications, we search and obtain the neural differential distinguishers of 9-round SIMON32/64, 10-round SIMON48/96 and 11-round SIMON64/128. For SIMON48/96, we choose $(0x0,0x100000)$ as the input difference and train 9-round and 10-round neural distinguishers of SIMON48/96. In addition, with the automatic search based on SAT, we extend the neural 9-round, 10-round distinguishers to 11-round, 12-round distinguishers by prepending the optimal 2-round differential transition $(0x400000,0x100001) xrightarrow{2^{-4}}left( 0x0,0x100000 right)$. Based on the 11-round and 12-round neural distinguisher, we complete a 14-round key recovery attack of SIMON48/96. Our attack takes about 1550s to recover the final subkey. Its average time complexity is no more than $2^{22.21}$ 14-round encryption of SIMON48/96, and the data complexity is about $2^{12.8}$. Similar to 14-round key recovery attack, we perform 13-round key recovery attack for SIMON32/64 with input difference $(0x0,0x80)$ with a success rate of more than 90$%$. It takes about 23s to complete an attack with the data complexity no more than $2^{12.5}$ and the time complexity no more than $2^{16.4}$. It is worth mentioning that the attacks are practical for 13-round SIMON32/64 and 14-round SIMON48/96.

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