Neural-Inspired Advances in Integral Cryptanalysis

The study by Gohr et al. at CRYPTO 2019 and sunsequent related works have shown that neural networks can uncover previously unused features, offering novel insights into cryptanalysis. Motivated by these findings, we employ neural networks to learn features specifically related to integral properties and integrate the corresponding insights into optimized search frameworks. These findings validate the framework of using neural networks for feature exploration, providing researchers with novel insights that advance established cryptanalysis methods. Neural networks have inspired the development of more precise integral search models. By comparing the integral distinguishers obtained via neural networks with those identified by classical methods, we observe that existing automated search models often fail to find optimal distinguishers. To address this issue, we develop a meet-in-the-middle search framework that balances model accuracy and computational efficiency. As a result, we reduce the number of active plaintext bits required for an 11-round integral distinguisher on SKINNY-64-64, and further identify a 12-round key-dependent integral distinguisher-achieving one additional round over the previous best-known result. The integral distinguishers discovered by neural networks enable keyrecovery attacks on more rounds. We identify a 7-round key-independent integral distinguisher from neural networks with even only one active plaintext cell, which is based on linear combinations of bits. This distinguisher enables a 15-round key-recovery attack on SKINNY-n-n through a strategy with 3 rounds of forward decryption and 5 rounds of backward encryption, improving upon the previous record by one round. The same distinguisher also enhances attacks on SKINNY-n-2n and SKINNY-n-3n. Additionally, we discover an 8-round key-dependent integral distinguisher using neural network that further reduces the time complexity of keyrecovery attacks against SKINNY.