Approximating neural distinguishers using differential-linear imbalance

At CRYPTO 2019, Gohr first proposed neural distinguishers (NDs) on SPECK32, which are superior to the distinguishers based on the differential distribution table (DDT). Benamira et al. noted that NDs rely on the differential distribution of the last three rounds, and Bao et al. pointed out that NDs depend on the strong correlations between the bit values of ciphertext pairs satisfying the expected differential. Hence, one may guess that there exist deep relations between NDs and the differential-linear imbalances. To approximate NDs under a single ciphertext pair, we utilize differential-linear imbalances to construct simplified distinguishers. These newly constructed distinguishers offer comparable distinguishing advantages to that of NDs but with reduced time complexities. For instance, one such simplified distinguisher has only \(2^{-1.35}\) of the original time complexity of NDs. Our experiments demonstrate that these new distinguishers achieve a matching rate of 98.2% for 5-round SPECK32 under a single ciphertext pair. Furthermore, we achieve the highest accuracies for 7-round and 8-round SPECK32 up to date by using a maximum of 512 ciphertext pairs. Finally, by replacing NDs with simplified distinguishers, we significantly reduce the time complexities of differential-neural attacks on 11–14 rounds of SPECK32.