LMND: Language-Model Neural Distinguishers via Conditional Generative Modeling

Block ciphers are a cornerstone of modern secure communication. Differential cryptanalysis assesses their security by distinguishing ciphertext pairs generated under a fixed input difference from random ones. Neural differential methods replace hand-crafted differential statistics with trained deep neural networks, learning directly from data the weak residual dependencies that are difficult to characterize explicitly, and thereby extending effective analysis to more rounds. Existing CNN-based neural distinguishers, typically cast this task as binary classification: each ciphertext pair receives only one sample-level label, yielding coarse supervisory granularity, while the sigmoid output lacks an explicit probabilistic reference, making it difficult to endow the score with statistical meaning or to accumulate evidence across samples. To address these issues, we propose LMND, a neural distinguisher built on conditional generative modeling. Conditioned on one ciphertext, LMND autoregressively predicts the eight nibble tokens of the other, providing position-level supervision for every real pair. Exploiting the fact that fixed-key encryption is a permutation, it takes the uniform distribution as an analytic reference and converts the conditional likelihood into a distinguishing score that requires no negative training samples, no threshold fitting, and accumulates across pairs, with shared-weight bidirectional scoring enforcing invariance under ciphertext exchange. On 5$\sim$8-round Speck32/64, LMND attains the highest single-pair accuracy among all evaluated models; in a 9-round subkey-ranking experiment, it reduces the mean rank from $52.1$ to $24.2$ and raises the rank-0 success rate from $0.358$ to $0.416$ relative to Gohr's baseline.