NoMod: A Non-modular Attack on Module Learning With Errors
This is an incremental improvement in cryptanalysis for post-quantum security, addressing a specific bottleneck in secret recovery.
The paper tackles the threat quantum computing poses to classical cryptography by attacking the Module Learning With Errors problem, achieving full recovery of binary secrets for dimension n=350 and sparse secrets in CRYSTALS-Kyber settings.
The advent of quantum computing threatens classical public-key cryptography, motivating NIST's adoption of post-quantum schemes such as those based on the Module Learning With Errors (Module-LWE) problem. We present NoMod ML-Attack, a hybrid white-box cryptanalytic method that circumvents the challenge of modeling modular reduction by treating wrap-arounds as statistical corruption and casting secret recovery as robust linear estimation. Our approach combines optimized lattice preprocessing--including reduced-vector saving and algebraic amplification--with robust estimators trained via Tukey's Biweight loss. Experiments show NoMod achieves full recovery of binary secrets for dimension $n = 350$, recovery of sparse binomial secrets for $n = 256$, and successful recovery of sparse secrets in CRYSTALS-Kyber settings with parameters $(n, k) = (128, 3)$ and $(256, 2)$. We release our implementation in an anonymous repository https://anonymous.4open.science/r/NoMod-3BD4.