NoMod: A Non-modular Attack on Module Learning With Errors

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.