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

• URL: http://arxiv.org/abs/2510.02162v1
• Date: Thu, 02 Oct 2025 16:12:13 GMT
• Title: NoMod: A Non-modular Attack on Module Learning With Errors
• Authors: Cristian Bassotto, Ermes Franch, Marina Krček, Stjepan Picek,
• Abstract summary: Quantum computing threatens classical public-key cryptography.<n>We present NoMod ML-Attack, a hybrid white-box cryptanalytic method.<n>We release our implementation in an anonymous repository.
• Score: 16.228565693406576
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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