标题： NoMod：一种针对基于误差的模块学习的非模块化攻击 显示英文标题

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

摘要： 量子计算的出现对经典公钥密码学构成了威胁，这促使NIST采用了基于模块学习误差（模块-LWE）问题等后量子方案。我们提出了NoMod ML-Attack，这是一种混合白盒密码分析方法，通过将环绕作为统计扰动来规避模运算建模的挑战，并将秘密恢复视为鲁棒线性估计。我们的方法结合了优化的格预处理——包括缩减向量保存和代数放大——以及通过Tukey的双权重损失训练的鲁棒估计器。实验表明，NoMod在维度$n = 350$时能够完全恢复二进制秘密，在$n = 256$时能够恢复稀疏二项式秘密，并在参数为$(n, k) = (128, 3)$和$(256, 2)$的CRYSTALS-Kyber设置中成功恢复稀疏秘密。我们将在匿名仓库 https://anonymous.4open.science/r/NoMod-3BD4 中发布我们的实现。 显示英文摘要

摘要： 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.