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 CRYST ALS-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. The dawn of quantum computing presents a significant and growing threat to current cryptographic systems, many of which may be vulnerable to decryption through quantum-based attacks. At the heart of this risk is Shor's algorithm, a quantum-based algorithm developed in 1994 by Peter Shor, which can efficiently factor large integers and compute discrete logarithms. These two mathematical problems are computationally challenging for classical computers when the input size is large. In particular, while classical algorithms to factor integers, such as the General Number Field Sieve (GNFS), run in sub-exponential time, Shor's algorithm could run in polynomial time, when implemented on a sufficiently robust quantum computer Shor (1994; 1997). This development poses a significant threat to the security assumptions underlying widely used public-key cryptographic schemes, such as RSA, Elliptic Curve Cryptography (ECC), and the Diffie-Hellman key exchange. These algorithms are central to the Public Key Infrastructure (PKI) that secures virtually all modern digital communications.