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

arXiv: https://arxiv.org/abs/2510.02162 · HTML: https://mlsanity.com/paper/2510.02162/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [Classical Hardness of Learning with Errors](https://mlsanity.com/paper/1306.0281/) (2013)
- [SALSA PICANTE: a machine learning attack on LWE with binary secrets](https://mlsanity.com/paper/2303.04178/) (2023)
- [The cool and the cruel: separating hard parts of LWE secrets](https://mlsanity.com/paper/2403.10328/) (2024)
- [Benchmarking Attacks on Learning with Errors](https://mlsanity.com/paper/2408.00882/) (2024)
- [An efficient algorithm for integer lattice reduction](https://mlsanity.com/paper/2303.02226/) (2023)
- [Post Quantum Cryptography: Readiness Challenges and the Approaching Storm](https://mlsanity.com/paper/2101.01269/) (2021)

## Abstract (arXiv)

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.