# Improving ML Attacks on LWE with Data Repetition and Stepwise Regression

arXiv: https://arxiv.org/abs/2604.03903 · HTML: https://mlsanity.com/paper/2604.03903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 16 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [Emergent properties with repeated examples](https://mlsanity.com/paper/2410.07041/) (2024)
- [SALSA PICANTE: a machine learning attack on LWE with binary secrets](https://mlsanity.com/paper/2303.04178/) (2023)
- [SALSA VERDE: a machine learning attack on Learning With Errors with sparse small secrets](https://mlsanity.com/paper/2306.11641/) (2023)
- [Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors](https://mlsanity.com/paper/2402.01082/) (2024)
- [Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic](https://mlsanity.com/paper/2410.03569/) (2024)
- [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)

## Abstract (arXiv)

The Learning with Errors (LWE) problem is a hard math problem in lattice-based cryptography. In the simplest case of binary secrets, it is the subset sum problem, with error. Effective ML attacks on LWE were demonstrated in the case of binary, ternary, and small secrets, succeeding on fairly sparse secrets. The ML attacks recover secrets with up to 3 active bits in the "cruel region" (Nolte et al., 2024) on samples pre-processed with BKZ. We show that using larger training sets and repeated examples enables recovery of denser secrets. Empirically, we observe a power-law relationship between model-based attempts to recover the secrets, dataset size, and repeated examples. We introduce a stepwise regression technique to recover the "cool bits" of the secret.