Improving ML Attacks on LWE with Data Repetition and Stepwise Regression
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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.
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.
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References · 9
- 2017Attention Is All You Needcited by 60,361
- 2022SALSA: Attacking Lattice Cryptography with Transformerscited by 28
- 2023SALSA PICANTE: a machine learning attack on LWE with binary secretscited by 11
- 2024Emergent properties with repeated examplescited by 11
- 2023SALSA VERDE: a machine learning attack on Learning With Errors with sparse small secretscited by 8
- 2024Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errorscited by 7
- 2024The cool and the cruel: separating hard parts of LWE secretscited by 4
- 2024Benchmarking Attacks on Learning with Errorscited by 4
- 2024Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmeticcited by 4
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