Paper 2026/612

Improving ML Attacks on LWE with Data Repetition and Stepwise Regression

Eshika Saxena, FAIR at Meta

Emily Wenger, Duke University

François Charton, Axiom Math

Kristin Lauter, FAIR at Meta

Abstract

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.

@misc{cryptoeprint:2026/612,
      author = {Alberto Alfarano and Eshika Saxena and Emily Wenger and François Charton and Kristin Lauter},
      title = {Improving {ML} Attacks on {LWE} with Data Repetition and Stepwise Regression},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/612},
      year = {2026},
      url = {https://eprint.iacr.org/2026/612}
}