Improving ML Attacks on LWE with Data Repetition and Stepwise Regression

2026-04-04

AI Summary

This work addresses the challenge of recovering high-density secret vectors in Learning With Errors (LWE) problems, where existing machine learning approaches have shown limited efficacy. The authors propose a novel attack framework that integrates data augmentation, repeated sampling, and stepwise regression. By introducing repeated samples to enhance training data diversity and employing stepwise regression to accurately identify “cold bits” in the secret vector, the method achieves substantially improved recovery performance. Experimental results reveal that the success rate of secret recovery follows a power-law relationship with both dataset size and the number of repetitions. Notably, this approach breaks through the prior limitation of handling at most three active bits, successfully recovering significantly denser secret vectors and thereby expanding the applicability boundary of machine learning–based attacks on LWE instances.

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.

Problem

• LWE
• machine learning attacks
• secret recovery
• dense secrets
• subset sum with error

Innovation

• data repetition
• stepwise regression
• LWE
• machine learning attacks
• secret recovery