Improving ML Attacks on LWE with Data Repetition and Stepwise Regression

TL;DR

This paper enhances machine learning attacks on the LWE problem by using larger datasets, repeated samples, and a stepwise regression method to recover denser secrets more effectively.

Contribution

It introduces a novel approach combining larger datasets, repeated examples, and stepwise regression to improve secret recovery in ML attacks on LWE.

Findings

Larger training sets and repeated samples improve secret recovery.

A power-law relationship exists between dataset size, repetitions, and attack success.

Stepwise regression helps recover the 'cool bits' of secrets.

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.