Improving ML Attacks on LWE with Data Repetition and Stepwise Regression
This work addresses a specific challenge in cryptographic security for lattice-based systems, representing an incremental improvement over prior ML attacks.
The paper tackles the problem of improving machine learning attacks on the Learning with Errors (LWE) problem in lattice-based cryptography by using larger training sets and repeated examples to recover denser secrets, achieving recovery of secrets with up to 3 active bits in the 'cruel region'.
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.