Improving ML attacks on LWE with data repetition and stepwise regression

The Learning with Errors (LWE) problem is a hard math problem used in lattice-based cryptography. In the simplest case of binary secrets, it is simply the subset sum problem. Effective ML attacks on LWE have been demonstrated in the case of binary, ternary, and small secrets, but they only succeed on fairly sparse secrets. After lattice BKZ pre-processing, ML attacks can recover secrets with up to three non-zero bits in the ''cruel region'' (Nolte et al., 2024). 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, a substantial improvement over prior work.