International Association
for Cryptologic Research

Learning with Errors (LWE) is a hard math problem underlying post-quantum cryptography (PQC) systems for key exchange and digital signatures, recently standardized by NIST. Prior work [Wenger et al., 2022; Li et al., 2023a;b] proposed new machine learning (ML)-based attacks on LWE problems with small, sparse secrets, but these attacks require millions of LWE samples to train on and take days to recover secrets. We propose three key methods—better pre-processing, angular embeddings and model pre-training—to improve these attacks, speeding up preprocessing by 25× and improving model sample efficiency by 10×. We demonstrate for the first time that pre-training improves and reduces the cost of ML attacks on LWE. Our architecture improvements enable scaling to larger-dimension LWE problems: this work is the first instance of ML attacks recovering sparse binary secrets in dimension n = 1024, the smallest dimension used in practice for homomorphic encryption applications of LWE where sparse binary secrets are proposed.